Eigenvalue assignment enabled control law for multivariable nonlinear systems with mismatched uncertainties

Abstract

This paper presents an adaptive filtering output feedback control architecture for multivariable nonlinear systems with mismatched uncertainties enabled by an eigenvalue assignment method. A piecewise constant adaptive law updates the adaptive parameters which represent the uncertainty estimates by solving the error dynamics between the output predictor and the real system with the neglection of unknowns. By employing a computationally efficient eigenvalue assignment method, the multivariable nonlinear system is transformed into Frobenius canonical form. A novel filtering control law which allows the desired system to be nonminimum-phase and does not require dynamic inversion of the desired system is designed to compensate the nonlinear uncertainties and track a given trajectory, following a performance determined by the eigenvalues assigned to the controller. The uniform performance bounds are derived for the system state and control input as compared to the corresponding signals of a bounded virtual reference system, which defines the best performance that can be achieved by the closed-loop system. Numerical examples are provided to illustrate the effectiveness of the eigenvalue assignment enabled control law, comparisons between the proposed controller and funnel controller are carried out.