Stochastic receding horizon control of nonlinear stochastic systems with probabilistic state constraints

TL;DR

This paper presents a receding horizon control framework for nonlinear stochastic systems with probabilistic constraints, enabling real-time implementation and ensuring system stability through reference path planning and stochastic control.

Contribution

It introduces a novel control design that decomposes the problem into reference path planning and stochastic control, with solutions suitable for real-time application.

Findings

Closed-form solutions for stochastic control in some cases.

Pre-computed numerical solutions for general cases.

Simulation results confirm theoretical stability and performance.

Abstract

The paper describes a receding horizon control design framework for continuous-time stochastic nonlinear systems subject to probabilistic state constraints. The intention is to derive solutions that are implementable in real-time on currently available mobile processors. The approach consists of decomposing the problem into designing receding horizon reference paths based on the drift component of the system dynamics, and then implementing a stochastic optimal controller to allow the system to stay close and follow the reference path. In some cases, the stochastic optimal controller can be obtained in closed form; in more general cases, pre-computed numerical solutions can be implemented in real-time without the need for on-line computation. The convergence of the closed loop system is established assuming no constraints on control inputs, and simulation results are provided to corroborate the theoretical predictions.