Abstract We consider a class of discrete-time stochastic control systems, with Borel state and action spaces, and possibly unbounded costs. The processes evolve according to the equation xt+1 = F (xt, at, ξt), t = 0, 1, . . . , where the ξt are i.i.d. random vectors whose common distribution is unknown. Assuming observability of {ξt}, we use the empirical estimator of its distribution to constr...

While the current robust nonlinear control toolbox includes a number of methods for systems aane in a deterministic bounded disturbances, the problem when the disturbance is unbounded stochastic noise has hardly been considered. We present a control design which achieves global asymptotic (Lyapunov) stability in probability for a class of strict-feedback nonlinear continuous-time systems driven...

The optimal control of nonlinear stochastic systems is considered in this paper. The central role played by the Fokker-Planck-Kolmogorov equation in the stochastic control problem is shown under the assumption of asymptotic stability. A computational approach for the problem is devised based on policy iteration/ successive approximations, and a finite dimensional approximation of the control pa...

This article is a survey of the early development of selected areas in nonlinear continuous-time stochastic control. Key developments in optimal control and the dynamic programming principle, existence of optimal controls under complete and partial observations, nonlinear filtering, stochastic stability, the stochastic maximum principle and ergodic control are discussed. Issues concerning wide ...

We introduce a technique for quantifying and then exploiting uncertainty in nonlinear stochastic control systems. The approach is suboptimal though robust and relies upon the approximation of the forward and inverse plant models by neural networks, which also estimate the intrinsic uncertainty. Sampling from the resulting Gaussian distributions of the inversion based neurocontroller allows us t...

Abstract. In this paper, the existence and uniqueness of mild solution is initially obtained by use of measure of noncompactness and simple growth conditions. Then the conditions for approximate controllability are investigated for the distributed second-order neutral stochastic differential system with respect to the approximate controllability of the corresponding linear system in a Hilbert s...

This paper addresses the robust stability for a class of linear discrete-time stochastic systems with convex polytopic uncertainties. The system to be considered is subject to both interval time-varying delays and convex polytopic type uncertainties. Based on the augmented parameter-dependent Lyapunov-Krasovskii functional, new delay-dependent conditions for the robust stability are established...

Optimal trajectories of deterministic systems satisfy Pontryagin’s maximum principle and can be computed efficiently. Related results for stochastic systems exist but they lack the simplicity and computational efficiency of the deterministic case. Here we show that a certain class of both discrete-time and continuous-time nonlinear stochastic control problems obey a classic maximum principle, i...

We consider a stochastic control problem, where the control domain is convex and the system is governed by a nonlinear backward stochastic differential equation. With a L1 terminal data, we derive necessary optimality conditions in the form of stochastic maximum principle. AMS Subject Classification. 93Exx