ADAPTIVE VARIABLE-STRUCTURE CONTROL OF FAST TIME-VARYING PLANTS

In this paper, a combination of adaptive control and variable structur e control methodology is proposed to solve the general fast time-varyi ng plants with totally unstructured parameters. We show that the contr ol scheme will work only under the assumptions of known order, relativ e degree, sign of high frequency gain and minimum-phase property and w ithout any assumptions on the time-varying rate or time-varying struct ure of the system's parameters. In contrast to the conventional approa ches, where the variable structure design is applied mainly to the ada ptation of some traditional parameters Theta by using the knowledge of bounds on control parameters, a new adaptation scheme for a small set of control parameters incorporating the variable structure concept is given. Owing to this new scheme, we forsake the standard requirement of the upper bounds on some parameters, which is frequently adopted in the field of robust linear MRAC, using variable structure design. Fur thermore, without any persistent excitation, the tracking error will c onverge to zero in finite time for relative degree one plants and expo nentially to a small residual set (whose size depends on a design para meter) for plants with any higher relative degree.