Dissipativity properties in constrained optimal control

A computational approach

authored by: Julian Berberich, Johannes Köhler, Frank Allgöwer, Matthias A. Müller
Abstract: In this paper, we consider discrete-time nonlinear optimal control problems with possibly non-convex cost subject to constraints on states and inputs. For these problems, we present a computational approach for the verification of strict dissipativity properties, which have recently been employed to study optimal system operation, turnpike phenomena, and closed-loop properties of economic model predictive control schemes. Based on a non-strict dissipation inequality, we provide necessary and sufficient conditions for strict dissipativity by explicitly computing the set w.r.t. which the system is strictly dissipative as well as the corresponding storage function. We focus on strict dissipativity w.r.t. periodic orbits and steady-states, being the most relevant cases of strict dissipativity, although our approach can be directly extended to strict dissipativity w.r.t. more general sets. For polynomial optimal control problems, the presented approach leads to a polynomial optimization problem, which is solved via sum-of-squares programming. The optimal periodic orbit can then be constructed, without a priori knowledge of its period length, as the set of points for which a suitable non-strict dissipation inequality holds with equality. In addition, we consider the important special case of indefinite linear quadratic optimal control problems subject to quadratic constraints, for which an optimal periodic orbit resulting from our construction is always located on the boundary of the constraint set.
Organisation(s): Institute of Automatic Control
External Organisation(s): University of Stuttgart
Type: Article
Journal: Automatica
Volume: 114
ISSN: 0005-1098
Publication date: 04.2020
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Electrical and Electronic Engineering, Control and Systems Engineering
Sustainable Development Goals: SDG 10 - Reduced Inequalities
Electronic version(s): https://doi.org/10.1016/j.automatica.2020.108840 (Access: Closed)