Abstract
This chapter extends the ideas presented in Chap. 8 to develop discrete-time models for nonlinear deterministic systems. In particular, we develop sampled models based on up-sampling and on truncated Taylor series expansion of the normal form. The approximation errors are precisely characterized.
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Further Reading
A general introduction to the accuracy of numerical integration schemes is given in
Butcher JC (2008) Numerical methods for ordinary differential equations, 2nd edn. Wiley, New York
Normal forms for nonlinear systems are described in detail in
Isidori A (1995) Nonlinear control systems, 3rd edn. Springer, Berlin
Discrete-time normal forms are discussed in
Califano C, Monaco S, Normand-Cyrot D (1998) On the discrete-time normal form. IEEE Trans Autom Control 43(11):1654–1658
State-space models for nonlinear systems, in both continuous time and discrete time, are discussed in
Belikov J, Kotta U, Tonso M (2012) State-space realization of nonlinear control systems: unification and extension via pseudo-linear algebra. Kybernetika 48(6):1100–1113
Approximate models for nonlinear systems based on variable truncated Taylor series were first described in
Yuz JI, Goodwin GC (2005) On sampled-data models for nonlinear systems. IEEE Trans Autom Control 50(10):1477–1489
The definitions of vector truncation errors and an associated accuracy study of truncated Taylor series models were first presented in
Carrasco DS, Goodwin GC, Yuz JI (2013) Vector measures of accuracy for sampled data models of nonlinear systems. IEEE Trans Autom Control 58(1):224–230
Sampled-data models for Hamiltonian systems have been proposed in
Laila D, Astolfi A (2006) Construction of discrete-time models for port-controlled Hamiltonian systems with applications. Syst Control Lett 55:673–680
Monaco S, Normand-Cyrot D, Tiefensee F (2011) Sampled-data stabilization; a PBC approach. IEEE Trans Autom Control 56(4):907–912
The problem of sampled-data control for nonlinear systems has been extensively investigated. See, for example
Laila D, Nesic D, Astolfi A (2006) Sampled-data control of nonlinear systems. In: Advanced topics in control systems theory II, pp 91–137
Nesic D, Teel AR (2004) A framework for stabilization of nonlinear sampled-data systems based on their approximate discrete-time models. IEEE Trans Autom Control 49(7):1103–1122
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Yuz, J.I., Goodwin, G.C. (2014). Approximate Models for Nonlinear Deterministic Systems. In: Sampled-Data Models for Linear and Nonlinear Systems. Communications and Control Engineering. Springer, London. https://doi.org/10.1007/978-1-4471-5562-1_9
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DOI: https://doi.org/10.1007/978-1-4471-5562-1_9
Publisher Name: Springer, London
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