Bounded invariant verification for time-delayed nonlinear networked dynamical systems |
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| Institution: | 1. Dept. of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al Khodh 123, Oman;2. Dept. of Pure Mathematics, University of Waterloo, Waterloo, ON, N2L 3G1, Canada;1. School of Information Engineering, Dalian University, Dalian 116622, China;2. Department of Mathematics, Swinburne University of Technology, Hawthorn VIC 3122, Australia;3. School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China;1. College of Information Science and Engineering, Northeastern University, Shenyang, 110819, PR China;2. State Key Laboratory of Synthetical Automation of Process Industries, Northeastern University, Shenyang, 110819, PR China;1. Centre for Research in Automatic Control of Nancy (CRAN), University of Lorraine, France;2. Systems & Control Engineering, Indian Institute of Technology Bombay, Powai, Mumbai - 400076, India;1. Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, United States of America;2. Physics Department, Brandeis University, Waltham, MA 02454, United States of America |
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| Abstract: | We present a technique for bounded invariant verification of nonlinear networked dynamical systems with delayed interconnections. The underlying problem in precise bounded-time verification lies with computing bounds on the sensitivity of trajectories (or solutions) to changes in initial states and inputs of the system. For large networks, computing this sensitivity with precision guarantees is challenging. We introduce the notion of input-to-state (IS) discrepancy of each module or subsystem in a larger nonlinear networked dynamical system. The IS discrepancy bounds the distance between two solutions or trajectories of a module in terms of their initial states and their inputs. Given the IS discrepancy functions of the modules, we show that it is possible to effectively construct a reduced (low dimensional) time-delayed dynamical system, such that the trajectory of this reduced model precisely bounds the distance between the trajectories of the complete network with changed initial states. Using the above results we develop a sound and relatively complete algorithm for bounded invariant verification of networked dynamical systems consisting of nonlinear modules interacting through possibly delayed signals. Finally, we introduce a local version of IS discrepancy and show that it is possible to compute them using only the Lipschitz constant and the Jacobian of the dynamic function of the modules. |
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| Keywords: | Compositional verification Delayed dynamical systems Simulation-based verification Input-to-state stability |
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