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We consider finite model approximations of a large class of static and dynamic team problems where these models are constructed through uniform quantization of the observation and action spaces of the agents. The strategies obtained from these finite models are shown to approximate the optimal cost with arbitrary precision under mild technical assumptions. In particular, quantized team policies are asymptotically optimal. This result is then applied to Witsenhausen's celebrated counterexample and the Gaussian relay channel problem. For Witsenhausen's counterexample, our approximation approach provides, to our knowledge, the first rigorously established result that one can construct an $\varepsilon$-optimal strategy for any $\varepsilon > 0$ through a solution of a simpler problem. [ABSTRACT FROM PUBLISHER]

In this paper, we consider the following problem: what passivity properties can be inferred for a system by studying only an approximate mathematical model for it. Our results show that an excess of passivity (whether in the form of input strictly passive, output strictly passive or very strictly passive) in the approximate model guarantees a certain passivity index for the system, provided that the norm of the error between the approximate and the true models is sufficiently small in a suitably defined sense. Further, we consider $(Q,S,R)$-dissipative systems and show that $(Q,S,R)$- dissipativity has a similar robustness property, even though the supply rates for the system and its approximation may be different. These results may be particularly useful if either the approximate model is much easier to analyze, or if the precise system model is unknown. We illustrate the results by considering particular approximation methods, e.g., model reduction, discretization, quantization, and linearization around an equilibrium point. [ABSTRACT FROM PUBLISHER]

We investigate the stabilization of unstable multidimensional partially observed single-sensor and multi-sensor (single-controller) discrete-time linear systems driven by unbounded noise and controlled over discrete noiseless channels. Stability is achieved under fixed-rate communication requirements that are asymptotically tight in the limit of large sampling periods. Through the use of similarity transforms, sampling and random-time drift conditions we obtain a coding and control policy leading to the existence of a unique invariant distribution and finite second moment for the sampled state. We obtain tight necessary and sufficient conditions for the general multi-sensor case under an assumption related to the Jordan form structure of such systems. In the absence of this assumption, we give sufficient conditions for stabilization. [ABSTRACT FROM AUTHOR]

In this paper, a new H\infty filtering approach is developed for a class of discrete time-varying systems subject to missing measurements and quantization effects. The missing measurements are modeled via a diagonal matrix consisting of a series of mutually independent random variables satisfying certain probabilistic distributions on the interval [0,1]. The measured output is quantized by a logarithmic quantizer. Attention is focused on the design of a stochastic H\infty filter such that the H\infty estimation performance is guaranteed over a given finite-horizon in the simultaneous presence of probabilistic missing measurements, quantization effects as well as external non-Gaussian disturbances. A necessary and sufficient condition is first established for the existence of the desired time-varying filters in virtue of the solvability of certain coupled recursive Riccati difference equations (RDEs). Owing to its recursive nature, the proposed RDE approach is shown to be suitable for online application without the need of increasing the problem size. The simulation experiment is carried out for the mobile robot localization problem with non-Gaussian disturbances, missing measurements and quantization effects. The effectiveness of the proposed method is demonstrated in the numerical example. [ABSTRACT FROM PUBLISHER]

In this paper, we study the problem of state feedback stabilization of a linear time-invariant (LTI) discrete-time multi-input system with imperfect input channels. Each input channel is modeled in three different ways. First it is modeled as an ideal transmission system together with an additive norm bounded uncertainty, introducing a multiplicative uncertainty to the plant. Then it is modeled as an ideal transmission system together with a feedback norm bounded uncertainty, introducing a relative uncertainty to the plant. Finally it is modeled as an additive white Gaussian noise channel. For each of these models, we properly define the capacity of each channel whose sum yields the total capacity of all input channels. We aim at finding the least total channel capacity for stabilization. Different from the single-input case that is available in the literature and boils down to a typical \cal H\infty or \cal H2 optimal control problem, the multi-input case involves allocation of the total capacity among the input channels in addition to the design of the feedback controller. The overall process of channel resource allocation and the controller design can be considered as a case of channel-controller co-design which gives rise to modified nonconvex optimization problems. Surprisingly, the modified nonconvex optimization problems, though appear more complicated, can be solved analytically. The main results of this paper can be summarized into a universal theorem: The state feedback stabilization can be accomplished by the channel-controller co-design, if and only if the total input channel capacity is greater than the topological entropy of the open-loop system. [ABSTRACT FROM AUTHOR]

This paper investigates an optimal quantizer design problem for multisensor estimation of a hidden Markov model (HMMs) whose description depends on unknown parameters. The sensor measurements are simply binary quantized and transmitted to a remote fusion center over noisy flat fading wireless channels under an average sum transmit power constraint. The objective is to determine a set of optimal quantization thresholds and sensor transmit powers, called an optimal policy, which minimizes the long run average of a weighted combination of the expected state estimation error and sum transmit power. We analyze the problem by formulating an adaptive Markov decision process (MDP) problem. In this framework, adaptive optimal control policies are obtained using a nonstationary value iteration (NVI) scheme and are termed as NVI-adaptive policies. These NVI-adaptive policies are adapted to the HMM parameter estimates obtained via a strongly consistent maximum likelihood estimator. In particular, HMM parameter estimation is performed by a recursive expectation–maximization (EM) algorithm which computes estimates of the HMM parameters by maximizing a relative entropy information measure using the received quantized observations and the trajectory of the MDP. Under some regularity assumptions on the observation probability distributions and a geometric ergodicity condition on an extended Markov chain, the maximum-likelihood estimator is shown to be strongly consistent. It is shown that the NVI-adaptive policy based on this sequence of strongly consistent HMM parameter estimates is (asymptotically, under appropriate assumptions) average-optimal. Essentially, it minimizes the long run average cost of the weighted combination of the expected state estimation error and sum transmit power across the sensors for the HMM with true parameters in a time-asymptotic sense. The advantage of this scheme is that the policies are obtained recursively without the need to solve the Bellman equation at each time step, which can be computationally prohibitive. As is usual with value iteration schemes, practical implementation of the NVI-adaptive policy requires discretization of the state and action space, which results in some loss of optimality. Nevertheless, numerical results illustrate the asymptotic convergence properties of the parameter estimates and the asymptotically close to optimal performance of the adaptive MDP algorithm compared to the performance of an MDP based dynamic quantization and power allocation algorithm designed with perfect knowledge of the true parameters. [ABSTRACT FROM PUBLISHER]

This paper deals with systems involving input saturation and quantized control laws, which can be of two types: input quantization case and state quantization case. In both cases, the state feedback control design problem is addressed. Therefore, based on some modified sector conditions and appropriate variable changes, regional (local) uniform ultimate boundedness stabilization problem is tackled. Computational oriented solutions are derived to solve suboptimal convex optimization problems able to give a constructive solution to the design problem of the state feedback gain. [ABSTRACT FROM PUBLISHER]

Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main drawbacks: either they can only be applied to restrictive classes of systems, or they require the exact computation of reachable sets. In this paper, we propose a new abstraction technique that is applicable to any nonlinear sampled-data control system as long as we are only interested in its behavior in a compact set. Moreover, the exact computation of reachable sets is not required. The effectiveness of the proposed results is illustrated by synthesizing a controller to steer a vehicle. [ABSTRACT FROM PUBLISHER]

This paper addresses a problem of finding an optimal dynamic quantizer for nonlinear control subject to discrete-valued signal constraints, i.e., to the condition that some signals must take a value on a discrete and countable set at each time instant. The quantizers to be studied are in the form of a nonlinear difference equation which maps continuous-valued signals into discrete-valued ones. They are evaluated by a performance index expressing the difference between the resulting quantized system and the unquantized system, in terms of the input–output relation. In this paper, we present a closed-form solution, which globally minimizes the performance index. This result shows the performance limitation of a general class of dynamic quantizers. In addition to this, some results on the structure and the stability are given in order to clarify the mechanism of the best dynamic quantization in nonlinear control systems. [ABSTRACT FROM PUBLISHER]

We consider the problem of achieving input-to-state stability (ISS) with respect to external disturbances for control systems with quantized measurements. Quantizers considered in this paper take finitely many values and have an adjustable “center” and “zoom” parameters. Both the full state feedback and the output feedback cases are considered. Similarly to previous techniques from the literature, our proposed controller switches repeatedly between “zooming out” and “zooming in.” However, here we use two modes to implement the “zooming in” phases, which allows us to attenuate an unknown disturbance while using the minimal number of quantization regions. Our analysis is trajectory-based and utilizes a cascade structure of the closed-loop hybrid system. We further show that our method is robust to modeling errors using a specially adapted small-gain theorem. The main results are developed for linear systems, but we also discuss their extension to nonlinear systems under appropriate assumptions. [ABSTRACT FROM PUBLISHER]

This paper deals with the distributed averaging problem over a connected network of agents, subject to a quantization constraint. It is assumed that at each time update, only a pair of agents can update their own states in terms of the quantized data being exchanged. The agents are also required to communicate with one another in a stochastic fashion. It is shown that a quantized consensus is reached for an arbitrary quantizer by means of the stochastic gossip algorithm proposed in a recent paper. The expected value of the time at which a quantized consensus is reached is lower and upper bounded in terms of the topology of the graph for a uniform quantizer. In particular, it is shown that these bounds are related to the principal submatrices of the weighted Laplacian matrix. A convex optimization is also proposed to determine a set of probabilities used to pick a pair of agents that leads to a fast convergence of the gossip algorithm. [ABSTRACT FROM PUBLISHER]