Receding horizon control of nonlinear systems

Abstract

The receding horizon control strategy provides a relatively simple method for determining feedback control for linear or non-linear systems ; the method is especially useful for the control of slow non-linear systems, such as chemical batch processes, where it is possible to solve, sequentially, open-loop, fured-horizon, optimal control problems on-line. The method has been shown to yield a stable closed-loop system when applied to timeinvariant or time-varying linear systems. In this paper we show that the method also yields a stable closed-loop system when applied to non-linear systems. There exist many methods, including classical frequency-domain techniques, for designing stabilizing control laws for time-invariant linear systems. In contrast, there exist relatively few methods for time-varying linear systems and fewer still for non-linear systems. The major difficulty in the design of (feedback) control laws for non-linear systems arises from the necessity to explore the whole state space. Determination of an optimal open-loop control, for a given initial state is, on the other hand, relatively simple, and this fact makes receding horizon control feasible in many situations. In receding horizon control the (current) control at state x and time t is obtained by determining on-line (the open-loop) optimal control ii over the interval [t, t + T] and setting the current control equal to ii(t). Repeating this calculation continuously, yields a feedback control (since G(t) clearly depends on the current state x). The optimal control problem, P(x,t), is usually posed as minimizing a quadratic function (over the interval [t, t + TI) subject to the terminal constraint x(t + T) = 0 and solved on-line. Receding horizon control of linear systems is fully discussed by Kwon and Pearson [l] and Kwon, Bruckstein and Kailath [2]. In this paper we consider the application of receding horizon control to the time-invariant non-linear system denoted by