Coordinated decentralized sliding mode MRAC with control cost optimization for a class of nonlinear systems

In this paper, we develop an approach for solving the problem of sliding mode decentralized adaptive state-feedback tracking with continuous control actions for a class of uncertain nonlinear dynamical systems. In addition to the traditional asymptotic zero error tracking specification in the sliding mode decentralized model reference adaptive control (MRAC) problem formulation, here an additional requirement is specified explicitly in the problem statement. The tracking objective is described by a set of admissible reference trajectories, called a performance tube. The input signal to the reference model, selected within specified bounds, is used as a design parameter. The best reference trajectory is found by solving an additional optimization problem whose criterion penalizes the variance of the control signal.