Journal of Computational Dynamics (JCD)

Numerical event-based ISS controller design via a dynamic game approach

Pages: 65 - 81, Volume 2, Issue 1, June 2015      doi:10.3934/jcd.2015.2.65

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Lars Grüne - University of Bayreuth, Chair of Applied Mathematics, Universitätsstraße 30, 95440 Bayreuth, Germany (email)
Manuela Sigurani - University of Bayreuth, Chair of Applied Mathematics, Universitãtsstraße 30, 95440 Bayreuth, Germany (email)

Abstract: We present an event-based numerical design method for an input-to-state practically stabilizing (ISpS) state feedback controller for perturbed nonlinear discrete time systems. The controllers are designed to be constant on quantization regions which are not assumed to be small. A transition of the state from one quantization region to another triggers an event upon which the control value changes.
    The controller construction relies on the conversion of the ISpS design problem into a robust controller design problem which is solved by a set oriented discretization technique followed by the solution of a dynamic game on a hypergraph. We present and analyze this approach with a particular focus on keeping track of the quantitative dependence of the resulting gain and the size of the exceptional region for practical stability from the design parameters of our event-based controller.

Keywords:  Event-based control, input-to-state-stability, dynamic game, set oriented numerics, nonlinear systems.
Mathematics Subject Classification:  93B51, 93D09, 65P40.

Received: April 2014;      Revised: January 2015;      Available Online: August 2015.