Conference Paper

Picard Discretization of Nonlinear Systems: Symbolic or Numeric Implementation?

DOI: 10.1007/978-3-540-75867-9_16 Conference: Computer Aided Systems Theory - EUROCAST 2007, 11th International Conference on Computer Aided Systems Theory, Las Palmas de Gran Canaria, Spain, February 12-16, 2007, Revised Selected Papers
Source: DBLP

ABSTRACT In this paper we report the numeric implementation of previously proposed symbolic non-standard discretization methods for
nonlinear dynamical control systems. We discuss the advantages and disadvantages of both symbolic and numeric implementations,
and illustrate them through their applications to case studies.

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    ABSTRACT: In this work we report the validity, through implementation on a nonlinear dynamical control system: the simple pendulum, of the non-standard discretization methods, named: Euler, Euler-Picard and Euler-Taylor-Picard discretization methods. Those methods are based on Euler polygons, Picard iteration and Taylor series expansions, and were developed in previously works to digitize nonlinear dynamics. This work represents, the first step implementing discrete-time nonlinear control law using the non-standard discretization methods. The nonlinear control laws are designed using extended and exact linearization, for the states feedback control laws technique.
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