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An optimization approach to verifying and synthesizing K-cooperative systems

Kousoulidis, D and Forni, F (2020) An optimization approach to verifying and synthesizing K-cooperative systems. IFAC-PapersOnLine, 53. pp. 4635-4642.

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Differential positivity and K-cooperativity, a special case of differential positivity, extend differential approaches to control to nonlinear systems with multiple equilibria, such as switches or multi-agent consensus. To apply this theory, we reframe conditions for strict Kcooperativity as an optimization problem. Geometrically, the conditions correspond to finding a cone that a set of linear operators leave invariant. Even though solving the optimization problem is hard, we combine the optimization perspective with the geometric intuition to construct a heuristic cone-finding algorithm centered around Linear Programming (LP). The algorithm we obtain is unique in that it modifies existing rays of a candidate cone instead of adding new ones. This enables us to also take a first step in tackling the synthesis problem for K-cooperative systems. We demonstrate our approach on some examples, including one in which we repurpose our algorithm to obtain a novel alternative tool for computing polyhedral Lyapunov functions of bounded complexity.

Item Type: Article
Uncontrolled Keywords: math.OC math.OC cs.SY eess.SY
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 22 Nov 2019 20:33
Last Modified: 05 Aug 2021 05:07
DOI: 10.1016/j.ifacol.2020.12.499