A distributed NMPC scheme without stabilizing terminal constraints
Abstract:
We consider a distributed NMPC problem in which the individual subsystems are coupled via state constraints. A simple example for this setting are mobile robots which have individual goals but need to avoid collisions when moving in space. In order to avoid violation of the constraints, the subsystems communicate their individual predictions to the other subsystems once in each sampling period. For this setting, Richards and How [CDC 2004, Int. J. Control 2007] have proposed a distributed MPC formulation with stabilizing terminal constraints which is shown to be stable and feasible if the solutions at initial time are feasible.In this talk we show how the scheme can be extended to MPC without stabilizing terminal constraints or costs. We show that under a suitable controllability condition stability and feasibility can be ensured even for rather short prediction horizons. In particular, this allows for resolving conflicts between the subsystems at runtime, i.e., no feasibility assumption at initial time is needed. This feature is illustrated by numerical simulations.
The main drawback of the scheme is that the optimization in the individual subsystems has to be performed sequentially. We will discuss some first ideas on how this requirement can be relaxed and hope that further ideas can be developed in collaboration with other researchers at LCCC.
Biography:
Lars Grüne is Professor and Head of the Chair of Applied Mathematics at the University of Bayreuth, Germany. He received his Diploma and Ph.D. in Mathematics in 1994 and 1996, respectively, from the University of Augsburg. From 1997 until 2002 he was scientific assistant and lecturer at the J.W. Goethe University in Frankfurt/M. He held several visiting positions, including a guest professorship at the University Paris IX - Dauphine, France, and visits at the Universities of Melbourne, Australia, Padova, Italy, and La Sapienza in Rome, Italy.
Prof. Grüne is Editor in Chief of the Journal Mathematics of Control, Signals and Systems (MCSS) and Associate Editor of the Journal of Applied Mathematics and Mechanics (ZAMM). He is a member of the steering committee of the International Symposium on Mathematical Theory of Networks and Systems (MTNS) and served as Associate Editor for several other conferences, including the IFAC NOLCOS Symposium and the IEEE Conference on Decision and Control.
His research interests lie in the area of mathematical systems and control theory, in particular on numerical and optimization based methods for nonlinear systems.