Feedback linearization based controller design for control affine nonlinear MIMO systems using direct adaptive neural networks

Abstract

Among the various nonlinear control strategies that have developed over the last 30 or 40 years, feedback linearization has a prominent place because of its value to academic research as well as to practical applications. Feedback linearization algebraically transforms a nonlinear dynamic system into a linear one, on the basis of differential geometric analysis of the system. Despite the success of differential geometry in the design and analysis of nonlinear control systems, it is severely restricted by the need of the exact knowledge of all the system nonlinearities if they are to be cancelled. Given a situation in which an affine system has unknown nonlinearities, except for certain bounds, computational intelligence method must be used to estimate the nonlinearities. These estimates are then used by the controller to linearize the system. The need for intelligent control within a nonlinear system is predicted by characteristics such as environmental alterations, changes in performance criteria, unmodelled dynamic processes and disruptions and the lack of generalized controller design tools. Intelligent control systems make use of fuzzy logic and neural networks due to their learning capabilities and function approximation ability. In this work, a direct adaptive controller design technique based on Radial Basis Function Neural Networks (RBF NNs) is proposed to track the output for a class of control affine nonlinear systems. This concept possesses several advantages over indirect adaptive control techniques. While a direct adaptive control law has been derived along with weight update rules for SISO systems for both these cases, it has been extended to a MIMO system only for the first case. In the second case, no attempt has been made to derive a control law for MIMO systems as yet, leaving it an open problem for research. newline