Let u(epsilon) be a solution to the system div(A(epsilon)(x)del u(epsilon)(x)) = 0 in D, u(epsilon)(x) = g(x, x/epsilon) on partial derivative D, where D subset of R-d (d >= 2), is a smooth uniformly convex domain, and g is 1-periodic in its second variable, and both A(epsilon) and g are sufficiently smooth. Our results in this paper are twofold. First we prove L-p convergence results for solutions of the above system and for the non-oscillating operator A(epsilon)(x) = A(x), with the following convergence rate for all 1 <= p < infinity parallel to u(epsilon) - u(0)parallel to (LP(D)) <= C-P {epsilon(1/2p), d = 2, (epsilon vertical bar ln epsilon vertical bar)(1/p), d = 3, epsilon(1/p), d >= 4, which we prove is (generically) sharp for d >= 4. Here u(0) is the solution to the averaging problem. Second, combining our method with the recent results due to Kenig, Lin and Shen (Commun Pure Appl Math 67(8): 1219-1262, 2014), we prove (for certain class of operators and when d >= 3) ||u(epsilon) - u(0)||(Lp(D)) <= C-p[epsilon(ln(1/epsilon))(2)](1/p) for both the oscillating operator and boundary data. For this case, we take A(epsilon) = A(x/epsilon), where A is 1-periodic as well. Some further applications of the method to the homogenization of the Neumann problem with oscillating boundary data are also considered.

A benchmark problem on atmospheric sound propagation over irregular terrain has been solved using a stable fourth-order accurate finite difference approximation of a high-fidelity acoustic model. A comparison with the parabolic equation method and ray tracing methods is made. The results show that ray tracing methods can potentially be unreliable in the presence of irregular terrain.

The dynamic phasor model of a time-periodic system is used to derive a stability test involving a harmonic Lyapunov function. This reveals a new interpretation of the harmonic Lyapunov function with an appealing time-domain representation. Most importantly, it indicates that the ideas behind the harmonic Lyapunov equation can be generalized to include cyclic switching systems that have different pulse form in each period.

This paper develops a mathematical model for the feedback control of glucose regulation in the healthy human being and is based on the work of Sorensen (1985). The proposed model serves as a starting point for modeling type H diabetes. Four agents - glucose and the three hormones insulin, glucagon, and incretins - are assumed to have an effect on glucose metabolism. By letting compartments represent anatomical organs, the model has a close resemblance to a real human body. Mass balance equations that account for blood flows, exchange between compartments, and metabolic sinks and sources are written, and these result in simultaneous differential equations that are solved numerically. The metabolic sinks and sources - removing or adding glucose, insulin, glucagon, and incretins - describe physiological processes in the body. These processes function as feedback control systems and have nonlinear behaviors. The results of simulations performed for three different clinical test types indicate that the model is successful in simulating intravenous glucose, oral glucose, and meals containing mainly carbohydrates.

We consider two theorems from the theory of compressive sensing. Mainly a theorem concerning uniform recovery of random sampling matrices, where the number of samples needed in order to recover an s-sparse signal from linear measurements (with high probability) is known to be m greater than or similar to s(ln s)(3) ln N. We present new and improved constants together with what we consider to be a more explicit proof. A proof that also allows for a slightly larger class of m x N-matrices, by considering what is called effective sparsity. We also present a condition on the so-called restricted isometry constants, delta s, ensuring sparse recovery via l(1)-minimization. We show that delta(2s) < 4/root 41 is sufficient and that this can be improved further to almost allow for a sufficient condition of the type delta(2s) < 2/3.

We introduce a criterion for robustness to strategic uncertainty in games with continuum strategy sets. We model a player's uncertainty about another player's strategy as an atomless probability distribution over that player's strategy set. We call a strategy profile robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence of strategy profiles in which every player's strategy is optimal under his or her uncertainty about the others. When payoff functions are continuous we show that our criterion is a refinement of Nash equilibrium and we also give sufficient conditions for existence of a robust strategy profile. In addition, we apply the criterion to Bertrand games with convex costs, a class of games with discontinuous payoff functions and a continuum of Nash equilibria. We show that it then selects a unique Nash equilibrium, in agreement with some recent experimental findings.

Direct methods for trajectory optimization are traditionally based on a priori temporal dis- cretization and collocation methods. In this work, the problem of node distribution is for- mulated as an optimization problem, which is to be included in the underlying non-linear mathematical programming problem (NLP). The benefits of utilizing the suggested method for on-line trajectory optimization are illustrated by a missile guidance example.

This paper addresses the problem of designing a real time high performance controller and trajectory generator for air vehicles. The control objective is to use information about terrain and enemy threats to fly low and avoid radar exposure on the way to a given target. The proposed algorithm builds on the well known approach of Receding Horizon Control (RHC) combined with a terminal cost, calculated from a graph representation of the environment. Using a novel safety maneuver, and under an assumption on the maximal terrain inclination, we are able to prove safety as well as task completion. The safety maneuver is incorporated in the short term optimization, which is performed using Nonlinear Programming (NLP). Some key characteristics of the trajectory planner are highlighted through simulations.

We model a stream of cash flows as an optional stochastic process, and value the cash flows by using a continuous and strictly positive linear functional. By applying a representation theorem from the general theory of stochastic processes we are able to study this valuation principle, as well as properties of the stochastic discount factor it implies. This approach to valuation is useful in the non-presence of a financial market, as is often the case when valuing cash flows arising from insurance contracts and in the application of real options.

In this paper, mean-field type games between two players with backward stochastic dynamics are defined and studied. They make up a class of non-zero-sum, non-cooperating, differential games where the players’ state dynamics solve backward stochastic differential equations (BSDE) that depend on the marginal distributions of player states. Players try to minimize their individual cost functionals, also depending on the marginal state distributions. Under some regularity conditions, we derive necessary and sufficient conditions for existence of Nash equilibria. Player behavior is illustrated by numerical examples, and is compared to a centrally planned solution where the social cost, the sum of playercosts, is minimized. The inefficiency of a Nash equilibrium, compared to socially optimal behavior, is quantified by the so-called price of anarchy. Numerical simulations of the price of anarchy indicate how the improvement in social cost achievable by a central planner depends on problem parameters.

This thesis consists of five appended papers, primarily addressingtopics in pedestrian crowd modeling and the formation of conventions.The first paper generalizes a pedestrian crowd model for competingsubcrowds to include nonlocal interactions and an arbitrary (butfinite) number of subcrowds. Each pedestrian is granted a ’personalspace’ and is effected by the presence of other pedestrians within it.The interaction strength may depend on subcrowd affinity. The paperinvestigates the mean-field type game between subcrowds and derivesconditions for the reduction of the game to an optimization problem.The second paper suggest a model for pedestrians with a predeterminedtarget they have to reach. The fixed and non-negotiablefinal target leads us to formulate a model with backward stochasticdifferential equations of mean-field type. Equilibrium in the game betweenthe tagged pedestrians and a surrounding crowd is characterizedwith the stochastic maximum principle. The model is illustrated by anumber of numerical examples.The third paper introduces sticky reflected stochastic differentialequations with boundary diffusion as a means to include walls andobstacles in the mean-field approach to pedestrian crowd modeling.The proposed dynamics allow the pedestrians to move and interactwhile spending time on the boundary. The model only admits a weaksolution, leading to the formulation of a weak optimal control problem.The fourth paper treats two-player finite-horizon mean-field typegames between players whose state trajectories are given by backwardstochastic differential equations of mean-field type. The paper validatesthe stochastic maximum principle for such games. Numericalexperiments illustrate equilibrium behavior and the price of anarchy.The fifth paper treats the formation of conventions in a large populationof agents that repeatedly play a finite two-player game. Theplayers access a history of previously used action profiles and form beliefson how the opposing player will act. A dynamical model wheremore recent interactions are considered to be more important in thebelief-forming process is proposed. Convergence of the history to acollection of minimal CURB blocks and, for a certain class of games,to Nash equilibria is proven.

This article examines mean-field games for marriage. The results support the argument that optimizing the long-term wellbeing through effort and social feeling state distribution (mean-field) will help to stabilize marriage. However, if the cost of effort is very high, the couple fluctuates in a bad feeling state or the marriage breaks down. We then examine the influence of society on a couple using mean-field sentimental games. We show that, in mean-field equilibrium, the optimal effort is always higher than the one-shot optimal effort. We illustrate numerically the influence of the couple's network on their feeling states and their well-being.

We design fast dynamic algorithms for proper vertex and edge colorings in a graph undergoing edge insertions and deletions. In the static setting, there are simple linear time algorithms for ( δ + 1)vertex coloring and (2 δ 1)edge coloring in a graph with maximum degree δ. It is natural to ask if we can efficiently maintain such colorings in the dynamic setting as well. We get the following three results. (1) We present a randomized algorithm which maintains a ( δ+1)-vertex coloring with O(log δ) expected amortized update time. (2) We present a deterministic algorithm which maintains a (1 + o(1)) δ-vertex coloring with O(polylog δ) amortized update time. (3) We present a simple, deterministic algorithm which maintains a (2 δ)edge coloring with O(log δ) worst-case update time. This improves the recent O( δ)-edge coloring algorithm with Õ ( p δ) worst-case update time [4].

Importance sampling in the setting of heavy tailed random variables has generally focused on models with additive noise terms. In this work we extend this concept by considering importance sampling for the estimation of rare events in Markov chains of the form Xn+1 = A(n+1)X(n) + Bn+1; X-0 = 0, where the B-n's and A(n)'s are independent sequences of independent and identically distributed ( i.i.d.) random variables and the B-n's are regularly varying and the An's are suitably light tailed relative to B-n. We focus on efficient estimation of the rare event probability P(X-n > b) as b NE arrow infinity. In particular we present a strongly efficient importance sampling algorithm for estimating these probabilities, and present a numerical example showcasing the strong efficiency.

A new method for variable selection and estimation called Iteratively Scaled Ridge Regression, ISRR, is proposed. The method is an iterative algorithm based on ridge regression. Simulation studies show that ISRR shares the properties of both subset selection and ridge regression. It selects an optimal subset of the regressor variables and is robust to small changes in the data set. The ISRR algorithm was primarily developed for linear models, but is quite simple and general and can easily be extended to more general linear and nonlinear models.

This paper treats iterative solution methods for the generalized Lyapunov equation. Specifically, a residual-based generalized rational-Krylov-type subspace is proposed. Furthermore, the existing theoretical justification for the alternating linear scheme (ALS) is extended from the stable Lyapunov equation to the stable generalized Lyapunov equation. Further insights are gained by connecting the energy-norm minimization in ALS to the theory of H2-optimality of an associated bilinear control system. Moreover it is shown that the ALS-based iteration can be understood as iteratively constructing rank-1 model reduction subspaces for bilinear control systems associated with the residual. Similar to the ALS-based iteration, the fixed-point iteration can also be seen as a residual-based method minimizing an upper bound of the associated energy norm.

For nonlinear mobile systems equipped with exteroceptive sensors, the observability does not only depend on the initial conditions, but also on the control and the environment. This presents an interesting issue: how to design an observer together with the exciting control. In this note, the problem of designing an observer based on range sensor readings is studied. A design method based on periodic excitations is proposed for unicycle robotic systems.

In the paper, an extension of LaSalle's Invariance Principle to a class of switched linear systems is studied. One of the motivations is the consensus problem in multi-agent systems. Unlike most existing results in which each switching mode in the system needs to be asymptotically stable, this paper allows that the switching modes are only Lyapunov stable. Under certain ergodicity assumptions, an extension of LaSalle's Invariance Principle for global asymptotic stability is obtained. Then it is used to solve the consensus reaching problem of certain multi-agent systems in which each agent is modeled by a double integrator, and the associated interaction graph is switching and is assumed to be only jointly connected.

We study a detection method for continuous mechanical deformations of coaxial cylindrical waveguide boundaries, using perturbation theory. The inner boundary of the waveguide is described as a continuous PEC structure with deformations modeled by suitable continuous functions. In the present approach, the computation complexity is significantly reduced compared to discrete conductor models studied in our previous work. If the mechanically deformed metallic structure is irradiated by the microwave fields of appropriate frequencies, then, by means of measurements of the scattered fields at both ends, we can reconstruct the continuous deformation function. We apply the first-order perturbation method to the inverse problem of reconstruction of boundary deformations, using the dominant TEM-mode of the microwave radiation. Different orders of Tikhonov regularization, using the L-curve criterion, are investigated. Using reflection data, we obtain reconstruction results that indicate an agreement between the reconstructed and true continuous deformations of waveguide boundaries.

We present a 2+1 dimensional quantum gauge theory model with correlated fermions that is exactly solvable by bosonization. This model gives an effective description of partially gapped fermions on a square lattice that have density-density interactions and are coupled to photons. We show that the photons in this model are massive due to gauge-invariant normal-ordering, similarly as in the Schwinger model. Moreover, the exact excitation spectrum of the model has two gapped and one gapless mode. We also compute the magnetic field induced by an external current and show that there is a Meissner effect. We find that the transverse photons have significant effects on the low-energy properties of the model even if the fermion-photon coupling is small.

In this paper I ask the question: what has literature to offer computer science? Can a bilateral programme of research be started with the aim of discovering the same kind of deep intertwining of ideas between computer science and literature, as already exists between computer science and linguistics? What practical use could such results yield? I begin by studying a classic forum for some of the most unintelligible pieces of prose ever written, the computer manual. Why are these books so hard to understand? Could a richer diet of metaphor and onomatopoeia help me get my laser printer working? I then dig down a little deeper and explore computer programs themselves as literature. Do they exhibit aesthetics, emotion and all the other multifarious aspects of true literature? If so, does this support their purpose and understandability? Finally I explore the link between computer code and the human writer. Rather than write large amounts of code directly, we encourage students to write algorithms as pseudo-code as a first step. Pseudo-code tells a story within a semi-formalised framework of conventions. Is this the intertwining we should be looking for?

This thesis focuses on investigating the usage of statistical models for estimating fuel consumption of heavy duty vehicles. Several statistical models are assessed, along with machine learning using artificial neural networks.

Data recorded by sensors on board trucks in the EU describe the operational usage of the vehicle. The usage of this data for estimating the fuel consumption is assessed, and several variables originating from the operational data is modelled and tested as possible input parameters.

The estimation model for real world fuel consumption uses 8 parameters describing the operational usage of the vehicles, and 8 parameters describing the vehicles themselves. The operational parameters describe the average speed, topography, variation of speed, idling, and more. This model has an average relative error of 5.75%, with a prediction error less than 11.14% for 95% of all tested vehicles.

When only vehicle parameters are considered, it is possible to make predictions with an average relative error of 9.30%, with a prediction error less than 19.50% for 95% of all tested vehicles.

Furthermore, a computer software called Vehicle Energy Consumption Calculation tool(VECTO) must be used to simulate the fuel consumption for all heavy duty vehicles, according to legislation by the EU. Running VECTO is a slow process, and this thesis also investigates how well statistical models can be used to quickly estimate the VECTO fuel consumption. The model estimates VECTO fuel consumption with an average relative error of 0.32%and with a prediction error less than 0.65% for 95% of all tested vehicles

This work presents a method for information fusion in source localization applications. The method utilizes the concept of optimal mass transport in order to construct estimates of the spatial spectrum using a convex barycenter formulation. We introduce an entropy regularization term to the convex objective, which allows for low-complexity iterations of the solution algorithm and thus makes the proposed method applicable also to higher-dimensional problems. We illustrate the proposed method's inherent robustness to misalignment and miscalibration of the sensor arrays using numerical examples of localization in two dimensions.

Given output data of a stationary stochastic process estimates of the covariances and cepstrum parameters can be obtained. Methods of moments have been applied to these parameters for designing ARMA processes, and it has been shown that these two sets of parameters in fact form local coordinates for the set of ARMA processes, but that some combinations of cepstrum parameters and covariances cannot be matched exactly within this class of processes. Therefore, another class of processes is considered in this paper in order to be able to match any combination of covariances and cepstrum parameters. The main result is that a process with spectral density of the form phi(z) = exp {Sigma(m)(k=0) p(k)(z(k) + z(-k))}/Sigma(n)(k=0) q(k)(z(k) + z(-k))/2 can always match given covariances and cepstrum parameters. This is proven using a fixed-point argument, and a non-linear least-squares problem is proposed for determining a solution.

Given an elliptic curve E defined over <inline-graphic xlink:href="RNS280IM1" xmlns:xlink="http://www.w3.org/1999/xlink"/> and a prime p of good reduction, let <inline-graphic xlink:href="RNS280IM2" xmlns:xlink="http://www.w3.org/1999/xlink"/> denote the group of <inline-graphic xlink:href="RNS280IM3" xmlns:xlink="http://www.w3.org/1999/xlink"/>-points of the reduction of E modulo p, and let e(p) denote the exponent of this group. Assuming a certain form of the generalized Riemann hypothesis (GRH), we study the average of e(p) as <inline-graphic xlink:href="RNS280IM4" xmlns:xlink="http://www.w3.org/1999/xlink"/> ranges over primes of good reduction, and find that the average exponent essentially equals p center dot c(E), where the constant c(E)> 0 depends on E. For E without complex multiplication (CM), c(E) can be written as a rational number (depending on E) times a universal constant, <inline-graphic xlink:href="RNS280IM5" xmlns:xlink="http://www.w3.org/1999/xlink"/>, the product being over all primes q. Without assuming GRH, we can determine the average exponent when E has CM, as well as give an upper bound on the average in the non-CM case.

We present derivations of shallow water model equations of Korteweg-de Vries and Boussinesq type for equatorial tsunami waves in the f-plane approximation and discuss their applicability. This article is part of the theme issue 'Nonlinear water waves'.

This master thesis was performed at the section of Flight Mechanics and Performance at SAAB Aeronautics in Linköping as a part of my Master of Science in Engineering Physics at KTH, Stockholm. The aim of the thesis is to enable desktop simulations of missions from take-off to landing of JAS 39 Gripen.

The mission is set up by a series of task to be performed. Each tasks then link to a pilot model that controls the aircraft to perform the given task. The main part of the work has been to create these pilot models as an extension of the work by Ajdén and Backlund presented in [1].

The tasks that are simulated are, take-off, climb, turn, cruise, combat simulation, descent and landing at a given point. In order to perform these tasks both open and closed loop controls are used. To perform the landing first a path planing based on Dubins minimum path is calculated and then the nonlinear guidance logic presented by Park, Desyst and How in \cite{Park4} is implemented and used for trajectory tracking.

The results from a simulation of a test mission are presented and shows that mission simulations are possible and that the pilot models perform the intended tasks.

The set of residue classes modulo an element pi in the rings of Gaussian integers, Lipschitz integers and Hurwitz integers, respectively, is used as alphabets to form the words of error correcting codes. An error occurs as the addition of an element in a set E to the letter in one of the positions of a word. If epsilon is a group of units in the original rings, then we obtain the Mannheim, Lipschitz and Hurwitz metrics, respectively. Some new perfect 1-error-correcting codes in these metrics are constructed. The existence of perfect 2-error-correcting codes is investigated by computer search.

Using Balmer-Favi's generalized idempotents, we establish the telescope conjecture for many algebraic stacks. Along the way, we classify the thick tensor ideals of perfect complexes of stacks.

A simplified model of the longitudinal motion around a constant velocity trajectory of a wheel loader is developed, for the purpose of finding a control that actively damps oscillations in the acceleration, following an up shifting gear change. Measurements from different drivers and different gear changes indicate similar oscillation frequencies for the investigated vehicle. The model parameters and the gear change induced disturbance are adjusted so that the model output closely fits the true measurements of the vehicle acceleration after a gear change, in the investigated frequency band. With the engine as a torque actuator, active damping of the oscillations in the acceleration is investigated through simulations. The possible improvements using feedback from measured engine speed seem to be limited, while a predefined feed-forward programme shows promising results.

A descriptor is a set of sentences that are truth-functional combinations of expressions of the form , where is a metalinguistic belief predicate and p a sentence in the object language in which beliefs are expressed. Descriptor revision (denoted ) is an operation of belief change that takes us from a belief set K to a new belief set where is a descriptor representing the success condition. Previously studied operations of belief change are special cases of descriptor revision, hence sentential revision can be represented as , contraction as , multiple contraction as , replacement as , etc. General models of descriptor revision are constructed and axiomatically characterized. The common selection mechanisms of AGM style belief change cannot be used, but they can be replaced by choice functions operating directly on the set of potential outcomes (available belief sets). The restrictions of this construction to sentential revision () and sentential contraction give rise to operations with plausible properties that are also studied in some some detail.

Eradication is a radical form of contraction that removes not only a sentence but also all of its non-tautological consequences from a belief set. Eradication of a single sentence that was included in the original belief set coincides with full meet contraction, but if the sentence is external to the belief set then the two operations differ. Multiple eradication, i.e. simultaneous eradication of several sentences, differs from full meet contraction even if the sentences to be contracted are all included in the original belief set. Eradication is axiomatically characterized and its properties investigated. It is shown to have close connections with the recovery postulate for multiple contraction. Based on these connections it is proposed that eradication rather than full meet contraction is the appropriate lower limiting case for multiple contraction operators.

Various systems exhibit universal behavior at the critical point. A typical example of the non-equilibrium critical behavior is the directed bond percolation that exhibits an active-to-absorbing state phase transition in the vicinity of critical percolation probability. An interesting question is how the turbulent mixing influences its critical behavior. In this work we assume that the turbulent mixing is generated by the compressible Navier-Stokes equation where the compressibility is described by an additional field related to the density. Using field-theoretic models and renormalization group methods we investigate large scale and long time behavior.

An order book consists of a list of all buy and sell offers, represented by price and quantity, available to a market agent. The order book changes rapidly, within fractions of a second, due to new orders being entered into the book. The volume at a certain price level may increase due to limitorders, i.e. orders to buy or sell placed at the end of the queue, or decrease because of market orders or cancellations.

In this paper a high-dimensional Markov chain is used to represent the state and evolution of the entire order book. The design and evaluation of optimal algorithmic strategies for buying and selling is studied within the theory of Markov decision processes. General conditions are provided that guarantee the existence of optimal strategies. Moreover, a value-iteration algorithm is presented that enables finding optimal strategies numerically.

As an illustration a simple version of the Markov chain model is calibrated to high-frequency observations of the order book in a foreign exchange market. In this model, using an optimally designed strategy for buying one unit provides a significant improvement, in terms of the expected buy price, over a naive buy-one-unit strategy.

This thesis concerns classical and quantum aspects of minimal manifolds embedded in flat Minkowski space. In particular, we study the Lie algebra of diffeomorphisms on 2 dimensional compact manifolds as well as discuss singularity formation for relativistic minimal surfaces in co-dimension one. We also present a new approach to the Lorentz anomaly in string theory based on operator product expansion. Finally, we consider the spectrum of a family of Schr\"odinger operators describing quantum minimal surfaces and provide bounds for the eigenvalues for finite $N$ as well as in the limit where N tends to infinity.

Mathematics has a unique subject language that students need to master in writing as well as verbally. Shortcomings in the oral mathematical communication capacity contribute to the fact that students with mathematical difficulties do not receive an approved grade in mathematics for grade 9. These students need help and support from their environment in order not to risk being disapproved. This study has been conducted with the purpose of portraying and analyzing mathematics teachers' views on supportive factors for students with mathematical difficulties focusing on oral mathematical communication skills. As a method, a content analytical research approach with inductive thematic methodology has been used and the study is based on five semi structured interviews. Mathematics teachers' views have been judged to be possible to be depicted and analyzed by the following six themes:

1. The balance between oral and written communication

2. The oral mathematical communications skills components

3. Activities based on the students' needs

4. Supporting learning environment for the student

5. The student's participation in mathematical discussions

6. Cooperation with the parents

Teachers agree that students with mathematical difficulties need adaptations of content and knowledge objectives for oral mathematical ability. However, there is no unanimity in the teacher's view of adequate goals and content, but this is considered being the result of a variety of factors such as the student's knowledge, teacher's interpretation of the curriculum, the written focus in mathematics, the lack of adequate situations to assess oral capacity, stress and time shortages and the less good availability of special educators. Students with mathematical difficulties also need support in the context they are in. This believes teachers can be managed by either blending the context of differences in student knowledge or ensuring that students with mathematical difficulties interact with friends who they feel safe interacting with. Teachers also try to support the students with control, control and order, which can be explained by the fact that these students experience through their teens. The teacher makes a subjective assessment of the students' need for governance, and this then paves the way for the students to participate and influence in different ways. Teachers also have different expectations of student performance in a participation, where some teachers believe that the students are performing, with which some people are content with a participation. Teachers thus have different focus on these students ‐ either knowledge or value goals. The last theme concerns teachers' views on cooperation with the parents. Some teachers are interpreted believing that this contact contributes positively whereas others have not been interpreted having the same beliefs.

In this paper, a mathematical model for target tracking using nonlinear scalar range sensors is formulated first. A time-shift sensor scheduling strategy is addressed on the basis of a k-barrier coverage protocol and all the sensors are divided into two classes of clusters, active cluster, and submissive cluster, for energy-saving. Then two types of time-shift nonlinear filters are proposed for both active and submissive clusters to estimate the trajectory of the moving target with disturbed dynamics. The stochastic stability of the two filters is analyzed. Finally, some numerical simulations are given to demonstrate the effectiveness of the new filters with a comparison of EKF.

This paper studies the consensus problem of multi-agent systems in which all agents are modeled by a general linear system. The authors consider the case where only the relative output feedback between the neighboring agents can be measured. To solve the consensus problem, the authors first construct a static relative output feedback control under some mild constraints on the system model. Then the authors use an observer based approach to design a dynamic relative output feedback control. If the adjacent graph of the system is undirected and connected or directed with a spanning tree, with the proposed control laws, the consensus can be achieved. The authors note that with the observer based approach, some information exchange between the agents is needed unless the associated adjacent graph is completely connected.

Robustness of periodic oscillations in autonomous feedback systems are considered for systems with separable nonlinearities. Local quadratic separation of the nonlinear dynamics from the linear part of the dynamics is used to characterize a set of systems that exhibit periodic oscillation in a bounded frequency and amplitude range. The main analysis condition can be formulated as a feasibility problem for linear matrix inequalities.

Primal and dual formulations of stability criteria based on multipliers will be discussed. The foundation for multiplier-based stability analysis is the use of a convex cone of multipliers to characterize the uncertainty in a system. The primal and dual stability criteria are formulated as convex feasibility tests involving the nominal dynamics and multipliers from the cone and the polar cone, respectively. The motivation for introducing the dual is that it provides additional insight into the stability criterion and that it is sometimes easier to use than the primal. The case considered in this chapter is that of uncertainty as it represents the interconnection of a complex network. The multipliers are used to describe characteristic properties of the network such as the spectral location or the structure of the underlying graph.

A framework for robust stability of large scale systems consisting of linear time-invariant systems interconnected over a network will be surveyed and applied to solve heterogeneous consensus problems. The purpose of distributed consensus algorithms is to reach an agreement regarding a certain quantity of interest that depends on the state of all systems. In most of consensus literature, dynamics of all agents in the network are assumed to be the same and of low dimensions. This simplifies the analysis and, for the most elementary networks, stability and the rate of convergence can be determined from the eigenvalues of the interconnection matrix. Here we discuss analogous results for the case where the individual dynamics are heterogeneous and possibly of infinite dimensions. Our criterion for consensus resembles the classical Nyquist criterion. An interesting aspect of this criterion is that in some instances a three-dimensional plot is required in order to make analysis accurate.

Geostatistical methods have rarely been applied to area-level offense data. This article demonstrates their potential for improving the interpretation and understanding of crime patterns using previously analyzed data about car-related thefts for Estonia, Latvia, and Lithuania in 2000. The variogram is used to inform about the scales of variation in offense, social, and economic data. Area-to-area and area-to-point Poisson kriging are used to filter the noise caused by the small number problem. The latter is also used to produce continuous maps of the estimated crime risk (expected number of crimes per 10,000 habitants), thereby reducing the visual bias of large spatial units. In seeking to detect the most likely crime clusters, the uncertainty attached to crime risk estimates is handled through a local cluster analysis using stochastic simulation. Factorial kriging analysis is used to estimate the local- and regional-scale spatial components of the crime risk and explanatory variables. Then regression modeling is used to determine which factors are associated with the risk of car-related theft at different scales.

Many conservative partial differential equations correspond to geodesic equations on groups of diffeomorphisms. Stability of their solutions can be studied by examining sectional curvature of these groups: negative curvature in all sections implies exponential growth of perturbations and hence suggests instability, while positive curvature suggests stability. In the first part of the paper we survey what we currently know about the curvature-stability relation in this context and provide detailed calculations for several equations of continuum mechanics associated to Sobolev H0 and H1 energies. In the second part we prove that in most cases (with some notable exceptions) the sectional curvature assumes both signs.

The stability of uncertain feedback interconnections of causal time-varying linear systems is studied in terms of a recently established generalisation of the nu-gap metric. In particular, a number of robustness results from the well-known linear time-invariant theory are extended. The time-varying generalisations include: sufficient conditions for robust stability; a bound on robust performance; and two-sided bounds on the induced norm of the variation in a closed-loop mapping as an open-loop component of the feedback interconnection is perturbed. Underlying assumptions are verified for causal systems that exhibit linear periodically time-varying behaviour. This includes a class of sampled-data systems as a special case. Within the periodic context considered, it can be shown that a robust stability condition is also necessary.