Class Of Discrete-time Stochastic Systems Research Articles

Optimal linear filter design for systems with correlation in the measurement matrices and noises: recursive algorithm and applications

This paper addresses the optimal least-squares linear estimation problem for a class of discrete-time stochastic systems with random parameter matrices and correlated additive noises. The system presents the following main features: (1) one-step correlated and cross-correlated random parameter matrices in the observation equation are assumed; (2) the process and measurement noises are one-step autocorrelated and two-step cross-correlated. Using an innovation approach and these correlation assumptions, a recursive algorithm with a simple computational procedure is derived for the optimal linear filter. As a significant application of the proposed results, the optimal recursive filtering problem in multi-sensor systems with missing measurements and random delays can be addressed. Numerical simulation examples are used to demonstrate the feasibility of the proposed filtering algorithm, which is also compared with other filters that have been proposed.

H∞ fault detection with randomly occurring nonlinearities and channel fadings

In this paper, the H∞ fault detection problem is investigated for a class of discrete-time stochastic systems with both channel fadings and randomly occurring nonlinearities. Due to Doppler effect and multi-path delays, channel fadings are inevitable and also cause unpredictable dynamic behaviour. The Lth Rice fadings model, which is accounted for both channel fadings and time delays, can be employed to describe this phenomenon. Meanwhile, by using a Bernoulli distributed white sequence, a kind of non-linear disturbance appearing in a random way is also considered in the H∞ fault detection issue. The purpose of the addressed problem is to design a fault detection filter such that, in the presence of channel fadings, the overall fault detection dynamics is stochastically stable and, at the same time, the error between the residual (generated by the fault detection filter) and the fault signal is made as small as possible. By utilising the Lyapunov stability theory associated with the intensive stochastic analysis techniques, sufficient conditions are established under which the addressed H∞ fault detection problem is recast as solving a convex optimisation problem via the semi-definite programme method. Finally, a simulation example is exploited to show the effectiveness of the method proposed in this paper.

Robust fault detection for discrete‐time stochastic systems with non‐homogeneous jump processes

The problem of robust fault detection (RFD) is studied for a class of discrete-time stochastic systems with non-homogeneous jump processes. First, a filter-based residual signal generator is constructed. To guarantee the sensitivity to faults and robustness against unknown inputs, both H ∞ performance and a new performance index are considered. Then an FD filter, which minimises the influences of the disturbances, modelling uncertainties and increases the sensitivity to faults, is designed. A sufficient condition for ensuring the existence of RFD filter in terms of linear-matrix inequalities is established. A simulation is carried out, illustrating that the proposed RFD filter can detect the faults after their occurrences in a timely manner.

Joint estimation and identification for stochastic systems with unknown inputs

Motivated by tracking a manoeuvring target in electronic counter environments, the authors present the problem of joint estimation and identification of a class of discrete-time stochastic systems with unknown inputs in both the plant and sensors. Based on the expectation-maximum criterion, the joint optimisation scheme of state estimation, parameter identification and iteration terminate decision were derived. A numerical example of tracking a manoeuvring target accompanied range gate pull-off is utilised to verify the proposed scheme.

Filtering for Discrete-Time Stochastic Systems with Nonlinear Sensor and Time-Varying Delay

The filtering problem for a class of discrete-time stochastic systems with nonlinear sensor and time-varying delay is investigated. By using the Lyapunov stability theory, sufficient conditions are proposed to guarantee the asymptotical stablity with an prescribe performance level of the filtering error systems. These conditions are dependent on the lower and upper bounds of the discrete time-varying delays and are obtained in terms of a linear matrix inequality (LMI). Finally, two numerical examples are provided to illustrate the effectiveness of the proposed methods.

Observer‐based H ∞ control for discrete‐time stochastic systems with quantisation and random communication delays

In this study, the authors are concerned with the observer-based quantised H ∞ control problem for a class of discrete-time stochastic systems with random communication delays. The system under consideration involves signals quantisation, state-dependent disturbance as well as random communication delays. The measured output and the control input quantisation are considered simultaneously by using the sector bound approach, while the random communication delays from the sensor to the controller and from the controller to the plant are modelled by a linear function of the stochastic variable satisfying Bernoulli random binary distribution. It is aimed at designing an observer-based controller such that the dynamics of the closed-loop system is guaranteed to be exponentially stable in the mean square, and a prescribed H ∞ disturbance attenuation level is also achieved. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

Nonfragile Gain-Scheduled Control for Discrete-Time Stochastic Systems with Randomly Occurring Sensor Saturations

This paper is devoted to tackling the control problem for a class of discrete-time stochastic systems with randomly occurring sensor saturations. The considered sensor saturation phenomenon is assumed to occur in a random way based on the time-varying Bernoulli distribution with measurable probability in real time. The aim of the paper is to design a nonfragile gain-scheduled controller with probability-dependent gains which can be achieved by solving a convex optimization problem via semidefinite programming method. Subsequently, a new kind of probability-dependent Lyapunov functional is proposed in order to derive the controller with less conservatism. Finally, an illustrative example will demonstrate the effectiveness of our designed procedures.

H<sub>∞</sub> Dynamic Output Feedback Control for a Class of Discrete-Time Stochastic Systems with Sector Nonlinearities and Mixed Time-Delays

This paper deals with the dynamic output feedback control problem for a class of discrete-time stochastic systems involving sector nonlinearities and mixed time-delays. Based on the control theory and Lyapunov-Krasovskii functional method, an effective approach is proposed to design a dynamic output feedback controller such that the resultant closed-loop system is stochastically stable with a prescribed disturbance attention in the mean square sense and has a performance level. A numerical example demonstrates the effectiveness of the method.

Improved Delay-Dependent Robust Stability Criteria for Discrete-Time Stochastic Uncertain Networks with Time-Varying Delays

In this paper, the mean square asymptotical stability is investigated for a class of discrete-time stochastic systems with time-varying delays and norm-bounded uncertainties,a numerical example is presented to show the usefulness of the derived LMI-based stability condition.

A note on control of a class of discrete-time stochastic systems with distributed delays and nonlinear disturbances

This paper is concerned with the state feedback control problem for a class of discrete-time stochastic systems involving sector nonlinearities and mixed time-delays. The mixed time-delays comprise both discrete and distributed delays, and the sector nonlinearities appear in the system states and all delayed states. The distributed time-delays in the discrete-time domain are first defined and then a special matrix inequality is developed to handle the distributed time-delays within an algebraic framework. An effective linear matrix inequality (LMI) approach is proposed to design the state feedback controllers such that, for all admissible nonlinearities and time-delays, the overall closed-loop system is asymptotically stable in the mean square sense. Sufficient conditions are established for the nonlinear stochastic time-delay systems to be asymptotically stable in the mean square sense, and then the explicit expression of the desired controller gains is derived. A numerical example is provided to show the usefulness and effectiveness of the proposed design method.

Limiting average cost control problems in a class of discrete-time stochastic systems

We consider a class of $ {\Bbb R} ^d$-valued stochastic control systems, with possibly unbounded costs. The systems evolve according to a discrete-time equation $x_{t+1}=G_n(x_t,a_t)+\xi _t$ ($t=0,1,\dots $), for each fixed $n=0,1,\dots , $ where the $\x

Optimal nonlinear estimation for a class of discrete-time stochastic systems

Recursive estimation for nonlinear discrete-time stochastic systems with additive white Gaussian observation noise is investigated. It is proved that for certain classes of systems, described either by finite Volterra series expansions or by state-linear realizations under certain algebraic conditions, the optimal conditional mean estimator is recursive and of fixed finite dimension. An example is presented to illustrate the structure of the estimators.

A minimum principle for a class of discrete-time stochastic systems

A minimum principle is obtained for discrete-time stochastic systems described by the stochastic difference equation x_{k+1} = A_{k}x_{k} + \phi_{k}(u_{k})+w_{k} where \{w_{k}, k = 0, ... ,N - \} is la sequence of independent random vector variables. The control action u k is constrained to belong to a compact set U k , and the set \phi_{k}(U_{k}), k = 0,..., N - 1 is convex. The system is open-loop.

On the design of optimal stochastic terminal control systems

The problem of optimizing a class of discrete-time stochastic systems in such a way as to make a prescribed set of terminal conditions "most likely" is treated. The class of systems in question is described by a set of time-varying difference equations which are linear in the state and nonlinear in the control where the performance index is quadratic in the state but not necessarily in the control. Random disturbances are present in both the plant equations and the observation equations. "Hard" constraints on the set of admissible controls are also permitted. The equivalence of this problem to two "standard" deterministic optimization problems is demonstrated.