Suboptimal model predictive control (feasibility implies stability)

Abstract

Abstract-Practical difficulties involved in implementing stabilizing model predictive control laws for nonlinear systems are well known. Stabilizing formulations of the method normally rely on the assumption that global and exact solutions of nonconvex, nonlinear optimization problems are possible in limited computational time. In this paper, we first establish conditions under which suboptimal model predictive control (MPC) controllers are stabilizing; the conditions are mild holding out the hope that many existing controllers remain stabilizing even if optimality is lost. Second, we present and analyze two suboptimal MPC schemes that are guaranteed to be stabilizing, provided an initial feasible solution is available and for which the computational requirements are more reasonable.Index Terms-Dual-mode control, nonconvex nonlinear optimization, nonlinear model predictive control, suboptimal control.

A model predictive controller for robots to follow a virtual leader

“…It has been shown that the suboptimal solution (obtained by several optimization iterations from a feasible solution) can also guarantee the MPC stability. 24,29 The longer the optimization time, the better the control performance. However, a long computation time is not achievable for a real-time control.…”

“…18,19 Recently, the researches in refs. [20][21][22][23][24] show that nonlinear controllers can be used to find the terminal state region as long as a stability condition is met. The works in refs.…”

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“…Problem P τ N (x) differs from a standard nominal MPC problem in two main aspects: the use of the tube based robust MPC problem setup in Mayne et al (2005) to provide recursive feasibility of the state and input constraints and a Lyapunov constraint enforcing input-to-state stability at all iterations following the ideas in Scokaert, Mayne, and Rawlings (1999).…”

Receding horizon optimal control for infinite dimensional systems

“…Receding horizon techniques have proved to be effective numerically both for optimal control problems governed by ordinary (e.g. [3,[11][12][13]15,16]) and for partial differential equations, e.g. in the form of the instantaneous control technique for problems in fluid mechanics [2,4,5,9].…”