LMI-based design of multichannel anisotropic suboptimal controllers with application to control of gyrostabilized platform

Abstract

This paper is devoted to attenuation of uncertain stochastic disturbances in linear discrete time invariant system where certain input/output channels are grouped together to satisfy certain closed-loop performance specifications. The grouping takes into account some technical features of a system and closeness (in a sense) of the signals' properties. It is assumed that different groups of channels are characterized by different statistical uncertainty levels measured in terms of the mean anisotropy functional. The disturbance attenuation capabilities of the different groups of channels are quantified by the anisotropic norm which is applied in the performance specifications. The designed anisotropic suboptimal controller is required to stabilize the closed-loop system and ensure some specified levels of disturbance attenuation for certain groups of channels. The general procedure of synthesis of a fixed-order controller results in solving a system of convex inequalities with repect to the determinants of the positive definite matrices and LMIs in reciprocal matrices; the optimization problem is not convex. Standard convexification procedures lead to the convex optimization problems in the full information case (state-feedback controller) and in the case of full-order controller synthesis. The developed anisotropy-based approach is applied to control of angular position of a gyrostabilized platform and compared with the ℋ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> /ℋ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> mixed control. The proposed multichannel setting of the anisotropy-based robust stochastic control design has never been considered before. It allows the anisotropic norm to be applied in the well-developed framework of the multiobjective control design together with other specifications that can be formulated in terms of LMIs and convex constraints.