Indirect Adaptive Robust Control of Uncertain Systems With Unknown Asymmetric Input Deadband Using a Smooth Inverse

In this paper, we present an indirect adaptive robust controller (IARC) for output tracking of a class of uncertain nonlinear systems with unknown input asymmetric deadband in presence of uncertain nonlinearities and parametric uncertainties. Most of the parameter adaptation algorithms, such as, gradient-type and least squares-type require that the unknown parameters of a system appear in affine with known regressor functions globally. However, deadband nonlinearity can not be represented in those global linear parametric form. Therefore, the existing parameter estimation algorithms for deadband focus on some approximate linear parametric model. Hence, even in absence of any other uncertain nonlinearities and disturbances, these algorithms can never achieve asymptotic tracking. Departing from those approximate deadband estimation, we design an indirect parameter estimation algorithm with online condition monitoring. This parameter estimation algorithm in conjunction with a well-designed robust controller and a deadband inverse function can be used to obtain asymptotic tracking without restoring to discontinuous control law. With this strong result in our repertoire, we proceed to design a smooth deadband inverse (SDI) function to avoid certain problems during implementation, e.g, control input chattering and significant appearance of high-frequency dynamics. The effect of such an approximation on the L₂-norm of output tracking error is analytically determined. We also show that while operating away from the deadband, the proposed controller even with an SDI can achieve asymptotic tracking. In presence of disturbances and other uncertain nonlinearities, the proposed IARC controller attains guaranteed transient performance and final tracking accuracy.