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.