An Optimization Approach to Verifying and Synthesizing K-cooperative Systems. Issue 2 (2020)

• Record Type: Journal Article
• Authors: Kousoulidis, Dimitris; Forni, Fulvio
• Is Part Of: IFAC-PapersOnLine. Volume 53:Issue 2(2020)
• Page Start: 4635
• Page End: 4642
• Publication Date: 2020
• Subjects: Nonlinear control -- Differential positivity -- Linear programming -- Monotone systems -- Bistability -- Consensus; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2020.12.499
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: 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 K- cooperativity 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.