Title :
A variational approach to ℋ∞ control with transients
Author :
Lu, Wayne W. ; Balas, Gary J. ; Lee, E.B.
Author_Institution :
Center for Control Sci. & Dynamical Syst., Minnesota Univ., Minneapolis, MN, USA
fDate :
10/1/1999 12:00:00 AM
Abstract :
This paper presents a variational approach to ℋ∞ 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 (LTI) plant on the infinite horizon. By this approach, it can be directly concluded that only suboptimal ℋ∞ state feedback control can be achieved in an input-output point of view and that the performance measure γ (μ1/2 used in this paper) is a strict upper bound
Keywords :
H∞ control; Riccati equations; state feedback; suboptimal control; time-varying systems; transients; variational techniques; ℋ∞ control; I/O control; LTI plant; LTV plant; finite horizon plant; indefinite Riccati equations; infinite horizon; input-output control; linear controller; linear time-invariant plant; linear time-variant plant; necessary and sufficient conditions; state feedback; suboptimal ℋ∞ state feedback control; transients; variational approach; Differential equations; Integral equations; Riccati equations;
Journal_Title :
Automatic Control, IEEE Transactions on
