Decentralized simple adaptive control of nonlinear systems

Recently, the passivity results for linear time-invariant systems were successfully extended to nonlinear and nonstationary systems, thus guaranteeing stability of adaptive control of nonlinear square systems. Based on this theoretical development, this paper presents the development of a new class of direct adaptive controllers, which employ a new decentralized adaptation law mechanism that is developed from the simple adaptive control technique. The resulting direct adaptive control methodology is referred to as decentralized simple adaptive control. A simplification of this new control algorithm, referred to as decentralized modified simple adaptive control, is also presented. In addition, it is shown that both control methodologies can be modified to avoid divergence in practical situations, where the trajectory tracking errors cannot reach zero. Using Lyapunov direct method and Lasalle’s invariance principle for nonautonomous systems, the formal proof of stability is established. As well, a numerical simulation study for a trajectory tracking problem by a rigid-joint manipulator is presented to illustrate the new adaptive control approaches. Copyright © 2013 John Wiley & Sons, Ltd.