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.

[1]  David Angeli,et al.  On Average Performance and Stability of Economic Model Predictive Control , 2012, IEEE Transactions on Automatic Control.

[2]  L. Grüne,et al.  Nonlinear Model Predictive Control : Theory and Algorithms. 2nd Edition , 2011 .

[3]  David Angeli,et al.  On convergence of averagely constrained economic MPC and necessity of dissipativity for optimal steady-state operation , 2013, 2013 American Control Conference.

[4]  David Angeli,et al.  Receding horizon cost optimization for overly constrained nonlinear plants , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[5]  Karl Worthmann,et al.  An Exponential Turnpike Theorem for Dissipative Discrete Time Optimal Control Problems , 2014, SIAM J. Control. Optim..

[6]  David Angeli,et al.  Economic optimization using model predictive control with a terminal cost , 2011, Annu. Rev. Control..

[7]  David Angeli,et al.  On Necessity and Robustness of Dissipativity in Economic Model Predictive Control , 2015, IEEE Transactions on Automatic Control.

[8]  Matthias A. Muller,et al.  Economic model predictive control without terminal constraints: Optimal periodic operation , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[9]  J. Willems.  Dissipative dynamical systems part I: General theory , 1972 .

[10]  Lars Grüne,et al.  Asymptotic stability and transient optimality of economic MPC without terminal conditions , 2014 .

[11]  Lars Grüne,et al.  Economic receding horizon control without terminal constraints , 2013, Autom..

[12]  Lars Grne,et al.  Nonlinear Model Predictive Control: Theory and Algorithms , 2011 .

[13]  S. Bittanti,et al.  Periodic Systems: Filtering and Control , 2008 .

[14]  Mario Zanon,et al.  A Lyapunov function for periodic economic optimizing Model Predictive Control , 2013, 52nd IEEE Conference on Decision and Control.

[15]  Moritz Diehl,et al.  A Lyapunov Function for Economic Optimizing Model Predictive Control , 2011, IEEE Transactions on Automatic Control.

[16]  J. Willems.  Dissipative dynamical systems Part II: Linear systems with quadratic supply rates , 1972 .