Discrete Stochastic Control Systems Research Articles

Fusion of PDF compensation and gain-scheduled control for discrete stochastic systems with randomly occurring nonlinearities

A fusion control strategy, including probability density function (PDF) compensation and gain-scheduled control, is proposed for discrete-time stochastic systems with randomly occurring nonlinearities. Usually, it is difficult to drive the tracking error strictly to zero in a random environment. So the proposed method aims to stabilize the closed-loop system in the exponentially mean square sense and guarantee the distribution of output error as close to the expected PDF as possible. The parameters of the gain-scheduled controller are obtained by solving appropriate linear matrix inequalities, and the parameters of the PDF compensator are updated in real time according to the Kullback–Leibler divergence between the PDF of output error and the desired one. The proposed method has the characteristics of low conservativeness and easy to implement. The effectiveness of the proposed method is shown by two examples.

Maximum Principle of Discrete Stochastic Control System Driven by Both Fractional Noise and White Noise

In this paper, we investigate the necessary optimality conditions of the discrete stochastic optimal control problems driven by both fractional noise and white noise. Here, the admissible control region is not necessarily convex. The corresponding variational inequalities are obtained by applying the classical variation method and Malliavin calculus. We also apply the stochastic maximum principle to a linear-quadratic optimal control problem to illustrate the main result.

Bilateral Estimation of the Bellman Function in the Problems of Optimal Stochastic Control of Discrete Systems by the Probabilistic Performance Criterion

Consideration was given to the optimal control of discrete stochastic systems by the probabilistic quality criterion. The new characteristics of the Bellman equation for this class of problems were examined, and the two-sided estimate of the Bellman function was determined. The problem of optimal control of the security portfolio with one riskless and a given number of risk assets was considered by way of example. The class of strategies featuring asymptotic optimality was established using the two-sided estimate of the Bellman function.

Robust Sliding Mode Control for Discrete Stochastic Systems With Mixed Time Delays, Randomly Occurring Uncertainties, and Randomly Occurring Nonlinearities

This paper investigates the robust sliding mode control (SMC) problem for a class of uncertain nonlinear stochastic systems with mixed time delays. Both the sectorlike nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and randomly occurring nonlinearities obey certain mutually uncorrelated Bernoulli distributed white noise sequences. The mixed time delays consist of both the discrete and the distributed delays. The time-varying delays are allowed in state. By employing the idea of delay fractioning and constructing a new Lyapunov-Krasovskii functional, sufficient conditions are established to ensure the stability of the system dynamics in the specified sliding surface by solving a certain semidefinite programming problem. A full-state feedback SMC law is designed to guarantee the reaching condition. A simulation example is given to demonstrate the effectiveness of the proposed SMC scheme.

LQG optimal control of discrete stochastic systems under parametric and noise uncertainties

In this paper, the linear-quadratic-Gaussian (LQG) optimal control problem is considered and a robust minimax controller composed of the Kalman filter and the optimal regulator is synthesized to guarantee the asymptotic stability of the discrete time-delay systems under both parametric uncertainties and uncertain noise covariances. Designed procedures are finally elaborated with an illustrative example.

Robust H∞ control for uncertain discrete stochastic time-delay systems

This paper deals with the problems of robust stabilization and robust H ∞ control for discrete stochastic systems with time-varying delays and time-varying norm-bounded parameter uncertainties. For the robust stabilization problem, attention is focused on the design of a state feedback controller which ensures robust stochastic stability of the closed-loop system for all admissible uncertainties, while for the robust H ∞ control problem, a state feedback controller is designed such that, in addition to the requirement of the robust stochastic stability, a prescribed H ∞ performance level is also required to be satisfied. A linear matrix inequality (LMI) approach is developed to solve these problems, and delay-dependent conditions for the solvability are obtained. It is shown that the desired state feedback controller can be constructed by solving certain LMIs. An example is provided to demonstrate the effectiveness of the proposed approach.

A Linear Quadratic Control for Discrete Systems with Random Parameters and Multiplicative Noise and Its Application to Investment Portfolio Optimization

A quadratic control for discrete stochastic systems with random parameters and additive and multiplicative noises dependent on state and controls is studied. Equations for the optimal linear static and dynamic output controllers are derived. The controllers are robust to the type of the distribution of the vector of random parameters. The results are applied to dynamic investment portfolio optimization.

An identification algorithm for linear stochastic systems with time delays†

Linear discrete stochastic control systems containing unknown multiple time delays, plant parameters and noise variances are considered. An algorithm is established which uses the maximum-likelihood technique to identify the unknown parameters. An estimated likelihood function is evaluated based on the previous parameter estimates, which in turn generates a new descent direction vector to update the unknown parameters. The delays and plant parameters are identified in their respective parameter spaces. An example of a second-order stochastic system has been implemented by digital simulation to demonstrate the applicability of the algorithm.

A stochastic integral equation in Hilbert space with a discrete version and application to stochastic systems

A stochastic integral equation of the Volterra type in the form $$x\left( {t;\omega } \right) = h\left( {t;\omega } \right) + \int\limits_0^t k \left( {t,\tau ;\omega } \right)f\left( {\tau ,x\left( {\tau ;\omega } \right)} \right)d\tau , t \geqslant 0,$$ , is formulated in Hilbert space, whereω ∈ Ω, the supporting set of a complete probability measure space (Ω,A, P). A theorem concerning the existence of a random solution of the equation is proven. A discrete version of the above stochastic integral equation is given in the form $$x_n \left( \omega \right) = h_n \left( \omega \right) + \sum\limits_{j = 1}^n {c_{n,j} \left( \omega \right)f_j \left( {x_j \left( \omega \right)} \right), n = 1,2, \cdot \cdot \cdot ,} $$ , and a theorem concerning the existence of a unique random solution is presented. Application to a discrete stochastic control system is given.

Stability of a reactor with a discrete stochastic control system

Stability of a reactor with a discrete stochastic control system