Modular‐based adaptive control of uncertain nonlinear time‐varying systems with piecewise jumping parameters

SUMMARY Nonlinear time‐varying systems exist widely in practice. Therefore, it is of great theoretical importance and practical value to investigate the problem of controlling such systems. However, the results available in developing adaptive control to address such a problem are still limited. Especially a majority of them are restricted to be slowly time‐varying linear systems. This paper presents a modular‐based adaptive control scheme for parametric strict feedback nonlinear time‐varying systems. The parameters considered include both continuous and piecewise time‐varying parameters, and they are not necessarily restricted to be slowly time‐varying or infrequent jumping. The technique of adaptive backstepping with nonlinear damping is employed in the control design module, while the parameter projection algorithm is performed on the parameter estimation module. It is proved that the uniform boundedness of all closed‐loop system signals can be guaranteed with the proposed control scheme. The performance of the tracking error in the mean square sense with respect to the parameter variation rate is also established. Furthermore, perfect asymptotically tracking can be achieved when the varying rates of unknown parameters are in the space.