Optimisation of transient and ultimate inescapable sets with polynomial boundaries for nonlinear systems

[EN] This paper addresses the problem of bounding the trajectories of nonlinear systems (transient and ultimate bounds) from initial conditions in given sets, when subject to possibly nonvanishing disturbances constrained by some finite-interval integral bounds, with a suitable controller. The so-called robustly inescapable sets are determined from such initial conditions and disturbance bounds. In order to get numerical results, the approach considers embedding the nonlinear dynamics in a convex combination of polynomials, and solving sum-of-squares (SOS) problems on them, optimising some inescapable-set size parameters. Determination of approximate (locally) optimal solutions usually requires an iterative evaluation of SOS problems, because of products of decision variables. (C) 2016 Elsevier Ltd. All rights reserved.
The research leading to these results has received funding from the European Union (FP7/2007-2013 no 604068) and from the Spanish Government (MINECO/FEDER DPI2015-70975-P, DPI2016-81002). The material in this paper was not presented at any conference. This paper was recommended for publication in revised form by Associate Editor Graziano Chesi under the direction of Editor Richard Middleton.