Brief Minimax controller design for a class of uncertain linear systems

Authors:
Paul Milliken;Clive Marsh;Bruce Van Brunt
Affiliations:
Institute of Technology and Engineering, College of Sciences, Massey University, Private Bag 11222, Palmerston North, New Zealand;Institute of Technology and Engineering, College of Sciences, Massey University, Private Bag 11222, Palmerston North, New Zealand;Institute of Fundamental Sciences, College of Sciencse, Massey University, Palmerston North, New Zealand
Venue:
Automatica (Journal of IFAC)
Year:
1999

Citing 2
Cited 3

Nonconvex optimization problem: the infinite-horizon linear-quadratic control problem with quadratic constraints

Systems & Control Letters
Linear robust control

Linear robust control

Semi-Markov Control Models with Partially Known Holding Times Distribution: Discounted and Average Criteria

Acta Applicandae Mathematicae: an international survey journal on applying mathematics and mathematical applications
Brief Min-max predictive control techniques for a linear state-space system with a bounded set of input matrices

Automatica (Journal of IFAC)
Brief Minimax control for discrete-time time-varying stochastic systems

Automatica (Journal of IFAC)

Quantified Score

Hi-index	22.15

Visualization

Abstract

This paper considers the design of minimax controllers for a class of linear systems. The system is perturbed by a known initial condition on the state and by a disturbance process constrainted by an L"2 norm bound. Structured undertainty is represented by perturbation feedback through L"2-induced norm bounded operators. The performance is measured by an integral quadratic cost function. The resultant controllers minimise the worst-case cost for all admissible distrubances and for all admissible systems. The design involves the optimal solution of a parametric algebraic Riccati equation. A new proof of minimax optimality is given using standard methods for linear systems. The multivariable optimisation problem is shown to be convex and the set of feasible parameter values is shown to be compact. Thus, the design procedure is computationally tractable.