Improved Robust Predictive Control for Lur’e Systems Using Set-based Learning

Abstract

Abstract Predictive control of uncertain nonlinear systems is challenging. Existing approaches often require to find a global minima of a nonconvex optimization problem, and often are conservative, as the worst case solution is considered. This paper presents a robust model predictive control scheme for Lur’e systems subject to constraints, which improves via learning over time and allows efficient implementation using Linear Matrix Inequalities. The approach utilizes Lipschitz continuity conditions for the unknown sector bounded nonlinearity. Based on reconstructions of the unknown function from past experiments and measurements, the bound on the uncertainty is improved - learned - in an set-based way. The system is controlled by a continuous time linear feedback law, where the feedback matrix used is updated in a sampled data fashion solving an infinite horizon robust control problem that guarantees constraint satisfaction and robust stability. To improve the performance, constraints based on the learned data are added to the LMI formulation, which allows to guarantee stability and satisfaction of input and state constraints. Due to convexity of the resulting LMI formulation its computational demand is low, allowing to implement the method on systems with limited computational capabilities. The effectiveness of the approach is illustrated by an example of a flexible link robotic arm.