This letter proposes a design of a distributed prescribed-time observer for nonlinear systems representable in a block-triangular observable canonical form. Using a weighted average of neighbor estimates exchanged over a strongly connected digraph, each observer estimates the system state despite the limited observability of local sensor measurements. The proposed design guarantees that distributed state estimation errors converge to zero at a user-specified convergence time, irrespective of observers' initial conditions. To achieve this prescribed-time convergence, distributed observers implement time-varying local output injection gains that monotonically increase and approach infinity at the prescribed time. The theoretical convergence is rigorously proven and validated through numerical simulations, where some implementation issues due to increasing gains have also been clarified.

This paper develops incentive mechanisms for promoting eco-driving with the overarching goal of minimizing emissions in transportation networks. The system operator provides drivers with energy-efficient driving guidance throughout their trips and measures compliance through vehicle telematics that capture how closely drivers follow this guidance. Drivers optimize their behaviors based on personal trade-offs between travel times and emissions. To design effective incentives, the operator elicits driver preferences regarding trip urgency and willingness to eco-drive, while determining optimal budget allocations and eco-driving recommendations. Two distinct settings based on driver behavior are analyzed. When drivers report their preferences truthfully, an incentive mechanism ensuring obedience (drivers find it optimal to follow recommendations) is designed by implementing eco-driving recommendations as a Nash equilibrium. When drivers may report strategically, the mechanism is extended to be both obedient and truthful (drivers find it optimal to report truthfully). Unlike existing works that focus on congestion or routing decisions in transportation networks, our framework explicitly targets emissions reduction by incentivizing drivers. The proposed mechanism addresses both strategic behavior and network effects arising from driver interactions, without requiring the operator to reveal system parameters to the drivers. Numerical simulations demonstrate the effects of budget constraints, driver types, and strategic misreporting on equilibrium outcomes and emissions reduction.

We consider a Stackelberg game in which a principal (she) establishes a two-stage contract with a non-myopic agent (he) whose type is unknown. The contract takes the form of an incentive function mapping the agent's first-stage action to his second-stage incentive. While the first-stage action reveals the agent's type under truthful play, a non-myopic agent could benefit from portraying a false type in the first stage to obtain a larger incentive in the second stage. The challenge is thus for the principal to design the incentive function so as to induce truthful play. We show that this is only possible with a constant, non-reactive incentive functions when the type space is continuous, whereas it can be achieved with reactive functions for discrete types. Additionally, we show that introducing an adjustment mechanism that penalizes inconsistent behavior across both stages allows the principal to design more flexible incentive functions.

This paper addresses the aggregated monitoring problem for large-scale network systems with a few dedicated sensors. Full state estimation of such systems is often infeasible due to unobservability and/or computational infeasibility; therefore, through clustering and aggregation, a tractable representation of a network system, called a projected network system, is obtained for designing a minimum-order average state observer. This observer estimates the average states of the clusters, which are identified under explicit consideration of estimation error. Moreover, given the clustering, the proposed observer design algorithm exploits the structure of the estimation error dynamics to achieve computational tractability. Simulations show that the computation of the proposed algorithm is significantly faster than the usual H2/H infinity observer design techniques. On the other hand, compromise on the estimation error characteristics is shown to be marginal.

This paper proposes a feedback design that effectively copes with uncertainties for reliable epidemic monitoring and control. There are several optimization-based methods to estimate the parameters of an epidemic model by utilizing past reported data. However, due to the possibility of noise in the data, the estimated parameters may not be accurate, thereby exacerbating the model uncertainty. To address this issue, we provide an observer design that enables robust state estimation of epidemic processes, even in the presence of uncertain models and noisy measurements. Using the estimated model and state, we then devise optimal control policies by minimizing a predicted cost functional. To demonstrate the effectiveness of our approach, we implement it on a modified SIR epidemic model. The results show that our proposed method is efficient in mitigating the uncertainties that may arise.

Designing Luenberger observers for nonlinear systems involves the challenging task of transforming the state to an alternate coordinate system, possibly of higher dimensions, where the system is asymptotically stable and linear up to output injection. The observer then estimates the system's state in the original coordinates by inverting the transformation map. However, finding a suitable injective transformation whose inverse can be derived remains a primary challenge for general nonlinear systems. We propose a novel approach that uses supervised physics-informed neural networks to approximate both the transformation and its inverse. Our method exhibits superior generalization capabilities to contemporary methods and demonstrates robustness to both neural network's approximation errors and system uncertainties.

Traditional observer design methods rely on certain properties of the system's nonlinearity, such as Lipschitz continuity, one-sided Lipschitzness, a bounded Jacobian, or quadratic boundedness. These properties are described by parameterized inequalities. However, enforcing these inequalities globally can lead to very large parameters, resulting in overly conservative observer design criteria. These criteria become infeasible for highly nonlinear applications, such as networked epidemic processes. In this paper, we present an observer design approach for estimating the state of nonlinear systems, without requiring any parameterization of the system's nonlinearities. The proposed observer design depends only on systems' matrices and applies to systems with any nonlinearity. We establish different design criteria for ensuring both asymptotic and exponential convergence of the estimation error to zero. To demonstrate the efficacy of our approach, we employ it for estimating the state of a networked SIR epidemic model. We show that, even in the presence of measurement noise, the observer can accurately estimate the epidemic state of each node in the network. To the best of our knowledge, the proposed observer is the first that is capable of estimating the state of networked SIR models.

This paper considers the problem of set-based state estimation for linear time-invariant (LTI) systems under time-varying sensor attacks. Provided that the LTI system is stable and observable via every single sensor and that at least one sensor is uncompromised, we guarantee that the true state is always contained in the estimated set. We use zonotopes to represent these sets for computational efficiency. However, we show that intelligently designed stealthy attacks may cause exponential growth in the algorithm's worst-case complexity. We present several strategies to handle this complexity issue and illustrate our resilient zonotope-based state estimation algorithm on a rotating target system.

This paper studies the problem of secure state estimation of a linear time-invariant (LTI) system with bounded noise in the presence of sparse attacks on an unknown, time-varying set of sensors. At each time, the attacker has the freedom to choose an arbitrary set of no more than p sensors and manipulate their measurements without restraint. To this end, we propose a secure state estimation scheme and guarantee a bounded estimation error irrespective of the attack signals subject to 2p-sparse observability and a mild, technical assumption that the system matrix has no degenerate eigenvalues. The proposed scheme comprises a design of decentralized observers for each sensor based on the local observable subspace decomposition. At each time step, the local estimates of sensors are fused by a median operator to obtain a secure estimation, which is then followed by a local detection-and-resetting process of the decentralized observers. The estimation error is shown to be upper-bounded by a constant which is determined only by the system parameters and noise magnitudes. Moreover, we design the detector threshold to ensure that the benign sensors never trigger the detector. The efficacy of the proposed algorithm is demonstrated by its application on a benchmark example of IEEE 14-bus system. We show that our proposed scheme can effectively tolerate sparse attacks on an unknown set of sensors, ensuring a bounded estimation error and effectively detecting and resetting the attacked sensors.

This paper proposes a data-driven set-based estimation algorithm for a class of nonlinear systems with polynomial nonlinearities. Using the system's input-output data, the proposed method computes a set that guarantees the inclusion of the system's state in real-time. Although the system is assumed to be a polynomial type, the exact polynomial functions, and their coefficients are assumed to be unknown. To this end, the estimator relies on offline and online phases. The offline phase utilizes past input-output data to estimate a set of possible coefficients of the polynomial system. Then, using this estimated set of coefficients and the side information about the system, the online phase provides a set estimate of the state. Finally, the proposed methodology is evaluated through its application on SIR (Susceptible, Infected, Recovered) epidemic model.