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Jump linear quadratic Gaussian control in continuous time

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2 Author(s)
Yuandong Ji ; Dept. of Syst. Eng., Case Western Reserve Univ., Cleveland, OH, USA ; Chizeck, H.J.

The optimal quadratic control of continuous-time linear systems that possess randomly jumping parameters which can be described by finite-state Markov processes is addressed. The systems are also subject to Gaussian input and measurement noise. The optimal solution for the jump linear-quadratic-Gaussian (JLQC) problem is given. This solution is based on a separation theorem. The optimal state estimator is sample-path dependent. If the plant parameters are constant in each value of the underlying jumping process, then the controller portion of the compensator converges to a time-invariant control law. However, the filter portion of the optimal infinite time horizon JLQC compensator is not time invariant. Thus, a suboptimal filter which does converge to a steady-state solution (under certain conditions) is derived, and a time-invariant compensator is obtained

Published in:

Automatic Control, IEEE Transactions on  (Volume:37 ,  Issue: 12 )