A crash course in: Real-time optimal control

Distribuited systems, performance and uncertainty

November 16, 2018
Versione stampabile

Venue: Room “Aula Seminari”@DII, Via Sommarive, 9 Povo (TN)
Time: 10:00am - 12:00am
           02:00pm - 04:00pm

Model Predictive Control (MPC) has recently gained popularity due to the development of efficient algorithms, which has made it possible to solve optimal control problems at unprecedented rates. The first part of the course will review the main features of the algorithms for real-time optimal control. The rest of the course will present three promising research directions.
The development of faster and more reliable wireless communication has recently opened the possibility for previously unimaginable applications of distributed control and optimisation. With a clever formulation of the optimisation problem, it is possible to reduce the need for communication to a minimum while retaining the fast convergence of second-order methods. In this course, we will present recent developments in real-time nonconvex distributed optimisation with application to the coordination of autonomous vehicles.
One of the most attractive advantages of optimisation-based control is the possibility of explicitly optimising a prescribed performance criterion, which often relates to an economic gain. Schemes directly optimising performance have therefore been named economic MPC, though this class of problems includes all formulations which do not explicitly penalise the deviation from a given setpoint or trajectory (e.g. minimum time problems). The main challenge for such schemes is twofold: the algorithmic omplexity is increased and it is not trivial to prove some form of stability. We will (a) present the main challenge faced when attempting at proving stability, (b) formally prove stability under suitable assumptions and (c) conclude by proposing a practical approach for stability-enforcing approximate economic MPC.
Dealing with uncertainty is been the main purpose of closed-loop control and several methods have been developed in the MPC context in order to deal with uncertainty in order to enforce safety and some work has also been devoted to optimality. The main issue with most approaches is the assumption of knowing the structure and magnitude of the uncertainty. Reinforcement Learning (RL), on the other hand, has been developed in order to learn the optimal policy under very weak assumptions. Unfortunately, safety and stability aspects are usually not accounted for in RL. In this course we will present a first attempt at bridging the gap between (economic) NMPC and RL, by using the former as a function approximator in the latter.


  • numerics for real-time optimisation
  • distributed non-convex optimal control
  • economic MPC
  • MPC and reinforcement learning


Mario Zanon received the Master’s degree in Mechatronics from the University of Trento, and the Diplôme d’Ingénieur from the Ecole Centrale Paris, in 2010.
After research stays at the KU Leuven, University of Bayreuth, Chalmers University, and the University of Freiburg he received the Ph.D. degree in Electrical Engineering from the KU Leuven in November 2015. He held a Post-Doc researcher position at Chalmers University until the end of 2017 and is now Assistant Professor at the IMT School for Advanced Studies Lucca. His research interests include numerical methods for optimisation, economic MPC, reinforcement learning, and the optimal control and estimation of nonlinear dynamic systems, in particular for aerospace and automotive applications.