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Tracking control of linear switched systems

Published online by Cambridge University Press:  17 February 2009

R. Li ,
Z.G. Feng ,
K.L. Teo  and
G.R. Duan
R. Li
Affiliation:
Center for Control Theory and Guidance Technology Harbin Institute of [email protected]
Z.G. Feng
Affiliation:
College of Mathematics and Computer Science Chongqing Normal UniversityChongqing, P.R.China
K.L. Teo
Affiliation:
Department of Mathematics & Statistics Curtin University of TechnologyPerth, WA 6845, [email protected].
G.R. Duan
Affiliation:
Center for Control Theory and Guidance Technology Harbin Institute of [email protected]
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Abstract

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This paper deals with the optimal tracking problem for switched systems, where the control input, the switching times and the switching index are all design variables. We propose a three-stage method for solving this problem. First, we fix the switching times and switching index sequence, which leads to a linear tracking problem, except different subsystems are defined in their respective time intervals. The optimal control and the corresponding cost function obtained depend on the switching signal. This gives rise to an optimal parameter selection problem for which the switching instants and the switching index are to be chosen optimally. In the second stage, the switching index is fixed. A reverse time transformation followed by a time scaling transform are introduced to convert this subproblem into an equivalent standard optimal parameter selection problem. The gradient formula of the cost function is derived. Then the discrete filled function is used in the third stage to search for the optimal switching index. On this basis, a computational method, which combines a gradient-based method, a local search algorithm and a filled function method, is developed for solving this problem. A numerical exampleis solved, showing the effectiveness of the proposed approach.

Keywords

optimal tracking controlswitched systemsa time scaling transformationlinear quadratic control theorydiscrete filled function.
Type
Articles
Information
The ANZIAM Journal , Volume 49 , Issue 2 , October 2007 , pp. 187 - 203
Copyright
Copyright © Australian Mathematical Society 2007

References

[1] Anderson, B.D. and Moore, J. B., Optimal control: Linear quadratic methods(Prentice Hall, Englewood Cliffs, NJ, 1990).Google Scholar
[2] Bengea, S. and DeCarlo, R.. “Optimal control of switching systems”, Automatica 41 (2005) 11–27.Google Scholar
[3] Devasia, S., Paden, B. and Rossi, C., “Exact-output tracking theory for systems with parameter jumps”, Int J Control 67(1997) 11–131.CrossRefGoogle Scholar
[4] Feng, Z. G., Teo, K. L. and Rehbock, V., “A discrete filled function method for the optimal control of switched systems in discrete time”, Submitted.Google Scholar
[5] Ge, R.P., “A filled function method for finding a global minimizer of a function of several variables”, Math Program 46 (1990) 191–204.Google Scholar
[6] Hedlund, S. and Rantzer, A., “Convex dynamic programming for hybrid systems”, IEEE Trans Automat Contr 47 (2002) 1536–1540.CrossRefGoogle Scholar
[7] Isidori, A., Nonlinear control systems,2nd ed. (Springer-Verlag, Berlin, 1989).CrossRefGoogle Scholar
[8] Jennings, L.S., Fisher, M.E., Teo, K.L. and Goh, C.J., MISER 3.3-Optimal control software: Theory and user manual, 2004.Google Scholar
[9] Lee, H.W.J., Teo, K.L., Rehbock, V. and Jennings, L.S., “Control parametrization enhancing technique for time optimal control problems”, Dyn Syst Appl 6 (1997) 243–261.Google Scholar
[10] Lewis, F.L., Optimal control,2nd ed. (John Wiley, New York, 1995).Google Scholar
[11] Ng, C.K., Zhang, L.S., Li, D. and Tian, W.W., “Discrete filled function method for discrete global optimization”, Comput Optim Appl 31 (2005) 87–115.CrossRefGoogle Scholar
[12] Piccoli, B., “Necessary conditions for hybrid optimization”, in Proc 38th IEEE CDC,(1999), 410–415.Google Scholar
[13] Riedinger, P., lung, C. and Kratz, F., “An optimal control approach for hybrid systems”, European J Contr 49 (2003) 449–458.CrossRefGoogle Scholar
[14] Sun, Z. and Ge, S.S., Switched linear systems-control and design(Springer, Berlin, 2004).Google Scholar
[15] Sussman, H., “A maximum principle for hybrid optimal control problems”, in Proc 38th IEEE CDC Phoenix USA,(1999), 425–430.Google Scholar
[16] Teo, K.L., Goh, C.J. and Wong, K.H., A unified computational approach to optimal control problems(Longman Scientific and Technical, United Kingdom, 1991).Google Scholar
[17] Wu, C.Z. and Teo, K.L., “Global impulsive optimal control computation”, J lnd Manag Optim 2 (2006) 435–450.Google Scholar
[18] Xu, X. and Antsaklis, P., “Optimal control of switched systems based on parameterization of the switching instants”, IEEE Trans Automat Contr 49 (2004) 2–16.CrossRefGoogle Scholar
[19] Yin, Y. and Hosoe, S., “Tracking control of discrete and continuous hybrid systems: modeling and servoing problem of dextrous hand manipulation”, in Proc 2004 IEEE Int Conf Control Applications, 2–4 Sept. 2004,(2004), 860–865.Google Scholar