Robust H∞ model predictive control for constrained Lipschitz non-linear systems

• Published in: Journal of process control Vol. 104; pp. 101 - 111
• Main Authors: Shokrollahi, Ali, Shamaghdari, Saeed
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2021
• Subjects: [formula omitted] norm; DC/AC converter; Laboratory tank; Lipschitz non-linear system; Robust model predictive control; Laboratory tank; Lipschitz non-linear system; H∞ norm; Robust model predictive control; DC/AC converter
• ISSN: 0959-1524; 1873-2771
• DOI: 10.1016/j.jprocont.2021.06.007

This paper is concerned with the robust H∞ model predictive control problem for a class of non-linear systems subject to state and input constraints and with norm bounded disturbances. It is well known that the disturbance degrades the control performance remarkably and can cause system instability. As well as, design the H∞ model predictive control based on the non-linear model is much more challenging, because the control problem changes to a non-convex non-linear problem. The main contribution is the introduction of the novel robust controller to stabilize the perturbed Lipschitz non-linear systems. The objective is to minimize the L2 gain between the disturbance input and the controlled output. The non-convex control problem is formulated as a linear matrix inequality optimization problem. The designed controller guarantees the closed-loop asymptotic stability with a prescribed H∞ disturbance attenuation level. In order to reduce conservatism, a sum of squares optimization problem is proposed to obtain the optimal value of Lipschitz coefficient. The proposed algorithm is applied to two non-linear systems, a laboratory tank and a DC/AC converter to evaluate its applicability and effectiveness. •A new robust H∞ MPC for non-linear systems subject to disturbance is introduced.•The nonconvex RMPC problem is described as a convex LMI based optimization problem.•The asymptotic stability of the proposed scheme is analyzed.•The value of Lipschitz coefficient is determined by an SOS optimization problem.•The efficacy is demonstrated through application to nonlinear systems.