Two-step MPC for systems with input non-linearity and norm-bounded disturbance

• Published in: IET control theory & applications Vol. 13; no. 2; pp. 183 - 190
• Main Authors: Wang, Jun, Ding, Baocang, Wang, Yong
• Format: Journal Article
• Language: English
• Published: The Institution of Engineering and Technology 29.01.2019
• Subjects: closed loop systems; closed‐loop system stability; control nonlinearities; desaturation; Hammerstein systems; input nonlinearity; intermediate control law; iterative methods; linear algebra; linear part; linear systems; nonlinear algebraic equation; nonlinear control systems; norm‐bounded disturbance; predictive control; quadratic boundedness technique; quadratic convergence; quadratic cost function minimisation; Research Article; Riccati equations; Riccati iterative equation; stability; sufficient conditions; two‐step model predictive control; two‐step MPC; unconstrained MPC problem; quadratic convergence; iterative methods; unconstrained MPC problem; intermediate control law; Hammerstein systems; sufficient conditions; control nonlinearities; linear part; linear algebra; stability; closed-loop system stability; two-step model predictive control; nonlinear algebraic equation; linear systems; Riccati iterative equation; closed loop systems; desaturation; quadratic cost function minimisation; input nonlinearity; Riccati equations; quadratic boundedness technique; nonlinear control systems; two-step MPC; norm-bounded disturbance; predictive control
• ISSN: 1751-8644; 1751-8652; 1751-8652
• DOI: 10.1049/iet-cta.2018.5091

In this study, a novel two-step model predictive control (MPC) for Hammerstein systems subject to norm-bounded disturbance is addressed. In the first step, the intermediate control law for the linear part of the system is posed as the solution to the unconstrained MPC problem that minimises a quadratic cost function over a given finite time, for which the solution is determined by a novel Riccati iterative equation. In the second step, the actual control move is obtained by solving non-linear algebraic equation group and desaturation. The quadratic boundedness technique is used to specify the stability for closed-loop system with norm-bounded disturbance, and the sufficient conditions for quadratic convergent of the system state are presented. Simulation results demonstrate the effectiveness of the proposed approach to this class of systems.