Adaptive control for a class of large scale non-linear systems

Abstract

The design of stabilizing controllers for multi-input multi-output (MIMO) non-linear plants with unknown non-linearities is a challenging problem. The inability to identify the non-linearities on-line or off-line accurately motivates the design of stabilizing controllers based on approximations or on approximate estimates of the plant non-linearities. However, the design of a centralized controller for large scale non-linear systems is often complex due to the high dimensionality and difficulty to implement in real time. In this paper a decentralized-like non-linear adaptive control algorithm is designed and analysed for a class of large scale non-linear systems with unknown non-linearities. The controller guarantees closed loop semi-global stability and convergence of the tracking error to a small residual set whose size can be specified a priori provided the neglected in the control design non-linear interconnections are small relative to the modelled non-linear parts. A procedure for choosing the various design parameters to guarantee that the tracking error bound will converge to within the specified a priori bound is presented. Even though the proposed controller is not purely decentralized it does reduce computations and makes the control design easier than a corresponding centralized approach.