Norm-bounded Structured Uncertainty Research Articles

Multi-objective robust generalised H 2 control

A novel multi-objective robust control problem is studied for systems with norm-bounded structured uncertainty and robust generalised norms as criteria. Necessary conditions for Pareto optimality are formulated from which it follows that Pareto optimal solutions are to be among optimal solutions for scalar multi-objective costs in the form of Germeyer convolution. The upper bounds of the multi-objective costs are used to compute Pareto suboptimal controllers in terms of linear matrix inequalities, while the lower bounds to estimate a ‘difference’ between Pareto suboptimal and unavailable Pareto optimal controllers. Two-criteria robust control problem for a mathematical model of the rotor rotating in active magnetic bearings is considered as an application of this theory.

Absolute Stabilization and Minimax Optimal Control of Uncertain Systems with Stochastic Uncertainty

Abstract This paper is concerned with existence and optimality properties of so called guaranteed cost controllers for an uncertain system subject to structured uncertainty. The uncertainty in the system is assumed to have a stochastic character and satisfy certain stochastic integral constraints. Such constraints emerge from some new classes of uncertainty, such as “soft” norm-bounded structured uncertainty, additive “colored noise” uncertainty etc. It is shown that a minimax optimal guaranteed cost dynamical state feedback controller for a stochastic system can be synthesized as a static state feedback controller absolutely stabilizing this system. For each initial state of the system, this controller can be found by parametric optimization of solutions of a parameter-dependent generalized matrix Riccati equation arising in stochastic H theory.