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Quantitative local \(L_2\)-gain and reachability analysis for nonlinear systems. (English) Zbl 1286.93032

Summary: This paper develops theoretical and numerical tools for quantitative local analysis of nonlinear systems. Specifically, sufficient conditions are provided for bounds on the reachable set and L2 gain of the nonlinear system subject to norm-bounded disturbance inputs. The main theoretical results are extensions of classical dissipation inequalities but enforced only on local regions of the state and input space. Computational algorithms are derived from these local results by restricting to polynomial systems, using convex relaxations, for example the S-procedure, and applying sum-of-squares optimizations. Several pedagogical and realistic examples are provided to illustrate the proposed approach.

MSC:

93B03 Attainable sets, reachability
93C10 Nonlinear systems in control theory
93C15 Control/observation systems governed by ordinary differential equations
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