Time-discretization of nonlinear control systems via Taylor methods
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abstract
A new discretization method for the calculation of a sampled-data representation of a nonlinear continuous-time system is proposed. It is based upon the well-known Taylor method and the zero-order hold (ZOH) assumption. The mathematical structure of the new discretization scheme is analyzed and characterized as being particularly useful in establishing concrete connections between numerical properties and system-theoretic properties. In particular, the effect of the Taylor discretization procedure on key properties of nonlinear systems, such as equilibrium properties and asymptotic stability, is examined. Within a control context, numerical aspects of Taylor discretization are also discussed, and 'hybrid' discretization schemes, that result from a combination of the 'scaling and squaring' technique with the Taylor method, are also proposed, especially under conditions of very low sampling rates. Practical issues associated with the selection of the method's parameters to meet CPU time and accuracy requirements, are examined as well. Finally, the performance of the proposed discretization procedure is evaluated in a chemical reactor example, that exhibits nonlinear behavior and is subject to various sampling rates.
