Optimization-based drift prevention for learning control of underdetermined linear and weakly nonlinear time-varying systems

In this paper an optimization-based method of drift prevention is presented for learning control of underdetermined linear and weakly nonlinear time-varying dynamic systems. By defining a fictitious cost function and the associated model-based sub-optimality conditions, a new set of equations results, whose solution is unique, thus preventing large drifts from the initial input. Moreover, in the limiting case where the modeling error approaches zero, the input that the proposed method converges to is the unique feasible (zero error) input that minimizes the fictitious cost function, in the linear case, and locally minimizes it in the (weakly) nonlinear case. Otherwise, under mild restrictions on the modeling error, the method converges to a feasible sub-optimal input