Control Of Continuous-time Stochastic Systems Research Articles

Stability of Stochastic Delayed Differential Equations with Exogenous Disturbances via Event-Triggered Scheme

This paper discusses the input-to-state practically stabilization (ISpS) issue for stochastic delayed differential equations (SDDEs) with exogenous disturbances. To reduce the transmission frequency of the feedback control signal, the proposed SDDSs are stabilized by an event-triggered strategy. The concept of the input-to-state practically stabilization is used to describe the dynamic performance of control target in the event-triggered schemes and exogenous disturbances. Making use of stochastic control theory, we demonstrate that the considered SDDEs is ISpS via an event-triggered feedback controller represented by linear matrix inequalities (LMIs). Moreover, lower bound of interaction time of control task is obtained to avoid the Zeno behavior. Compared with the large number of results for discrete-time stochastic systems, event-triggered control of continuous-time stochastic systems only yields a few results.

Sparse optimal stochastic control

In this paper, we investigate a sparse optimal control of continuous-time stochastic systems. We adopt the dynamic programming approach and analyze the optimal control via the value function. Due to the non-smoothness of the L0 cost functional, in general, the value function is not differentiable in the domain. Then, we characterize the value function as a viscosity solution to the associated Hamilton–Jacobi–Bellman (HJB) equation. Based on the result, we derive a necessary and sufficient condition for the L0 optimality, which immediately gives the optimal feedback map. Especially for control-affine systems, we consider the relationship with L1 optimal control problem and show an equivalence theorem.

Stabilization of Stochastic Nonlinear Delay Systems With Exogenous Disturbances and the Event-Triggered Feedback Control

This note is devoted to study the stabilization problem of stochastic nonlinear delay systems with exogenous disturbances and the event-triggered feedback control. By introducing the notation of input-to-state practical stability and an event-triggered strategy, we establish the input-to-state practically exponential mean-square stability of the suggested system. Moreover, we investigate the stabilization result by designing the feedback gain matrix and the event-triggered feedback controller, which is expressed in terms of linear matrix inequalities. Also, the lower bounds of interexecution times by the proposed event-triggered control method are obtained. Finally, an example is given to show the effectiveness of the proposed method. Compared with a large number of results for discrete-time stochastic systems, only a few results have appeared on the event-triggered control for continuous-time stochastic systems. In particular, there have been no published papers on the event-triggered control for continuous-time stochastic delay systems. This note is a first try to fill the gap on the topic.

Algorithms to Solve StochasticH2/H∞Control with State-Dependent Noise

This paper is concerned with the algorithms which solveH2/H∞control problems of stochastic systems with state-dependent noise. Firstly, the algorithms for the finite and infinite horizonH2/H∞control of discrete-time stochastic systems are reviewed and studied. Secondly, two algorithms are proposed for the finite and infinite horizonH2/H∞control of continuous-time stochastic systems, respectively. Finally, several numerical examples are presented to show the effectiveness of the algorithms.

On the stability of receding horizon control for continuous-time stochastic systems

We study the stability of receding horizon control for continuous-time non-linear stochastic differential equations. We illustrate the results with a simulation example in which we employ receding horizon control to design an investment strategy to repay a debt.

Time Discretisation and Rate of Convergence for the Optimal Control of Continuous-Time Stochastic Systems with Delay

We study a semi-discretisation scheme for stochastic optimal control problems whose dynamics are given by controlled stochastic delay (or functional) differential equations with bounded memory. Performance is measured in terms of expected costs. By discretising time in two steps, we construct a sequence of approximating finite-dimensional Markovian optimal control problems in discrete time. The corresponding value functions converge to the value function of the original problem, and we derive an upper bound on the discretisation error or, equivalently, a worst-case estimate for the rate of convergence.

Multirate LQG control of continuous-time stochastic systems

The LQG problem for stochastic continuous-time systems subject to multirate sampling of both input and output variables is considered. By restating the problem as a discrete-time periodic LQG problem, a sufficient condition for the existence of an optimal stabilizing regulator is given in terms of the structural properties of the original system and the cost function. This improves on previous contributions, where optimal control schemes were proposed without addressing existence and/or stability issues. The possibility of incorporating an integral action within the optimal LQG regulator is also briefly discussed.

A characterization of ε-optimal controls for stochastic systems with partial observations via the unnormalized conditional density

Abstract The paper considers optimal control for continuous-time stochastic systems with noisy measurements of the state. It is known that the optimum coat for this problem may not be achieved within the class of strict-sense controls. However, allowing for tolerances of size e, a characterization is given for e-optimal controls in terms of a semigroup formulation involving the unnormalized conditional density of the distribution of the state, given the observations.

A computational algorithm for the optimal control of continuous-time stochastic systems

An algorithm for computing optimal controls for a class of continuous-time stochastic systems is presented. For a linear example, it is shown that the generated control is precisely the optimal control. Numerical results for a nonlinear example suggest that the generated control is at least locally optimal.