Linear quadratic performance with worst case disturbance rejection
by
W. Lu, G.J. Balas and E.B. Lee
in
International Journal of Control, vol. 73, no. 16, Nov., pp. 1516-1524, 2000.
Category: Journal Article
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Abstract:
The method of the calculus of variations and the maximum principle are preposed for the design of `LQR’ controllers with the worst case disturbance rejection for a linear time-varying (LTV) plant on ® nite horizon. The disturbance is bounded by either the windowed L2-norm or the windowed L1-norm, or both. In the case of the windowed L2- normed disturbance, uncertain but norm bounded initial condition is also considered. Certain necessary and su cient condtions for the existence of a linear controller are derived with the proof of the solution existence and uniqueness. The results are extended to the steady state ones for the linear time-invariant (LTIV) plant on the in® nite horizon. A comparison to H1 control with transients is also presented. In the case of the windowed L1-normed or both normed disturbances, the solution for the worst case disturbance is of switching (or bang± bang) type.
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