A dissipativity based framework for analyzing stability of predictive controllers

Stabilizing conditions for nonlinear predictive control typically rely on standard Lyapunov functions and thus require a monotonically decreasing cost function. These conditions cannot certify stability of predictive controllers in the presence of non-monotonic cost functions. In this paper we develop new dissipativity-based stabilizing conditions for nonlinear predictive control that allow for non-monotonic cost functions. Firstly, we establish that dissipation inequalities with a cyclically negative supply imply asymptotic stability. Secondly, we show that closed-loop trajectories generated by predictive control satisfy a fundamental dissipation inequality. This enables dissipativity-based stabilizing conditions that do not require a special terminal cost and apply to both model-based and data-driven predictive control algorithms. Copyright (C) 2021 The Authors.