The estimation problem of stochastic Wiener-Hammerstein models is recognized to be challenging, mainly due to the analytical intractability of the likelihood function. In this contribution, we apply a computationally attractive prediction error method estimator to a real-data stochastic Wiener-Hammerstein benchmark problem. The estimator is defined using a deterministic predictor that is nonlinear in the input. The prediction error method results in tractable expressions, and Monte Carlo approximations are not necessary. This allows us to tackle several issues considered challenging from the perspective of the current mainstream approach. Under mild conditions, the estimator can be shown to be consistent and asymptotically normal. The results of the method applied to the benchmark data are presented and discussed.
Identification of dynamic networks has attracted considerable interest recently. So far the main focus has been on linear time-invariant networks. Meanwhile, most real-life systems exhibit nonlinear behaviors; consider, for example, two stochastic linear time-invariant systems connected in series, each of which has a nonlinearity at its output. The estimation problem in this case is recognized to be challenging, due to the analytical intractability of both the likelihood function and the optimal one-step ahead predictors of the measured nodes. In this contribution, we introduce a relatively simple prediction error method that may be used for the estimation of nonlinear dynamical networks. The estimator is defined using a deterministic predictor that is nonlinear in the known signals. The estimation problem can be defined using closed-form analytical expressions in several non-trivial cases, and Monte Carlo approximations are not necessarily required. We show, that this is the case for some block-oriented networks with no feedback loops and where all the nonlinear modules are polynomials. Consequently, the proposed method can be applied in situations considered challenging by current approaches. The performance of the estimation method is illustrated on a numerical simulation example.
In this paper, we present an algorithm for pose control of a team of mobile sensors for coverage and inspection applications. The region to cover is abstracted into a finite set of landmarks, and each sensor is responsible to cover some of the landmarks. The sensors progressively improve their coverage by adjusting their poses and by transferring the ownership of some landmarks to each other. Inter-sensor communication is pairwise and intermittent. The sensor team is formally modeled as a multi-agent hybrid system, and an invariance argument formally shows that the team reaches an equilibrium configuration, while a global coverage measure is improving monotonically. A numerical simulation corroborates the theoretical results.
We consider a networked control loop in which the sensors acquire partial state information and communicate to a remote controller through a lossy communication network. A scheduler, collocated with the sensors, decides to transmit a locally estimated state to the controller based on an event-triggered transmission policy with stochastic thresholds. Assuming that the local estimator either senses the communication channel or receives an ideal acknowledgment from the remote estimator, then the optimal control law can be shown to be a linear function of the conditional expectation of the state. However, the probability distribution of the state conditioned on the information available to the controller based on the mentioned transmission policy and network is not Gaussian, but rather described by a sum of Gaussians with an increasing number of terms at every time-step. We show that the optimal LQG control law can be determined without tracking this probability distribution for finding its expected value. Moreover, we establish that the stochastic event-triggered scheduler can be appropriately regulated in order to achieve a desired triggering probability at every time-step.
In this paper, we revisit maximum likelihood methods for identification of errors-in-variables systems. We assume that the system admits a parametric description, and that the input is a stochastic ARMA process. The cost function associated with the maximum likelihood criterion is minimized by introducing a new iterative solution scheme based on the expectation-maximization method, which proves fast and easily implementable. Numerical simulations show the effectiveness of the proposed method.
In this paper we introduce a novel method for linear system identification with quantized output data. We model the impulse response as a zero-mean Gaussian process whose covariance (kernel) is given by the recently proposed stable spline kernel, which encodes information on regularity and exponential stability. This serves as a starting point to cast our system identification problem into a Bayesian framework. We employ Markov Chain Monte Carlo (MCMC) methods to provide an estimate of the system. In particular, we show how to design a Gibbs sampler which quickly converges to the target distribution. Numerical simulations show a substantial improvement in the accuracy of the estimates over state-of-the-art kernel-based methods when employed in identification of systems with quantized data.
Undetectable attacks in security studies of cyber-physical systems render the measurements of the system equal to a possible physical response. In this paper, we investigate defense strategies against the undetectable single-attack for positive systems and second-order systems, which both can be reinterpreted in terms of graphs with nodes and edges, while the undetectable attack is added through one of the nodes. We show that an arbitrary placement of a sensor prevents undetectable single-attack for these classes of systems. It is worth emphasising that we do not need to measure at the corrupted node to prevent the undetectable single-attack, but can measure at any node. The defense strategy is of a low complexity and can be readily implemented.
The paper investigates the positive semidefiniteness of signed Laplacians. It is noted that a symmetric signed Laplacian defines a unique resistive electrical network, wherein the negative weights correspond to negative resistances. As such, the positive semidefiniteness of the signed Laplacians is equivalent to the passivity of the associated resistive networks. By utilizing n-port circuit theory, we obtain several equivalent conditions for signed Laplacians to be positive semidefinite with a simple zero eigenvalue. These conditions characterize a set of negative weights that maintain the semidefiniteness of the Laplacian. The results are used to analyze the small-disturbance angle stability of microgrids as an application.
The accuracy of identified linear time-invariant single-input multi-output (SIMO) models can be improved when the disturbances affecting the output measurements are spatially correlated. Given a linear parametrization of the modules composing the SIMO structure, we show that the correlation structure of the noise sources and the model structure of the othe modules determine the variance of a parameter estimate. In particular we show that increasing the model order only increases the variance of other modules up to a point. We precisely characterize the variance error of the parameter estimates for finite model orders. We quantify the effect of noise correlation structure, model structure and signal spectra.
A secure and private framework for inter-agent communication and coordination is developed. This allows an agent, in our case a fleet owner, to ask questions or submit queries in an encrypted fashion using semi-homomorphic encryption. The submitted query can be about the interest of the other fleet owners for using a road at a specific time of the day, for instance, for the purpose of collaborative vehicle platooning. The other agents can then provide appropriate responses without knowing the content of the questions or the queries. Strong privacy and security guarantees are provided for the agent who is submitting the queries. It is also shown that the amount of the information that this agent can extract from the other agent is bounded. In fact, with submitting one query, a sophisticated agent can at most extract the answer to two queries. This secure communication platform is used subsequently to develop a distributed coordination mechanisms among fleet owners.
The estimation of the Social Cost of Carbon Dioxide (SC-CO2) is one of the essential purposes of Integrated Assessment Models (IAMs) used in the economics of climate change. One of the most widely used IAMs in this context is DICE. However, the DICE geophysical subsystem fails to account for feedback from the climate subsystem to the carbon subsystem, an effect recently observed in climate physics. This paper investigates how to combine the recently proposed FAIR climate model with the socioeconomic subsystem of DICE. Based on an analysis of its differential-algebraic structure, we propose an efficient discretization of FAIR that provides a new discrete-time hybrid of DICE and FAIR denoted as FAIR-DICE. Finally, we compare estimates of the SC-CO2 obtained with DICE2013 with those obtained via FAIR-DICE.
In system identification, many structures and approaches have been proposed to deal with systems with non-linear behavior. When applicable, the prediction error method, analogously to the linear case, requires minimizing a cost function that is non-convex in general. The issue with non-convexity is more problematic for non-linear models, not only due to the increased complexity of the model, but also because methods to provide consistent initialization points may not be available for many model structures. In this paper, we consider a non-linear rational finite impulse response model. We observe how the prediction error method requires minimizing a non-convex cost function, and propose a three-step least-squares algorithm as an alternative procedure. This procedure is an extension of the Model Order Reduction Steiglitz-McBride method, which is asymptotically efficient in open loop for linear models. We perform a simulation study to illustrate the applicability and performance of the method, which suggests that it is asymptotically efficient.
For identification of systems in dynamic networks, two-stage and instrumental variable methods are common time-domain methods. These methods provide consistent estimates of a chosen module of the network without estimating other parts of the network or noise models. However, disregarding noise modeling may come at a cost in estimation error. To capture the noise contribution, we propose the following procedure: first, we estimate a non-parametric model of an appropriate part of the network; second, we estimate the module of interest using signals simulated with the non-parametric model. The simulated signals are derived from an asymptotic maximum likelihood criterion. Preliminary simulations suggest that the propose method is competitive with existing approaches and is particularly beneficial with colored noise.
For identification of systems embedded in dynamic networks, the prediction error method (PEM) with a correct parametrization of the complete network provides asymptotically efficient estimates. However, the network complexity often hinders a successful application of PEM, which requires minimizing a non-convex cost function that can become more intricate for more complex networks. For this reason, identification in dynamic networks often focuses in obtaining consistent estimates of modules of interest. A downside of these approaches is that splitting the network in several modules for identification often costs asymptotic efficiency. In this paper, we consider dynamic networks with the modules connected in serial cascade, with measurements affected by sensor noise. We propose an algorithm that estimates all the modules in the network simultaneously without requiring the minimization of a non-convex cost function. This algorithm is an extension of Weighted Null-Space Fitting (WNSF), a weighted least-squares method that provides asymptotically efficient estimates for single-input single-output systems. We illustrate the performance of the algorithm with simulation studies, which suggest that a network WNSF method may also be asymptotically efficient when applied to cascade structures. Finally, we discuss the possibility of extension to more general networks affected by sensor noise.
Kernel-based regularization has recently been shown to be a successful method for impulse response estimation. This technique usually requires choosing a vector of hyper-parameters in order to form an appropriate regularization matrix. In this paper, we develop an alternative way to obtain kernel-based regularization estimates by Bayesian model mixing. This new approach is tested against state-of-the-art methods for hyperparameter tuning in regularized FIR estimation, with favorable results in many cases.
In this work, we study the worst-case consequence of innovation-based integrity attacks with side information in a remote state estimation scenario. A new type of linear attack strategy based on both intercepted and sensing data is proposed and a corresponding stealthiness constraint is characterized. The evolution of the remote estimation error covariance is derived in the presence of the proposed malicious attack, based on which the worst-case attack policy is obtained in closed form. Furthermore, the system estimation performance under the proposed attack is compared with that under the existing attack strategy to determine which attack is more critical in deteriorating system functionality. Simulation examples are provided to illustrate the developed results.
The aim of this paper is to develop a method to estimate high order FIR and ARX models using least squares with re-weighted nuclear norm regularization. Typically, the choice of the tuning parameter in the reweighting scheme is computationally expensive, hence we propose the use of the SPARSEVA (SPARSe Estimation based on a VAlidation criterion) framework to overcome this problem. Furthermore, we suggest the use of the prediction error criterion (PEC) to select the tuning parameter in the SPARSEVA algorithm. Numerical examples demonstrate the veracity of this method which has close ties with the traditional technique of cross validation, but using much less computations.
In this paper, we consider the problem of active model discrimination amongst a finite number of affine models with uncontrolled and noise inputs, each representing a different system operating mode that corresponds to a fault type or an attack strategy, or to an unobserved intent of another robot, etc. The active model discrimination problem aims to find optimal separating inputs that guarantee that the outputs of all the affine models cannot be identical over a finite horizon. This will enable a system operator to detect and uniquely identify potential faults or attacks, despite the presence of process and measurement noise. Since the resulting model discrimination problem is a nonlinear non-convex mixed-integer program, we propose to solve this in a computationally tractable manner, albeit only approximately, by proposing a sequence of restrictions that guarantee that the obtained input is separating. Finally, we apply our approach to attack detection in the area of cyber-physical systems security.
In this paper, we propose a framework to generate communication schedulings for nonlinear model predictive control. The proposed method considers the case where multiple plants share a communication network, and the goal is to pre-plan for each plant a timing to communicate with the controller to solve an optimal control problem. The desired communication schedulings are generated such that: (i) no network collisions occur; (ii) convergence to a prescribed local set around the origin is guaranteed for all plants. When formulating an algorithm, we additionally propose an optimization problem that is similar to the standard collision avoidance problem of controlling multi-agent systems. To validate our proposed scheme, a control problem of three inverted pendulums is simulated.
In various interaction tasks using Underwater Vehicle Manipulator Systems (UVMSs) (e.g. sampling of the sea organisms, underwater welding), important factors such as: i) uncertainties and complexity of UVMS dynamic model ii) external disturbances (e.g. sea currents and waves) iii) imperfection and noises of measuring sensors iv) steady state performance as well as v) inferior overshoot of interaction force error, should be addressed during the force control design. Motivated by the above factors, this paper presents a model-free control protocol for force controlling of an Underwater Vehicle Manipulator System which is in contact with an unknown compliant environment, without incorporating any knowledge of the UVMS's dynamic model, exogenous disturbances and sensor's noise model. Moreover, the transient and steady state response as well as reduction of overshooting force error are solely determined by certain designer-specified performance functions and are fully decoupled by the UVMS's dynamic model, the control gain selection, as well as the initial conditions. Finally, a simulation study clarifies the proposed method and verifies its efficiency.
This paper proposes a decentralized traffic light control system in a multi-agent framework. Each signal controller at an intersection is modeled as an intelligent agent capable of making actions for signal operations according to received detection information. The controller agent works with a turning movement based phasing scheme. Duration of turning movement is determined by a multi-criteria reinforcement learning algorithm. In the design of agent, both traffic mobility and energy efficiency are taken into account. Then, a case study is carried out to assess the performance of the proposed decentralized signal control system. The simulation results outperforms an optimized vehicle-actuated control system by reducing average travel delay and average fuel consumption for vehicles. In particular, the decentralized control system is queue responsive and able to adapt to demand in its green time allocation.
The operation of traffic signal control is of significant importance in traffic management and operation practice, especially under oversaturated condition during the morning and afternoon peak hours. However, the conventional signal control systems showed the limitations in signal timing and phasing under oversaturated situations. This paper proposes a multi-agent adaptive signal control system in the context of group-based phasing techniques. The adaptive signal control system is able to acquire knowledge on-line based on the perceived traffic states and the feedback from the traffic environment. Reinforcement learning with eligibility trace is applied as the learning algorithm in the multi-agent system. As a result, the signal controller makes an intelligent timing decision. Feature-based function approximation method is incorporated into reinforcement learning framework to improve the learning efficiency as well as the quality of signal timing decisions. The learning process of the learning-based signal control is carried out with the aid of a microscopic traffic simulation model. A benchmarking system, an optimized group-based vehicle actuated signal control system, is compared with the proposed adaptive signal control systems. The simulation results show that the proposed adaptive group-based signal control system has the potential to improve the mobility efficiency under different congested situations.
Traffic signal control plays a crucial role in traffic management and operation practice. In the past decade, adaptive signal control systems have shown the abilities to improve the effectiveness of the transportation system in many aspects. This paper proposes an adaptive signal control system in the context of group-based phasing techniques. The adaptive signal control system is modeled as a multi agent System capable of acquiring knowledge on-line based on the perceived traffic states and the feedback from the external environment,. Reinforcement learning is applied as the learning algorithm resulting in intelligent timing decisions. Feature based function approximation method is incorporated into the reinforcement learning framework for the purpose of improving learning efficiency as well as the quality of signal timing decisions. The assessment of such a learning-based signal control system is carried out by using an opensource microscopic traffic simulation software, SUMO. A benchmarking system, the optimized group-based vehicle actuated signal control system, compared with the learning-based signal control systems regarding mobility efficiency. The simulation results show that the proposed adaptive group based signal control system has the potential to improve the mobility efficiency regardless of the settings of traffic demands.
This paper studies a joint transmission scheduling and controller design problem, which minimizes a linear combination of the control cost and expected energy usage of the sensor. Assuming that the sensor transmission decisions are event-based and determined using the random estimation error covariance information available to the controller, we show a separation in the design of the transmission scheduler and controller. The optimal controller is given as the solution to an LQG-type problem, while the optimal transmission policy is a threshold policy on the estimation error covariance at the controller.
In electricity distribution networks, the increasing penetration of renewable energy generation necessitates faster and more sophisticated voltage controls. Unfortunately, recent research shows that local voltage control fails in achieving the desired regulation, unless there is some communication between the controllers. However, the communication infrastructure for distribution systems are less reliable and less ubiquitous as compared to that for the bulk transmission system. In this paper, we design distributed voltage control that use limited communication. That is, only neighboring buses need to communicate few bits between each other before each control step. We investigate how these controllers can achieve the desired asymptotic behavior of the voltage regulation and we provide upper bounds on the number of bits that are needed to ensure a predefined accuracy of the regulation. Finally, we illustrate the results by numerical simulations.
This paper discusses algorithms for solving Markov decision processes (MDPs) that have monotone optimal policies. We propose a two-stage alternating convex optimization scheme that can accelerate the search for an optimal policy by exploiting the monotone property The first stage is a linear program formulated in terms of the joint state-action probabilities. The second stage is a regularized problem formulated in terms of the conditional probabilities of actions given states. The regularization uses techniques from nearly-isotonic regression. While a variety of iterative method can be used in the first formulation of the problem, we show in numerical simulations that, in particular, the alternating method of multipliers (ADMM) can be significantly accelerated using the regularization step.
Hidden Markov models have successfully been applied as models of discrete time series in many fields. Often, when applied in practice, the parameters of these models have to be estimated. The currently predominating identification methods, such as maximum- likelihood estimation and especially expectation-maximization, are iterative and prone to have problems with local minima. A non-iterative method employing a spectral subspace-like approach has recently been proposed in the machine learning literature. This paper evaluates the performance of this algorithm, and compares it to the performance of the expectation- maximization algorithm, on a number of numerical examples. We find that the performance is mixed; it successfully identifies some systems with relatively few available observations, but fails completely for some systems even when a large amount of observations is available. An open question is how this discrepancy can be explained. We provide some indications that it could be related to how well-conditioned some system parameters are.
This paper presents a novel framework combining abstraction refinement and plan revision for control synthesis problems under temporal logic specifications. The control problem is first solved on a simpler nominal model in order to obtain a satisfying plan to be followed by the real system. A controller synthesis is then attempted for an abstraction of the real system to follow this plan. Upon failure of this synthesis, cost functions are defined to guide towards either refining the initially coarse partition to obtain a finer abstraction, or looking for an alternative plan using the nominal model as above. This tentative synthesis is then repeated until a plan and an abstraction of the real system able to follow this plan are found. The obtained controller also ensures that the real system satisfies the initial specification.
In this paper, we consider a state estimation problem for stochastic linear dynamical systems in the presence of bias injection attacks. A Kalman filter is used as an estimator, and a chi-squared test is used to detect anomalies. We first show that the impact of the worst-case bias injection attack in a stochastic setting can be analyzed by a deterministic quadratically constrained quadratic program, which has an analytical solution. Based on this result, we propose a criterion for selecting sensors to secure in order to mitigate the attack impact. Furthermore, we derive a condition on the necessary number of sensors to secure in order for the impact to be less than a desired threshold.
This paper investigates the design of event-triggered scheduling and medium access control for the real-time coordination of multiple vehicles through an infrastructure node. The key motivation of our proposed event-triggered mechanism is to concurrently address safety aspects of the vehicle control and the efficient usage of network resources of the vehicle-to-infrastructure (V2I) protocol. While the real-time guarantees needed for safety are achieved by a novel coordination scheme in the medium access layer, the event-triggered mechanism improves the real-time performance of the control task. The coordination scheme enabled through the topology of the V2I network limits the number of successive data dropouts and we prove stability of the estimator at the infrastructure that monitors the state of the vehicle group. Numerical studies on a platooning case study validate our theoretical results.
Estimating the parameters of general state-space models is a topic of importance for many scientific and engineering disciplines. In this paper we present an online parameter estimation algorithm obtained by casting our recently proposed particle-based, rapid incremental smoother (PaRIS) into the framework of online expectation-maximization (EM) for state-space models proposed by Cappé (2011). Previous such particle-based implementations of online EM suffer typically from either the well-known degeneracy of the genealogical particle paths or a quadratic complexity in the number of particles. However, by using the computationally efficient and numerically stable PaRIS algorithm for estimating smoothed expectations of timeaveraged sufficient statistics of the model we obtain a fast algorithm with very limited memory requirements and a computational complexity that grows only linearly with the number of particles. The efficiency of the algorithm is illustrated in a simulation study.
In this paper, we consider the classic car overtake problem. There are three cars, two moving along the same direction in the same lane while the third car moves in the direction opposite to that of the first two cars in the adjacent lane. The objective of the trailing car is to overtake the car in front of it avoiding collision with the other cars in the scenario. The information available to the trailing car is the relative position, relative velocities with respect to other cars and its position and past actions. The relative position and relative velocity information is corrupted by noise. Given this information, the car needs to make a decision as to whether it wants to overtake or not. We present a control algorithm for the car which minimizes the probability of collision with both the cars. We also present the results obtained by simulating the above scenario with the control algorithm. Through simulations, we study the effect of the variance of the measurement noise and the time at which the decision is made on the probability of collision.
Conventional supervisory control synthesis techniques are not adequate anymore when a network between the plant and the supervisor introduces communication delays. This paper presents a method to synthesize a networked supervisor handling delays in both observation and control channels. To deal with the problem of delayed observations, we propose an automaton modeling the behaviour of the plant observed by a supervisor through a network, called observed plant. In this automaton, events observed by a supervisor are delayed from those occurring in the plant. Moreover, since observation channels are considered not to have the first in first out (FIFO) characteristic, events may not be necessarily observed in the same order as they occurred within the plant. A safe, observable, controllable and nonblocking supervisor is synthesized for the observed plant by means of an adapted synthesis algorithm for timed discrete-event systems (TDES). By enabling the achieved supervisor to predict the effects of control delays, it will be further transformed to a networked supervisor. The networked supervisor makes decisions ahead of time to ensure that the commands will be applied on the right (plant) state.
This paper studies static state estimation based on measurements from a set of sensors, a subset of which can be compromised by an attacker. The measurements from a compromised sensor can be manipulated arbitrarily by the adversary. A new notion is adopted to indicate the performance of an estimator, that is, the asymptotic exponential rate, with which the worst-case probability of estimate lying outside certain ball centered at the true underlying state goes to zero. An optimal estimator, which computes Chebyshev centers and only utilizes the information contained in the averaged measurements, is proposed. Numerical examples are given to elaborate the results.
We propose a method for nonparametric identification of Hammerstein models with Gaussian-process models for the impulse response of the linear block and for the input nonlinearity. Interpreting the Gaussian-processes as prior distributions, we can estimate the unknowns using the posterior means given the data. To estimate the hyperparameters we set up an iterative scheme, reminiscent of the expectation-maximization method, where the posterior expectation of the complete likelihood is iteratively maximized. In the Hammerstein case, the posterior density is intractable because, in general, it does not admit a closed form expression. In this work, we propose two approximation approaches to estimate the posterior mean. In the first, we make a particle approximation of the posterior using Markov Chain Monte Carlo. In the second, we use a variational Bayes approach with a mean-field hypothesis. We validate the proposed methods on synthetic datasets of Hammerstein systems.
We study the problem of identifying dynamic networks that do not present loops. We model the impulse responses of the modules in the network as zero-mean independent Gaussian processes. The covariance matrices of the processes can be used to encode prior information, such as stability and smoothness, about the impulse responses of the modules. To estimate the modules, we approximate the joint posterior distribution of the impulse responses using a variational Bayes approach. In particular, using a mean-field approximation, we assume a factorization of the posterior where each factor corresponds to a single module. We estimate the kernel hyperparameters and the measurement noise variances by combining variational Bayes with the expectation-maximization method. We evaluate the performance of the identification procedure in a simulation experiment, where we compare to other kernel-based approaches.
We analyze likelihood-based identification of systems that are linear in the parameters from quantized output data; in particular, we propose a method to find approximate maximum-likelihood and maximum-a-posteriori solutions. The method consists of appropriate least-squares projections of the middle point of the active quantization intervals. We show that this approximation maximizes a variational approximation of the likelihood and we provide an upper bound for the approximation error. In a simulation study, we compare the proposed method with the true maximum-likelihood estimate of a finite impulse response model.
A transformation to variant and invariant states, called extents, is used to decouple the dynamic effects of reaction systems and serves as basis for incremental model identification, in which kinetic models are identified individually for each dynamic effect. This contribution introduces a novel transformation to extents for the incremental model identification of two-phase distributed reaction systems. Distributed reaction systems are discussed for two cases, namely, when measurements along the spatial coordinate are available and when they are not. In the second case, several measurements made under appropriate operating conditions are combined to overcome the lack of measurements along the spatial coordinate. This novel method is illustrated via the simulated example of a two-phase tubular reactor.
In data-based modelling communities, such as system identification, machine learning, signal processing and statistics, benchmarks are essential for testing and comparing old and new techniques for the estimation of models. During the last years, it has become customary in system identification to rely on data sets built from randomly generated systems. In this article we discuss the implications of this practice, in particular when using data sets generated with the MATLABr command drss, and advocate the cautious use of comparisons based on these benchmarks.
We consider identification of linear systems with a certain order from a set of noisy input-output observations. We utilize the fact that the system order corresponds to the rank of the Hankel matrix associated with the system impulse response. Then, the system identification problem is formulated as the minimization of the output error subject to a rank constraint on a Hankel matrix. As this problem is non-convex, we propose a branch and bound (BB) solver, which is a powerful tool for solving non-convex problems to optimality. The main ingredients of the proposed BB method are a convex relaxation problem and a local minimizer of the original non-convex problem. We illustrate the promising performance of the proposed scheme in a system identification problem. The results demonstrate the higher accuracy and stability of our method in estimating the true system compared to the standard output error (OE) algorithm.
We consider a discrete-time networked LQG control problem in which state information must be transmitted to the controller over a noiseless binary channel using prefix-free codewords. Quantizer, encoder and controller are jointly designed to minimize average data-rate while satisfying required LQG control performance. We study the effects of selecting large block-lengths (data transmission intervals) from the perspectives of information-theoretic advantage due to coding efficiency and control-theoretic disadvantage due to delay. In particular, we demonstrate that the performance of networked control scheme by Tanaka et al. (2016) can be improved by adjusting the block-length optimally. As a byproduct of this study, we also show that the data-rate theorem for mean-square stability similar to Nair and Evans (2004) can be recovered by considering sufficiently large block-lengths.
We address the problem of attack detection and attack correction for multi-input multi-output discrete-time linear time-invariant systems under sensor attacks. More specifically, we consider the situation that a system with known input is corrupted by additive adversarial attack signals on some of the system's outputs. In this paper, we use system representation in a behavioural approach, which allows for natural and compact statements regarding linear system security. We extend our earlier results for systems with zero inputs to systems with non-zero inputs. We assume that these non-zero inputs are known.
In economic model predictive control (EMPC), the standard quadratic objective function of MPC is replaced with an economic objective such that the controller directly optimizes the economic performance of the plant. However, economic objective functions are likely to be monotone in some input direction, and this will typically lead to operation with constraints active. Operating the plant with active constraints is not economically robust; even small disturbances or errors could cause constraint violations which may lead to large costs. In this paper we address this issue by adding margins to the constraints in order to force the plant to operate in the interior of the feasible set, thereby providing some robustness to uncertainty. To determine the magnitude of these margins, we introduce an outer loop which optimizes the margins online based on measurements of the closed-loop economic performance. Our approach is simple to implement and introduces essentially no computational overhead as compared to the nominal EMPC problem. In addition, only minimal knowledge of the uncertainties present in the system is required.
The problem of maximizing the probability of two trucks being coordinated to merge into a platoon on a highway is considered. Truck platooning is a promising technology that allows heavy vehicles to save fuel by driving with small automatically controlled inter-vehicle distances. In order to leverage the full potential of platooning, platoons can be formed dynamically en route by small adjustments to their speeds. However, in heavily used parts of the road network, travel times are subject to random disturbances originating from traffic, weather and other sources. We formulate this problem as a stochastic dynamic programming problem over a finite horizon, for which solutions can be computed using a backwards recursion. By exploiting the characteristics of the problem, we derive bounds on the set of states that have to be explored at every stage, which in turn reduces the complexity of computing the solution. Simulations suggest that the approach is applicable to realistic problem instances.
This paper proposes a task-space control protocol for the collaborative manipulationof a single object by N robotic agents. The proposed methodology is decentralized in the sense that each agent utilizes information associated with its own and the object’s dynamic/kinematic parameters and no on-line communication takes place. Moreover, no feedback of the contact forces/torques is required, therefore employment of corresponding sensors is avoided. An adaptive version of the control scheme is also introduced, where the agents’ and object’s dynamic parameters are considered unknown. We also use unit quaternions to represent the object’s orientation. In addition, load sharing coefficients between the agents are employed and internalforce regulation is guaranteed. Finally, experimental studies with two robotic arms verify the validity and effectiveness of the proposed control protocol.
We study identification of stochastic Wiener dynamic systems using so-called indirect inference. The main idea is to first fit an auxiliary model to the observed data and then in a second step, often by simulation, fit a more structured model to the estimated auxiliary model. This two-step procedure can be used when the direct maximum-likelihood estimate is dificult or intractable to compute. One such example is the identification of stochastic Wiener systems, i.e., linear dynamic systems with process noise where the output is measured using a nonlinear sensor with additive measurement noise. It is in principle possible to evaluate the loglikelihood cost function using numerical integration, but the corresponding optimization problem can be quite intricate. This motivates studying consistent, but sub-optimal, identification methods for stochastic Wiener systems. We will consider indirect inference using the best linear approximation as an auxiliary model.We show that the key to obtain a reliable estimate is to use uncertainty weighting when fitting the stochastic Wiener model to the auxiliary model estimate. The main technical contribution of this paper is the corresponding asymptotic variance analysis. A numerical evaluation is presented based on a first-order finite impulse response system with a cubic non-linearity, for which certain illustrative analytic properties are derived.
In distributed or multiparty computations, optimization theory methods offer appealing privacy properties compared to cryptography and differential privacy methods. However, unlike cryptography and differential privacy, optimization methods currently lack a formal quantification of the privacy they can provide. The main contribution of this paper is to propose a quantification of the privacy of a broad class of optimization approaches. The optimization procedures generate a problem's data ambiguity for an adversarial observer, which thus observes the problem's data within an uncertainty set. We formally define a one-to-many relation between a given adversarial observed message and an uncertainty set of the problem's data. Based on the uncertainty set, a privacy measure is then formalized. The properties of the proposed privacy measure are analyzed. The key ideas are illustrated with examples, including localization and average consensus.
Identification of dynamic networks in prediction error setting often requires the solution of a non-convex optimization problem, which can be difficult to solve especially for large-scale systems. Focusing on ARMAX models of dynamic networks, we instead employ a method based on a sequence of least-squares steps. For single-input single-output models, we show that the method is equivalent to the recently developed Weighted Null Space Fitting, and, drawing from the analysis of that method, we conjecture that the proposed method is both consistent as well as asymptotically efficient under suitable assumptions. Simulations indicate that the sequential least squares estimates can be of high quality even for short data sets.
In this paper, event-triggered controllers and corresponding algorithms are proposed to establish the formation with connectivity preservation for multi-agent systems. Each agent needs to update its control input and to broadcast this control input together with the relative state information to its neighbors at its own triggering times, and to receive information at its neighbors' triggering times. Two types of system dynamics, single integrators and double integrators, are considered. As a result, all agents converge to the formation exponentially with connectivity preservation, and Zeno behavior can be excluded. Numerical simulations show the effectiveness of the theoretical results.
Weak (approximate) detectability of a labeled Petri net (LPN) system (with inhibitor arcs) is a property such that if the property is satisfied then there exists an infinite label sequence generated by the system such that all markings after a time step can determined (in a prescribed subset of reachable markings) by the label sequence. Specifically, we prove that the problems of deciding weak detectability of LPN systems with inhibitor arcs and weak approximate detectability of LPN systems are both undecidable.