Bayesian optimal control for a non-autonomous stochastic discrete time system

This paper presents the stabilization problem of a class of discrete-time stochastic linear systems with time delay using an event-triggered control(ETC) strategy. For the general linear systems, we propose a new event triggering mechanism and deduce sufficient conditions for mean square exponentially stabilizability(MSES) and almost sure exponentially stabilizability(ASES) via ETC. The results show that the stability of the system depends on the system parameters (time delay, noise, event trigger threshold parameter, and unstable characteristic value of the original system). When the feedback control is disturbed by low-intensity noise, the unstable system can be stable in the mean square. Finally, the validity of the theoretical results is illustrated through a simulation example.

The problem of intermittent fault (IF) detection is studied for a class of linear discrete-time stochastic systems with unknown disturbance under the influence of a class of networked phenomena by using the moving horizon estimation (MHE). Aiming to normalise the transmission of data in network systems, the Round-Robin (RR) protocol is introduced for linear discrete-time stochastic systems, so the system is converted to a linear periodic system. By using the lifting technique and superposition principle, the linear periodic discrete-time system is transformed into a linear discrete time-invariant system. An MHE strategy is developed to cope with unknown disturbance by introducing provisional estimates of external unknown disturbances. By utilizing the moving horizon estimator, a scalar residual decoupled from the unknown disturbance is designed. Finally, the effectiveness of the proposed method is verified by a simulation example.

Intermittent fault detection for linear discrete-time stochastic multi-agent systems

This paper mainly discusses the robust quadratic stability and stabilization of linear discrete time stochastic systems with state delay and uncertain parameters. By means of the linear matrix inequality (LMI) method, a sufficient condition is respectively obtained for the stability and stabilizability of the considered system. Moreover, an example with simulations is given to verify the effectiveness of our theoretical results.

In this paper we propose definitions of equivalence via stochastic bisimulation and of equivalence of stochastic external behavior for the class of discrete-time stochastic nonlinear control systems with possibly degenerate distributed disturbances. The notions are inspired by the analogue notions that exist for probabilistic chains and for behavioral systems, respectively. Connections between the two notions and also with stochastic reachability are discussed. For the subclass of discrete-time stochastic linear control systems with multivariate possibly degenerate normal distributed disturbances, geometric necessary and sufficient conditions for checking stochastic bisimulation equivalence and stochastic external behavior equivalence are derived. The proposed results nicely extend the theory of bisimulation equivalence and equivalence of external behavior known for non-deterministic control systems to a stochastic setting.

The decentralized control of discrete time stochastic linear systems is considered in this paper. The decentralized control laws are obtained by determining a sequential Nash equilibrium point for a set of quadratic cost functions. In the absence of disturbances, the Nash equilibrium set has the property of driving the state of the closed-loop system to the origin in finite time or asymptotically. In addition, the control law is a linear function of the instantaneous output measurements and can be computed on-line using relatively simple algorithms.

Linear discrete time stochastic dynamical systems with switching parameters may represent a wide class of physical processes. Given the fact that, for non linear systems, the conditional density has no finite parametrization, optimal filters for this class of models are generally infinite dimensional. An exact recursive hybrid filter form has been recently found by Elliott and al [3]. The purpose of this note is to present a new simple approximation scheme of this exact version, which avoids the exponential growth memory problem of the original form. This new numerical scheme is shown to be computationnally efficient. Its implementation is discussed and a comparison of its performances with the Interacting Multiple Models (IMM) algorithm [2] shows its efficiency.

This paper deals with the class of linear stochastic discrete-time systems with varying time-delay. The problems of stability and stabilizability for this class of systems are considered. Given an upper and a lower bounds on the time-varying delay sufficient conditions for checking the stability of this class of systems are developed. A control design algorithm is also provided. All the results developed in this paper are in the LMI formalism which makes their solvability easier using the existing tools. A numerical example is provided to show the effectiveness of the established results.

The strictly positive real (SPR) condition on the noise model is necessary for a discrete-time linear stochastic control system with unmodeled dynamics, even so for a time-invariant ARMAX system, in the past robust analysis of parameter estimation. However, this condition is hardly satisfied for a high-order and/or multidimensional system with correlated noise. The main work in this paper is to show that for robust parameter estimation and adaptive tracking, as well as closed-loop system stabilization, the SPR condition is replaced by a stable matrix polynomial. The main method is to design a "two-step" recursive least squares algorithm with or without a weighted factor and with a fixed lag regressive vector and to define an adaptive control with bounded external excitation and with randomly varying truncation.

This paper derives conditions under which co-diagonalization of the controllability and observability Gramians can be performed in a physically consistent manner for the class of linear quantum stochastic systems that are common in the fields of quantum optics and related areas like quantum nano- and optomechanical systems. Such a class is essentially a quantum analogue of classical (non-quantum) linear stochastic systems. However, unlike their classical counterparts, the laws of quantum mechanics impose nonlinear equality constraints on the system matrices of linear quantum stochastic systems, the so-called physical realizability constraints. Therefore, a meaningful model reduction procedure must yield a physically realizable reduced model satisfying these constraints. Previous work has shown that model reduction by subsystem truncation preserves physical realizability, but did not propose a method for truncating a subsystem. One candidate approach for this truncation is a quantum adaptation of the well-known balanced truncation method for classical linear time-invariant systems. It is shown in this paper that balanced realization for linear quantum stochastic systems is only possible under a strongly restrictive necessary and sufficient condition. However, the paper also derives less restrictive necessary and sufficient conditions for other realizations with simultaneously diagonal controllability and observability Gramians, and introduces the notion of a quasi-balanced realization. An example of the application of the results is provided to demonstrate quasi-balanced truncation in the linear quantum stochastic setting.

This paper addresses the problem of control of partially observed linear discrete time stochastic systems with unknown parameters taking values in a finite set. The solution approach is based on a decomposition of the cost function into a control and trajectory component and a dual or learning component. Similarly the control policy is decomposed into a trajectory and a dual policy. A novel identification feedback scheme which introduces duality into the problem is presented.

070 Optimal periodic selection of the measurement for the state estimation of linear discrete time stochastic systems

Minimal-order observer-based distributed fault detection and isolation for stochastic multi-agent systems

Techniques for the estimation of unknown additive trends present in the state and measurement processes of a Kalman–Bucy linear system are introduced. In real applications of the Kaiman filter to signal processing it is often found that unknown additive trends are present in the state and measurement processes. There is a vast literature on the estimation of finite dimensional parameters in discrete time linear stochastic systems. This chapter is concerned with the basic innovations representation of the observation process, identifiability, bias under misspecified trends, and schemes (I) and (II). Observation schemes may similarly be classified into two broad types: partial and full. In the survival analysis setting partial observation may arise from censoring, truncation, or grouping of the data.

The characterization of the behavior that can be achieved by a plant when interconnected with a controller is a topic widely investigated in mathematical systems theory. In this regard, many results have been obtained for several classes of continuous systems, and also for discrete-event and hybrid systems. However, current literature is rather scant in stochastic settings. In this letter we aim to start filling this gap and provide some necessary and some sufficient checkable conditions for enforcing desired stochastic behavior, in terms of stochastic bisimulation equivalence, on discrete-time stochastic linear systems through output feedback interconnection with deterministic linear controller systems.