Variable direct adaptive control for vector systems with unknown time-varying parameters

Variable Direct Adaptive Control Law (VDACL) is extended to vector systems with unknown time varying parameters and bounded disturbances. The analysis of VDACL can guarantee the regulating error approaches to some bound as disturbances exist and goes to zero in the absence of disturbance. Besides, its analysis guarantees the controller gain will not drift to infinity in the presence of disturbance. In comparison with Switching-Σ Adaptive Control Law (SSACL), VDACL can obtain better transient response, less overshoot, and less free parameters. Furthermore, the controller gains of VDACL reach constants faster than that of SSACL. In the simulations, the bounded disturbances and unknown time varying parameters are considered, to compare the performance of these two methods