## Brief Research Summary

#### Economic MPC

Economic model predictive control (EMPC) is a new and promising advanced control technique. Model predictive control consists in solving optimal control problems repeatedly every time a new state measurement or estimate is available, therefore introducing feedback. Traditional schemes rely on positive-definite cost functions (typically quadratic). Economic MPC instead, is based on minimizing more generic cost functions, which directly account for the control tasks, e.g., minimize time or energy, maximize profit, etc. Unfortunately, checking closed-loop stability of economic MPC can be extremely difficult in practice.

#### Automatic Tracking Cost Design

In my recent research, I have proven that, whenever economic MPC is locally stabilizing, tracking MPC schemes with quadratic positive-definite cost exist, which yield a first-order approximation of the economic MPC feedback control law. Future work will aim at including stochastic and robust considerations in the proposed approach.

#### Publications

**Journal:**

- S. Gros and M. Zanon.
**Economic MPC of Markov Decision Processes: Dissipativity in Undiscounted Infinite-Horizon Optimal Control.**Automatica, 2022 - M. Zanon and S. Gros.
**A New Dissipativity Condition for Asymptotic Stability of Discounted Economic MPC.**Automatica, 2022 - M. Zanon.
**A Gauss-Newton-Like Hessian Approximation for Economic NMPC.**IEEE Transactions on Automatic Control, 2021 - M. Zanon and S. Gros.
**Safe Reinforcement Learning Using Robust MPC.**IEEE Transactions on Automatic Control, 2021 - S. Gros and M. Zanon.
**Data-driven Economic NMPC using Reinforcement Learning.**IEEE Transactions on Automatic Control, 2020 - J. De Schutter, M. Zanon and M. Diehl.
**TuneMPC – A Tool for Economic Tuning of Tracking (N)MPC Problems.**IEEE Control System Letters, 2020 - J. Vasilj, S. Gros, D. Jakus and M. Zanon.
**Day-ahead scheduling and real-time Economic MPC of CHP unit in Micro-grid with Smart buildings.**IEEE Transactions on Smart Grid, 2019 - M. Zanon and T. Faulwasser.
**Economic MPC without terminal constraints: Gradient-correcting end penalties enforce stability.**Journal of Process Control, 2018 - M. Zanon, L. Grüne and M. Diehl.
**Periodic optimal control, dissipativity and MPC.**IEEE Transactions on Automatic Control, 2017 - M. Zanon, S. Gros and M. Diehl.
**A Tracking MPC Formulation that is Locally Equivalent to Economic MPC.**Journal of Process Control, 2016 - M. Zanon, S. Gros and M. Diehl.
**Indefinite Linear MPC and Approximated Economic MPC for Nonlinear Systems.**Journal of Process Control, 2014

**Conference:**

- S. Shin, T. Faulwasser, M. Zanon, V. M. Zavala.
**A Parallel Decomposition Scheme for Solving Long-Horizon Optimal Control Problems.**Proceedings of the Conference on Decision and Control (CDC), 2019 - M. Zanon, S. Gros and A. Bemporad.
**Practical Reinforcement Learning of Stabilizing Economic MPC.**Proceedings of the European Control Conference (ECC), 2019 - T. Faulwasser and M. Zanon.
**Asymptotic Stability of Economic NMPC: The Importance of Adjoints.**Proceedings of the IFAC Conference on Nonlinear Model Predictive Control (NMPC), 2018 - R. Hult, M. Zanon, S. Gros and P. Falcone.
**Energy-Optimal Coordination of Autonomous Vehicles at Intersections.**Proceedings of the European Control Conference (ECC), 2018 - M. Zanon, S. Gros, and M. Diehl.
**A Periodic Tracking MPC that is Locally Equivalent to Periodic Economic MPC.**Proceedings of the World Congress of the International Federation of Automatic Control, 2017 - M. Zanon, S. Gros and M. Diehl.
**A Lyapunov Function for Periodic Economic Optimizing Model Predictive Control.**Proceedings of the Conference on Decision and Control (CDC), 2013