American Institute of Mathematical Sciences

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October  2000, 6(4): 803-808. doi: 10.3934/dcds.2000.6.803

A gradient flow approach for computing jump linear quadratic optimal feedback gains

K.H. Wong 1, , C. Myburgh 1, and  L. Omari 1,

1. 

Department of Computational and Applied Mathematics, University of The Witwatersrand, Johannesburg, South Africa, South Africa, South Africa

Received  October 1998 Revised  May 2000 Published  August 2000

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 find the best feedback control law depending both on the measurable output as well as the mode of the system. A gradient flow based algorithm is derived for this problem. It is shown that an optimal solution can be successfully computed by finding the limiting solution of an ordinary differential equation which is given in terms of the gradient flow associated with the cost function. Several important properties are obtained. A numerical example is solved.
Keywords: Lyapunov differential equations, feedback control., jump linear quadratic systems, Gradient flow.
Mathematics Subject Classification: 49N35, 49N10, 93E2.
Citation: K.H. Wong, C. Myburgh, L. Omari. A gradient flow approach for computing jump linear quadratic optimal feedback gains. Discrete & Continuous Dynamical Systems, 2000, 6 (4) : 803-808. doi: 10.3934/dcds.2000.6.803
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