Colloquium Systems, Control and Optimization - Prof. Arjan van der Schaft, Emiritus University of Groningen

Title: Suboptimal control by primal-dual gradient dynamics

Abstract:

Recently there has been considerable interest in rendering model predictive control (MPC) computationally less intensive by resorting to suboptimal versions. In particular the use of standard primal-dual gradient algorithms (in discrete time) has been advocated for this purpose. In this talk we will start with a review of continuous time primal-dual gradient algorithms for static constrained convex optimization, including their port-Hamiltonian formulation. Then we will show how this can be extended to optimal control problems with linear dynamics and convex cost functions. The resulting dynamics is shown to be a port-Hamiltonian system of partial differential equations, involving ordinary physical time as well 'algorithmic time' corresponding to the continuous time primal-dual gradient dynamics. Exploiting the port-Hamiltonian structure convergence to the optimal control solution provided by the Pontryagin Minimum principle is indicated. It is argued that suboptimal control strategies could be derived starting from this partial differential equation formulation. Finally it will be discussed how the approach can be also used for interconnection to other port-Hamiltonian systems, either of physical or of optimization nature (distributed optimal control), and their closed-loop stability analysis.