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With the development of large-scale sensor networks, there is an increasing interest for high dimensional distributed decision fusion problem in statistical decision, machine learning, control theory, etc. In this article, we investigate the optimal sensor quantized rules of the distributed decision under a given fusion rule for conditionally dependent and high dimensional sensor observations. We provide a Monte Carlo importance sampling method to reduce the computational complexity of the distributed decision fusion. For the K-out-of-L rule, we derive a group of analytic sensor rules based on the necessary and sufficient condition of the optimal sensor rules. In term of efficiency, it is significantly better than the traditional iterative search algorithms, such as the Riemann sum approximation iteration algorithm. The analytic solution is also a general result since it does not rely on the specific K value of the K-out-of-L rule, the specific conditional probability density function and the dimension of sensor observations. Thus, it can be applied to multisensor decision fusion problems with high dimensional dependent sensor observations. For the general fusion rules rather than the K-out-of-L rule, the Monte Carlo Gauss–Seidel algorithm is also provided. The numerical examples demonstrate the effectiveness of the analytic solution and the Monte Carlo Gauss–Seidel algorithm. [ABSTRACT FROM AUTHOR]

Motivated by the recent applications of game-theoretical learning to the design of distributed control systems, we study a class of control problems that can be formulated as potential games with continuous action sets. We propose an actor-critic reinforcement learning algorithm that adapts mixed strategies over continuous action spaces. To analyze the algorithm, we extend the theory of finite-dimensional two-timescale stochastic approximation to a Banach space setting, and prove that the continuous dynamics of the process converge to equilibrium in the case of potential games. These results combine to give a provably-convergent learning algorithm in which players do not need to keep track of the controls selected by other agents. [ABSTRACT FROM PUBLISHER]

Numerical aspects are of central importance in identification and control. Many computations in these fields involve approximations using polynomial or rational functions that are obtained using orthogonal or oblique projections. The aim of this paper is to develop a new and general theoretical framework to solve a large class of relevant problems. The proposed method is built on the introduction of bi-orthonormal polynomials with respect to a data-dependent bi-linear form. This bi-linear form generalises the conventional inner product and allows for asymmetric and indefinite problems. The proposed approach is shown to lead to optimal numerical conditioning $(\kappa=1)$ in a recent frequency-domain instrumental variable system identification algorithm. In comparison, it is shown that these recent algorithms exhibit extremely poor numerical properties when solved using traditional approaches. [ABSTRACT FROM PUBLISHER]

We present a novel distributed algorithm for convex constrained optimization problems that are subject to noise corruption and uncertainties. The proposed scheme can be classified as a distributed stochastic approximation method, where a unique feature here is that we allow for multiple noise terms to appear in both the computation and communication stages of the distributed iterative process. Specifically, we consider problems that involve multiple agents optimizing a separable convex objective function subject to convex local constraints and linear coupling constraints. This is a richer class of problems compared to those that can be handled by existing distributed stochastic approximation methods which consider only consensus constraints and fewer sources of noise. The proposed algorithm utilizes the augmented Lagrangian (AL) framework, which has been widely used recently to solve deterministic optimization problems in a distributed way. We show that the proposed method generates sequences of primal and dual variables that converge to their respective optimal sets almost surely. [ABSTRACT FROM AUTHOR]

Reachability analysis of nonlinear uncertain hybrid systems, i.e., continuous-discrete dynamical systems whose continuous dynamics, guard sets and reset functions are defined by nonlinear functions, can be decomposed in three algorithmic steps: computing the reachable set when the system is in a given operation mode, computing the discrete transitions, i.e., detecting and localizing when (and where) the continuous flowpipe intersects the guard sets, and aggregating the multiple trajectories that result from an uncertain transition once the whole flow-pipe has transitioned so that the algorithm can resume. This paper proposes a comprehensive method that provides a nicely integrated solution to the hybrid reachability problem. At the core of the method is the concept of MSPB, i.e., geometrical object obtained as the Minkowski sum of a parallelotope and an axes aligned box. MSPB are a way to control the over-approximation of the Taylor's interval integration method. As they happen to be a specific type of zonotope, they articulate perfectly with the zonotope bounding method that we propose to enclose in an optimal way the set of flowpipe trajectories generated by the transition process. The method is evaluated both theoretically by analyzing its complexity and empirically by applying it to well-chosen hybrid nonlinear examples. [ABSTRACT FROM AUTHOR]

We develop a gradient algorithm for optimizing the performance of product-form networks through online adjustment of control parameters. The use of standard algorithms for finding optimal parameter settings is hampered by the prohibitive computational burden of calculating the gradient in terms of the stationary probabilities. The proposed approach instead relies on measuring empirical frequencies of the various states through simulation or online operation so as to obtain estimates for the gradient. Besides the reduction in computational effort, a further benefit of the online operation lies in the natural adaptation to slow variations in ambient parameters as commonly occurring in dynamic environments. On the downside, the measurements result in inherently noisy and biased estimates. We exploit mixing time results in order to overcome the impact of the bias and establish sufficient conditions for convergence to a globally optimal solution. We discuss our algorithm in the context of different systems, including queueing networks, loss networks, and wireless networks. We also illustrate how the algorithm can be used in such systems to optimize a service/cost trade-off, to map parameter regions that lead to systems meeting specified constraints, and to achieve target performance measures. For the latter application, we first identify which performance measures can be controlled depending on the set of configurable parameters. We then characterize the achievable region of performance measures in product-form networks, and finally we describe how our algorithm can be used to achieve the target performance in an online, distributed fashion, depending on the application context. [ABSTRACT FROM PUBLISHER]

This technical note extends the feedback particle filter (FPF) methodology and algorithms to the problem of filtering a continuous-time Markov chain. The main contribution is the development of a feedback control-based transformation of the Wonham filter, where the control input is realized via a time-modulated Poisson counter process. A complete characterization of the feedback mechanism that defines the FPF is obtained, which leads to tractable algorithms for the nonlinear filtering problem even for large state spaces. Numerical examples are introduced to help illustrate the application of these techniques. [ABSTRACT FROM PUBLISHER]

We investigate stochastic averaging theory for locally Lipschitz discrete-time nonlinear systems with stochastic perturbation and its applications to convergence analysis of discrete-time stochastic extremum seeking algorithms. Firstly, by defining two average systems (one is continuous time, the other is discrete time), we develop discrete-time stochastic averaging theorem for locally Lipschitz nonlinear systems with stochastic perturbation. Our results only need some simple and applicable conditions, which are easy to verify, and remove a significant restriction present in existing results: global Lipschitzness of the nonlinear vector field. Secondly, we provide a discrete-time stochastic extremum seeking algorithm for a static map, in which measurement noise is considered and an ergodic discrete-time stochastic process is used as the excitation signal. Finally, for discrete-time nonlinear dynamical systems, in which the output equilibrium map has an extremum, we present a discrete-time stochastic extremum seeking scheme and, with a singular perturbation reduction, we prove the stability of the reduced system. Compared with classical stochastic approximation methods, while the convergence that we prove is in a weaker sense, the conditions of the algorithm are easy to verify and no requirements (e.g., boundedness) are imposed on the algorithm itself. [ABSTRACT FROM AUTHOR]

We apply first- and second-order splitting schemes to the differential Riccati equation. Such equations are very important in, e.g., linear quadratic regulator (LQR) problems, where they provide a link between the state of the system and the optimal input. The methods can also be extended to generalized Riccati equations, e.g., arising from LQR problems given in implicit form. In contrast to previously proposed schemes such as BDF or Rosenbrock methods, the splitting schemes exploit the fact that the nonlinear and affine parts of the problem, when considered in isolation, have closed-form solutions. We show that if the solution possesses low-rank structure, which is frequently the case, then this is preserved by the method. This feature is used to implement the methods efficiently for large-scale problems. The proposed methods are expected to be competitive, as they at most require the solution of a small number of linear equation systems per time step. Finally, we apply our low-rank implementations to the Riccati equations arising from two LQR problems. The results show that the rank of the solutions stay low, and the expected orders of convergence are observed. [ABSTRACT FROM PUBLISHER]

We investigate the connections between compression learning and scenario based optimization. We first show how to strengthen, or relax the consistency assumption at the basis of compression learning and provide novel learnability conditions for the underlying algorithms. We then consider different constrained optimization problems affected by uncertainty represented by means of scenarios. We show that the compression learning perspective provides a unifying framework for scenario based optimization, since the issue of providing guarantees on the probability of constraint violation reduces to a learning problem for an appropriately chosen algorithm that satisfies some consistency assumption. To illustrate this, we revisit the scenario approach within the developed context. Moreover, using the compression learning machinery we provide novel results on the probability of constraint violation for the class of cascading optimization problems. [ABSTRACT FROM PUBLISHER]

Recently, Chen (2010) presented a new approach to recursive identification for ARMAX systems, which is a three-stage recursive scheme and assumes independent and identically distributed input signals. Here, we observe that, unless the time scale of the algorithm at one stage is reasonably faster than those at the previous stages, convergence to the true value may not take place. To remedy this issue, this note proposes a multi-time-scale modification of the algorithm in [5] such that convergence is achieved. In addition, the new scheme handles a wider class of input signals so that the input can be designed for some purpose.The advantage of the multi-time scale algorithm is verified with numerical examples. [ABSTRACT FROM PUBLISHER]

Recently, much progress has been made on particle swarm optimization (PSO). A number of works have been devoted to analyzing the convergence of the underlying algorithms. Nevertheless, in most cases, rather simplified hypotheses are used. For example, it often assumes that the swarm has only one particle. In addition, more often than not, the variables and the points of attraction are assumed to remain constant throughout the optimization process. In reality, such assumptions are often violated. Moreover, there are no rigorous rates of convergence results available to date for the particle swarm, to the best of our knowledge. In this paper, we consider a general form of PSO algorithms, and analyze asymptotic properties of the algorithms using stochastic approximation methods. We introduce four coefficients and rewrite the PSO procedure as a stochastic approximation type iterative algorithm. Then we analyze its convergence using weak convergence method. It is proved that a suitably scaled sequence of swarms converge to the solution of an ordinary differential equation. We also establish certain stability results. Moreover, convergence rates are ascertained by using weak convergence method. A centered and scaled sequence of the estimation errors is shown to have a diffusion limit. [ABSTRACT FROM AUTHOR]

We consider a cooperative conflict resolution problem that finds application, for example, in vehicle intersection crossing. We seek to determine minimally restrictive supervisors, which allow agents to choose all possible control actions that keep the system safe, that is, conflict free. This is achieved by determining the maximal controlled invariant set, and then by determining control actions that keep the system state inside this set. By exploiting the natural monotonicity of the agents dynamics along their paths, we translate this problem into an equivalent scheduling problem. This allows us to leverage existing results in the scheduling literature to obtain both exact and approximate solutions. The approximate algorithms have polynomial complexity and can handle large problems with guaranteed approximation bounds. We illustrate the application of the proposed algorithms through simulations in which vehicles crossing an intersection are overridden by the supervisor only when necessary to maintain safety. [ABSTRACT FROM AUTHOR]

Multi-dimensional stochastic optimization plays an important role in analysis and control of many technical systems. To solve the challenging multidimensional problems of nonstationary optimization, it is suggested to use a stochastic approximation algorithm (like SPSA) with perturbed input and constant step-size which has simple form. We get a finite bound of residual between estimates and time-varying unknown parameters when observations are made under an unknown but bounded noise. Applications of the algorithm are considered for a random walk, an optimization of UAV's flight, and a load balancing problem. [ABSTRACT FROM AUTHOR]

This paper deals with the update step of Gaussian MAP filtering. In this framework, we seek a Gaussian approximation to the posterior probability density function (PDF) whose mean is given by the maximum a posteriori (MAP) estimator. We propose two novel optimization algorithms which are quite suitable for finding the MAP estimate although they can also be used to solve general optimization problems. These are based on the design of a sequence of PDFs that become increasingly concentrated around the MAP estimate. The resulting algorithms are referred to as Kalman optimization (KO) methods. We also provide the important relations between these KO methods and their conventional optimization algorithms (COAs) counterparts, i.e., Newton's and Levenberg-Marquardt algorithms. Our simulations indicate that KO methods are more robust than their COA equivalents. [ABSTRACT FROM AUTHOR]

We propose a novel algorithm to compute low-complexity polytopic robust control invariant (RCI) sets, along with the corresponding state-feedback gain, for linear discrete-time systems subject to norm-bounded uncertainty, additive disturbances and state/input constraints. Using a slack variable approach, we propose new results to transform the original nonlinear problem into a convex/LMI problem whilst introducing only minor conservatism in the formulation. Through numerical examples, we illustrate that the proposed algorithm can yield improved maximal/minimal volume RCI set approximations in comparison with the schemes given in the literature. [ABSTRACT FROM AUTHOR]

Most of the controllers designed for systems with timedelays involve finite impulse response (FIR) filters in their structure, in particular prediction based controllers for systems with input/output delays. We present theory, algorithms and software to evaluate the frequency response, to approximate the filters by stable linear timeinvariant systems and to compute their induced \cal L2 gain. The approach is based on the theory of functions of matrices. In the approach pole zero cancelations in frequency domain representations are explicitly taken into account. [ABSTRACT FROM AUTHOR]

Matrix measures, also known as logarithmic norms, have historically been used to provide bounds on the divergence of trajectories of a system of ordinary differential equations. In this technical note we use them to compute guaranteed overapproximations of reachable sets for nonlinear continuous-time systems using numerically simulated trajectories and to bound the accumulation of numerical simulation errors along simulation traces. Our method employs a user-supplied bound on the matrix measure of the system's Jacobian matrix to compute bounds on the behavior of nearby trajectories, leading to efficient computation of reachable sets when such bounds are available. We demonstrate that the proposed technique scales well to systems with a large number of states. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a stochastic search algorithm for solving general optimization problems with little structure. The algorithm iteratively finds high quality solutions by randomly sampling candidate solutions from a parameterized distribution model over the solution space. The basic idea is to convert the original (possibly non-differentiable) problem into a differentiable optimization problem on the parameter space of the parameterized sampling distribution, and then use a direct gradient search method to find improved sampling distributions. Thus, the algorithm combines the robustness feature of stochastic search from considering a population of candidate solutions with the relative fast convergence speed of classical gradient methods by exploiting local differentiable structures. We analyze the convergence and converge rate properties of the proposed algorithm, and carry out numerical study to illustrate its performance. [ABSTRACT FROM AUTHOR]

In this paper, we study an approximate projected consensus algorithm for a network to cooperatively compute the intersection of convex sets, where each set corresponds to one network node. Instead of assuming exact convex projection that each node can compute, we allow each node to compute an approximate projection with respect to its own set. After receiving the approximate projection information, nodes update their states by weighted averaging with the neighbors over a directed and time-varying communication graph. The approximate projections are related to projection angle errors, which introduces state-dependent disturbance in the iterative algorithm. Projection accuracy conditions are presented for the considered algorithm to converge. The results indicate how much projection accuracy is required to ensure global consensus to a point in the intersection set when the communication graph is uniformly jointly strongly connected. In addition, we show that $\pi/4$ is a critical angle for the error of the projection approximation to ensure the boundedness. Finally, the results are illustrated by simulations. [ABSTRACT FROM AUTHOR]

We propose and analyze two dual methods based on inexact gradient information and averaging that generate approximate primal solutions for smooth convex problems. The complicating constraints are moved into the cost using the Lagrange multipliers. The dual problem is solved by inexact first-order methods based on approximate gradients for which we prove sublinear rate of convergence. In particular, we provide a complete rate analysis and estimates on the primal feasibility violation and primal and dual suboptimality of the generated approximate primal and dual solutions. Moreover, we solve approximately the inner problems with a linearly convergent parallel coordinate descent algorithm. Our analysis relies on the Lipschitz property of the dual function and inexact dual gradients. Further, we combine these methods with dual decomposition and constraint tightening and apply this framework to linear model predictive control obtaining a suboptimal and feasible control scheme. [ABSTRACT FROM AUTHOR]

We present a fast distributed solution to the convex network flow optimization problem. Our approach uses a family of dual descent algorithms that approximate the Newton direction to achieve faster convergence rates than existing distributed methods. The approximate Newton directions are obtained through matrix splitting techniques and sparse Taylor approximations of the inverse Hessian. We couple this descent direction with a distributed line search algorithm which requires the same information as our descent direction to compute. We show that, similarly to conventional Newton methods, the proposed algorithm exhibits super-linear convergence within a neighborhood of the optimal value. Numerical experiments corroborate that convergence times are between one to two orders of magnitude faster than existing distributed optimization methods. A connection with recent developments that use consensus to compute approximate Newton directions is also presented. [ABSTRACT FROM PUBLISHER]

The nu-gap metric was originally developed to evaluate robustness of a plant-controller feedback loop and it has many attractive properties. For example, performance of the closed loop changes continuously and stability is robust with respect to small perturbations of the plant (or the controller) in the nu-gap metric. In light of these properties, one can state that the nu-gap metric provides a good measure of distance between systems in a closed loop setting. This is very useful in model approximation, which is the focus of this technical note. The presented nu-gap approximation method is based on semidefinite programming and frequency response matching, which allows to extend the method to account for frequency-dependent weights in the objective function. The frequency-weighted extension is the major advantage of the presented method in comparison with other nu-gap model reduction methods. This extension is applied to approximation of controllers obtained by loop shaping and illustrated on a numerical example. [ABSTRACT FROM PUBLISHER]

We consider a multi-agent optimization problem where agents subject to local, intermittent interactions aim to minimize a sum of local objective functions subject to a global inequality constraint and a global state constraint set. In contrast to previous work, we do not require that the objective, constraint functions, and state constraint sets are convex. In order to deal with time-varying network topologies satisfying a standard connectivity assumption, we resort to consensus algorithm techniques and the Lagrangian duality method. We slightly relax the requirement of exact consensus, and propose a distributed approximate dual subgradient algorithm to enable agents to asymptotically converge to a pair of primal-dual solutions to an approximate problem. To guarantee convergence, we assume that the Slater's condition is satisfied and the optimal solution set of the dual limit is singleton. We implement our algorithm over a source localization problem and compare the performance with existing algorithms. [ABSTRACT FROM AUTHOR]

The technical note deals with state estimation of nonlinear stochastic dynamic systems. Traditional filters providing local estimates of the state, such as the extended Kalman filter, unscented Kalman filter, or the cubature Kalman filter, are based on computationally efficient but approximate integral evaluations. On the other hand, the Monte Carlo based Kalman filter takes an advantage of asymptotically exact integral evaluations but at the expense of substantial computational demands. The aim of the technical note is to propose a new local filter that utilises stochastic integration methods providing the asymptotically exact integral evaluation with computational complexity similar to the traditional filters. The technical note will demonstrate that the unscented and cubature Kalman filters are special cases of the proposed stochastic integration filter. The proposed filter is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

This technical note is dedicated to model order reduction of linear time-invariant systems. The main contribution of this technical note is the derivation of two scalable stability-preserving model reduction algorithms. Both algorithms constitute a development of a recently proposed model reduction method. The algorithms perform a curve fitting procedure using frequency response samples of a model and semidefinite programming methods. Computation of these samples can be done efficiently even for large scale models. Both algorithms are obtained from a reformulation of the model reduction problem. One proposes a semidefinite relaxation, while the other is an iterative semidefinite approach. The relaxation approach is similar to Hankel model reduction, which is a well-known and established method in the control literature. Due to this resemblance, the accuracy of approximation is also similar to the one of Hankel model reduction. An appealing quality of the proposed algorithms is the ability to easily perform extensions, e.g., introduce frequency-weighting, positive-real and bounded-real constraints. [ABSTRACT FROM AUTHOR]

Common random numbers and the standard clock method are examples of effective variance reduction techniques that also share information and simulation resources when generating realizations of different simulated systems whose performances are being compared. This sharing of computing resources and the potentially widely different computational requirements for different simulation models are important considerations in allocating simulation replications among the candidate designs with the objective of maximizing the probability of selecting the best design, and we formulate the optimal computing budget allocation problem under this scenario. The resulting formulation leads to an optimization problem that can be viewed as a generalization of a correlated version considered in earlier work. An approximation to the problem is introduced to allow a tractable solution, for which a heuristic two-stage sequential allocation algorithm is proposed, and several numerical examples are used to illustrate the potential improvements that can be gained. [ABSTRACT FROM AUTHOR]

This technical note deals with the estimation of the whole trajectory of a stochastic dynamic system with highest probability, conditionally upon the past observation process, using a maximum Gaussian mixture. We first recall the Gaussian sum technique applied to minimum variance filtering. It is then shown that the same concept of Gaussian mixture can be applied in that context, provided we replace the Sum operator by the Max operator. [ABSTRACT FROM AUTHOR]

Stochastic approximation (SA) algorithms are proposed to identify a multi-input and multi-output (MIMO) Wiener system, in which the system input is taken to be a sequence of independent and identically distributed (i.i.d.) Gaussian random vectors uk\in{\cal N}(0,I). The algorithm for identifying the nonlinear part is designed with multi-variable kernel functions. Under suitable conditions, we show that the estimates of the coefficients of the linear subsystem and of the values of the nonlinear function converge to the respective true values with probability one. [ABSTRACT FROM AUTHOR]

Many iterative algorithms employ operators which are difficult to evaluate exactly, but for which a graduated range of approximations exist. In such cases, “coarse-to-fine” algorithms are often used, in which a crude initial operator approximation is gradually refined with new iterations. In such algorithms, because the computational complexity increases over iterations, the algorithm's convergence rate is properly calculated with respect to cumulative computation time. This suggests the problem of determining an optimal rate of refinement for the operator approximation. This paper shows that, for linearly convergent algorithm, the optimal rate of refinement approaches the rate of convergence of the exact algorithm itself, regardless of the tolerance-complexity relationship. We illustrate this result with an analysis of “coarse-to-fine” grid algorithms for Markov decision processes with continuous state spaces. Using the methods proposed here we deduce an algorithm that presents optimal complexity results and consists solely of a non-adaptive schedule for the gradual decrease of grid size. [ABSTRACT FROM AUTHOR]

Sparse identification can be relevant in the automatic control field to solve several problems for nonlinear systems such as identification, control, filtering, fault detection. However, identifying a maximally sparse approximation of a nonlinear function is in general an NP-hard problem. The common approach is to use relaxed or greedy algorithms that, under certain conditions, can provide sparsest solutions. In this technical note, a combined \ell 1-relaxed-greedy algorithm is proposed and conditions are given, under which the approximation derived by the algorithm is a sparsest one. Differently from other conditions available in the literature, the ones provided here can be actually verified for any choice of the basis functions defining the sparse approximation. A Set Membership analysis is also carried out, assuming that the function to approximate is a linear combination of unknown basis functions belonging to a known set of functions. It is shown that the algorithm is able to exactly select the basis functions which define the unknown function and to provide an optimal estimate of their coefficients. [ABSTRACT FROM AUTHOR]

In this note, we study the consensus problem for multiagent systems with measurement noises. Different from the existing approach, the consensus problem is converted to a root finding problem for which the stochastic approximation theory can be applied. By choosing an appropriate regression function, we propose a consensus algorithm which is applicable to systems with more general measurement noise processes, including stationary autoregressive and moving average (ARMA) processes and infinite moving average (MA) processes. Further, we establish a relationship between the convergence rate and the exponent of the step size of the algorithm. Particularly, strong convergence rate for systems with a leader-follower topology is studied. [ABSTRACT FROM AUTHOR]

This paper considers both synchronous and asynchronous consensus algorithms with noisy measurements. For stochastic approximation based consensus algorithms, the existing convergence analysis with dynamic topologies heavily relies on quadratic Lyapunov functions, whose existence, however, may be difficult to ensure for switching directed graphs. Our main contribution is to introduce a new analytical approach. We first show a fundamental role of ergodic backward products for mean square consensus in algorithms with additive noise. Subsequently, we develop ergodicity results for backward products of degenerating stochastic matrices converging to a 0–1 matrix via a discrete time dynamical system approach. These results complement the existing ergodic theory of stochastic matrices and provide an effective tool for analyzing consensus problems. Under a joint connectivity assumption, our approach may deal with switching topologies, delayed measurements and correlated noises, and it does not require the double stochasticity condition typically assumed for the existence of quadratic Lyapunov functions. [ABSTRACT FROM AUTHOR]

We consider the problem of designing controllers to steer mobile robots to the source (the minimizer) of a signal field. In addition to the mobility constraints, e.g., posed by the nonholonomic dynamics, we assume that the field is completely unknown to the robot and the robot has no knowledge of its own position. Furthermore, the unknown field is randomly switching. In the case where the information of the field (e.g., the gradient) is completely known, standard motion planning techniques for mobile robots would converge to the known source. In the absence of mobility constraints, convergence to the minimum of unknown fields can be pursued using the framework of numerical optimization. By considering these facts, this paper exploits an idea of the stochastic approximation for solving the problem mentioned in the beginning and proposes a source seeking controller which sequentially generates the next waypoints such that the resulting discrete trajectory converges to the unknown source and which steers the robot along the waypoints, under the assumption that the robot can move to any point in the body fixed coordinate frame. To this end, we develop a rotation-invariant and forward-sided version of the simultaneous-perturbation stochastic approximation algorithm as a method to generate the next waypoints. Based on this algorithm, we design source seeking controllers. Furthermore, it is proven that the robot converges to a small set including the source in a probabilistic sense if the signal field switches periodically and sufficiently fast. The proposed controllers are demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

The convex approach to the absolute stability problem is considered. Gapski and Geromel's algorithm for computing Zames–Falb multipliers, used in determining stability, treats the problem as an optimization problem. It is found that their algorithm may terminate prematurely in some cases, failing to find the optimal multiplier. We propose an improvement that always finds an ascent direction and a multiplier that improves the objective function whenever one exists. [ABSTRACT FROM PUBLISHER]

We study the traveling salesman problem for a Dubins vehicle. We prove that this problem is NP-hard, and provide lower bounds on the approximation ratio achievable by some recently proposed heuristics. We also describe new algorithms for this problem based on heading discretization, and evaluate their performance numerically. [ABSTRACT FROM PUBLISHER]

We study a class of random sampling-based algorithms for solving general non-differentiable optimization problems. These are iterative approaches that are based on sampling from and updating an underlying distribution function over the set of feasible solutions. In particular, we propose a novel and systematic framework to investigate the convergence and asymptotic convergence rates of these algorithms by exploiting their connections to the well-known stochastic approximation (SA) method. Such an SA framework unifies our understanding of these randomized algorithms and provides new insight into their design and implementation issues. Our preliminary numerical experiments indicate that new implementations of these algorithms based on the proposed framework may lead to improved performance over existing procedures. [ABSTRACT FROM PUBLISHER]

We consider the problem of monitoring spatial phenomena, such as road speeds on a highway, using wireless sensors with limited battery life. A central question is to decide where to locate these sensors to best predict the phenomenon at the unsensed locations. However, given the power constraints, we also need to determine when to activate these sensors in order to maximize the performance while satisfying lifetime requirements. Traditionally, these two problems of sensor placement and scheduling have been considered separately; one first decides where to place the sensors, and then when to activate them. [ABSTRACT FROM AUTHOR]

In this paper, an algorithm for decentralized multi-agent estimation of parameters in linear discrete-time regression models is proposed in the form of a combination of local stochastic approximation algorithms and a global consensus strategy. An analysis of the asymptotic properties of the proposed algorithm is presented, taking into account both the multi-agent network structure and the probabilities of getting local measurements and implementing exchange of inter-agent messages. In the case of non-vanishing gains in the stochastic approximation algorithms, an asymptotic estimation error covariance matrix bound is defined as the solution of a Lyapunov-like matrix equation. In the case of asymptotically vanishing gains, the mean-square convergence is proved and the rate of convergence estimated. In the discussion, the problem of additive communication noise is treated in a methodologically consistent way. It is also demonstrated how the consensus scheme in the algorithm can contribute to the overall reduction of measurement noise influence. Some simulation results illustrate the obtained theoretical results. [ABSTRACT FROM AUTHOR]

Range-only tracking problems arise in extended data collection for inverse synthetic radar applications, robotics, navigation and other areas. For such problems, the conditional density of the state variable given the measurement history is multi-modal or exhibits curvature, even in seemingly benign scenarios. For this reason, the use of extended Kalman filter (EKF) and other nonlinear filtering techniques based on Gaussian approximations can result in inaccurate estimates. We introduce a new filter for such tracking problems in two dimensions called the Gaussian mixture range-only filter (GMROF), which generates Gaussian mixture approximations to the conditional densities. The filter equations are derived by analytic techniques based on the specific nonlinearities of range-only tracking. A slight modification of the standard measurement process model, “noise before nonlinearity,” is used to simplify the moment calculations. Implementation requires, at each step, the fitting of a low order Gaussian mixture to a simple exponentiated trigonometric function of a scalar variable. Simulations involving scenarios from earlier comparative studies indicate that the GMROF consistently outperformed the EKF, and achieved the accuracy of particle filters while significantly reducing the computational cost. [ABSTRACT FROM AUTHOR]