Title :
Optimal H2/l1 control via duality theory
Author :
Voulgaris, Petros G.
Author_Institution :
Coordinated Sci. Lab., Illinois Univ., Urbana, IL, USA
fDate :
11/1/1995 12:00:00 AM
Abstract :
In this paper we consider the problem of minimizing the H2 -norm of the closed-loop map while maintaining its l1-norm at a prescribed level. The problem is analyzed in the case of discrete-time, SISO closed-loop maps. Utilizing duality theory, it is shown that the optimal solution is unique, and, in the nontrivial case where the l1 constraint is active, the optimal solution has a finite impulse response. A finite step procedure is given for the construction of the exact solution. This procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods. Finally, continuity properties of the optimal solution with respect to changes in the l1-constraint are established
Keywords :
H∞ control; closed loop systems; discrete time systems; duality (mathematics); quadratic programming; H2-norm minimization; closed-loop map; continuity properties; discrete-time SISO closed-loop maps; duality theory; finite impulse response; finite step procedure; l1-constraint changes; l1-norm; optimal H2/l1 control; quadratic programming problems; Constraint theory; Fourier transforms; Functional analysis; Lagrangian functions; Optimal control;
Journal_Title :
Automatic Control, IEEE Transactions on
