Periodic Optimal Control, Dissipativity and MPC

Recent research has established the importance of (strict) dissipativity for proving stability of economic MPC in the case of an optimal steady state. In many cases, though, steady-state operation is not economically optimal and periodic operation of the system yields a better performance. In this technical note, we propose ways of extending the notion of (strict) dissipativity for periodic systems. We prove that optimal P-periodic operation and MPC stability directly follow, similarly to the steady-state case, which can be seen as a special case of the proposed framework. Finally, we illustrate the theoretical results with several simple examples

Periodic optimal control, dissipativity and MPC

Recent research has established the importance of dissipativity for proving stability of economic MPC in the case of a steady state. In many cases, though, steady state operation is not economically optimal and periodic operation of the system yields a better performance. In this paper, we propose three different ways of extending the notion of dissipativity for periodic systems and illustrate them with three examples

A generalized approach to Economic Model Predictive Control with terminal penalty functions

In this paper, we first introduce upper and a lower bounds of the best asymptotic average performance for nonlinear control systems based on the concepts of dissipativity and control storage functions. This allows to extend the formulation and analysis of Economic Model Predictive Control to more general optimal operation regimes, such as periodic solutions. A performance and stability analysis is carried out within this generalized framework. Finally two examples are proposed and discussed to show the merits of the proposed approach