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A computational method for a class of jump linear quadratic systems

Published online by Cambridge University Press:  17 February 2009

K. Kaji
Affiliation:
Dept of Computational and Applied Math., Univ. of the Witwatersrand, Johannesberg, South Africa.
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Abstract

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A class of linear systems subject to sudden jumps in parameter values is considered. To solve this class of stochastic control problem, we try to seek the best feedback control law depending only on the measurable output. Based on this idea, we convert the original problem into an approximate constrained deterministic optimization problem, which can be easily solved by any existing nonlinear programming technique. An example is solved to illustrate the efficiency of the method.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Athans, M., “The matrix maximum principle”, J. Inform. Control 11 (1967) 592606.CrossRefGoogle Scholar
[2]Florentin, J. J., “Optimal control of continuous – time, Markov, stochastic systems”, J. Electron. Control 10 (1961) 473488.CrossRefGoogle Scholar
[3]Krasovskii, N. N. and Lidskii, E. A., “Analytic design of controllers in systems with random attributes”, J. Automat. Remote Control 22 (1961) 10211025, 1141–1146, 1289–1294.Google Scholar
[4]Levine, W. S. and Athans, M., “On the determination of the optimal constant output feedback gains for linear multivariable systems”, IEEE Trans. Automat. Control AC-15 (1970) 4448.CrossRefGoogle Scholar
[5]Mariton, M., “On the influence of noise on jump linear systems”, IEEE Trans. Automat. Control AC-32 (1987) 10941097.CrossRefGoogle Scholar
[6]Mariton, M. and Bertrand, P., “Output feedback for a class of linear system with stochastic jump parameters”, IEEE Trans. Automat. Control AC-30 (1985) 898900.CrossRefGoogle Scholar
[7]McLane, P. J., “Optimal stochastic control of linear systems with state and control dependent disturbances”, IEEE Trans. Automat. ControlAC-16 (1971) 793798.CrossRefGoogle Scholar
[8]Sworder, D. D., “Feedback control of a class of linear systems with jump parameters”, IEEE Trans. Automat. ControlAC-14 (1969) 914.CrossRefGoogle Scholar
[9]Wonham, W. M., “On a matrix Riccati equation of stochastic control”, SIAM J. Control Optim. 6 (1968) 681697.CrossRefGoogle Scholar
[10]Wonham, W. M., “Random differential equations in control theory”, in Prob. methods in applied maths. 2 (ed. Bharucha-Reid, A. T.), (Academic, New York, 1970), 131212.Google Scholar