On the terminal region of model predictive control for non‐linear systems with input/state constraints

Abstract

This paper addresses the terminal region of model-based predictive control (MPC) for non-linear systems with control input and state constraints. Based on a stability condition of non-linear MPC, a method to determine the terminal weighting term in the performance index and the terminal stabilizing control law to enlarge the terminal region and thus the domain of attraction of the non-linear MPC is proposed. An LMI based optimization approach is developed to choose the terminal weighting item and fictitious terminal stabilizing control law so as to enlarge the terminal region of the non-linear MPC method. The proposed method is illustrated by a numerical example and compares favourably with existing results.

Enlarging the terminal region of quasi-infinite horizon NMPC based on T-S fuzzy model

“…A very strong penalty on the terminal states may have a bad influence on the achievement of the control performance which is specified by the finite horizon cost [1]. The trade off between a large terminal region and good achievement of the desired control performance can be made by limiting the norm of the matrix P [4]. Because of…”

“…For the case of constrained linear systems, [3] figure out terminal region by considering a saturated local control law. For nonlinear systems, using either local polytopic LDI representation [4] or local norm-bounded LDI representation [5], a terminal region is obtained by solving off-line an LMI optimization problem. In [6], a local LDI representation is used as well, and a polytopic terminal region and an associated terminal penalty are computed.…”

Robust adaptive constrained boundary control for a suspension cable system of a helicopter

“…According to the above stability analysis for the suspension cable system of a helicopter, the following conclusions can be drawn. (15) and (16), considering the auxiliary systems (27) and (28) and the control laws (29) and (30)…”

“…Input saturation has an effect on control performance, which has been investigated in the last few decades. [28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43] The Takagi-Sugeno fuzzy modeling approach was utilized to control the nonlinear systems with actuator saturation in the work of Cao and Lin. 37 The stabilization problem was addressed for a class of Hamiltonian systems with state time-delay and input saturation in the work of Sun.…”

Piecewise constant model predictive control for autonomous helicopters

“…This procedure can be further improved by adopting the method proposed in [24], where terminal region can be maximised using an optimisation algorithm to search the best terminal penalty P and terminal control.…”