Pareto suboptimal solutions in control and filtering problems under multiple deterministic and stochastic disturbances

Abstract

A new multi-objective H ∞ /γο problem is considered as a framework for control and filtering problems under multiple deterministic and stochastic disturbances in linear discrete-time systems with N disturbance inputs and a single objective output. Associated to each channel is defined one of the two disturbance attenuation criteria, the H ∞ norm for deterministic disturbances or the γ 0 norm for stationary Gaussian white zero-mean signals with bounded variances and unknown covariances. A necessary condition for Pareto optimality in the disturbance attenuation problem with multiple H ∞ and γ 0 criteria is derived. It is shown that as the Pareto suboptimal solutions can be chosen the optimal solutions with respect to the parameterized H ∞ /γ 0 norm and that the relative losses on each criterion of these solutions compared to the Pareto optimal solutions do not exceed 1-√N/N. The H ∞ /γ 0 norm is computed as a convex semidefinite program using linear matrix inequalities and H ∞ /γ 0 optimal controllers or filters are tradeoffs between optimal solutions to the H ∞ and γ 0 problems for the corresponding channels.