Design and Application of Suboptimal Mixed $H_{2}/H_{\infty}$ Controllers for Networked Control Systems

Abstract

This brief tackles the problem of designing suboptimal 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> controllers for linear networked control systems (NCS) subject to time-varying delays and packet dropouts. The formulation provides state feedback NCS controllers allowing to tradeoff performance and disturbance rejection. The control objective consists in designing an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> suboptimal control minimizing a quadratic performance index, with a disturbance rejection constraint (H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> constraint). To characterize the network, only the lower and upper bounds for the delay, as well as the maximum number of consecutive dropouts are required. The approach relies on the formulation of the problem in terms of the minimization of a single scalar parameter, that can be cast as a standard linear matrix inequality (LMI) problem, yielding a suboptimal cost-guaranteed solution. As a difference from previous works, the solution provided is independent of initial conditions. Stability and robustness properties of the proposed controller are theoretically demonstrated and tested on an experimental testbed consisting in the stabilization of a robot arm in the proximities of the unstable upright position. The application shows good performance and disturbance rejection capabilities even for stringent network conditions.