Model predictive control of nonlinear systems: Computational burden and stability

Abstract

• This is a journal article. It was published in the journal, IEE proceedings: control theory and applications and is subject to Institution of Engineering The stability condition presented in this paper enables the "fictitious" terminal control to be nonlinear, rather than only linear, and thus the stability region is greatly enlarged. Furthermore it is pointed out that nominal stability is still guaranteed even though the global, or even the local, minimisation of the objective cost is not achieved within the prescribed computational time.Keywords: Nonlinear systems, generalised predictive control, computational delay, optimisation, stability, constrained control online optimisation problem:subject to system dynamics,andfor τ ∈ [0, δ] where δ denotes the sampling time interval, R > 0, Q > 0 or Q ≥ 0 and non-zero x is detectable in the performance index and P > 0Fact 1: The constraint (3) is convex if the matrix P satisfies (4). Submitted to IEE Part D: Control Theory and Applications 3The constraint (3) can be written as

Experimental tests of autonomous ground vehicles with preview

“…The related problem has been investigated in ref. [15], in this paper we follow the relationship represented in Fig. 8.…”

Maximisation of feasibility/stability regions of model predictive control for constrained linear systems

“…subject to (1) and (2). The problem (4) is solved on-line using an optimisation solver, for example, quadratic programming (QP), and a control sequence…”

“…Lemma 1 [1,2]: Consider the MPC scheme described in Section 2 for the constrained system (1) and (2) under the performance index (3). Suppose that there exists u(k) satisfying (2) such that…”

“…Theorem: Consider a discrete-time linear system (1) subject to the input constraints (2). Suppose that there exist S > 0,S, W > 0 and W 1 such that…”

“…To guarantee stability of MPC, the most widely used method is to add a terminal weighting term in the performance index and (or) impose constraints on terminal state. Recently these results are extended from linear systems to the nonlinear case; for example, see [1], [2].…”