A Variational approach to _ ¥ control with transients
by
W. Lu, G.J. Balas and E.B. Lee
in
IEEE Transactions on Automatic Control, vol. 44, no. 10, October, pp. 1875-1879, 1999.
Category: Journal Article
Keywords: H1 control, optimal control, Riccati equations, solution
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Abstract:
This paper presents a variational approach to H1 control with transients in the state feedback case. The approach here provides a precise description with equality, instead of inequality, in the necessary and sufficient conditions for the existence of a linear controller. Furthermore, the solution existence and uniqueness are proved in terms of certain properties of the indefinite Riccati equations derived in this paper. The linear time-variant (LTV) plant on finite horizon is considered first, and then the results are extended to the linear time-invariant (LTIV) plant on the infinite horizon. By this approach, it can be directly concluded that only suboptimal H1 state feedback control can be achieved in an input–output point of view and that the performance measure ( 1=2 used in this paper) is a strict upper bound.
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