On the design of direct adaptive controllers

Direct adaptive control without the familiar reference models is considered. A framework for design using quadratic cost functions is presented, and corresponding error equations are derived using ideas from linear-quadratic optimal control. Convexity of a suitably defined cost function is studied, indicating that parameter estimation can be accomplished using standard optimization techniques. Conditions for existence of a global minimum are presented, and shown to depend crucially on the time variation of the actual feedback control used in the loop. A good starting point is to take a feeback gain random in intervals, and feed data from these intervals into a standard minimization algorithm.