Adaptive Control via Non-Convex Optimization

Suboptimal model predictive control (feasibility implies stability)

“…Let fx kjk ; x k+1jk ; 1 1 1 ; x k+Njk g where x kjk = x k denote the corresponding state sequence. The current control action u k is chosen to be the first vector in the sequence k , i.e., u k = v kjk (3) for all k. If the control u is a continuous function of the state x, Lyapunov stability theory establishes convenient conditions for asymptotic stability. In suboptimal control, the control employed is not unique and may also vary discontinuously with the state.…”

“…The theory behind nonlinear MPC is consequently often inapplicable, although in some applications it may be possible to employ global optimization. This has been done in the context of specific control applications [3], but not yet in MPC.…”

Adaptive H/sub ∞/ control with application to systems with structural flexibility

“…First a priori knowledge of the damping is specified. Second, it can guarantee that the nominal model belongs to the admissible set [13]. This set has been chosen so that the resulting synthesis model gives a feasible problem.…”

“…This set can be characterized in terms of a set of bilinear constraints and is therefore not convex. The algorithm for nonconvex optimization described in [13], which is based on branch and bound, can be applied to solve this problem. Our experiments, however, show that we obtain wellconditioned models and a feasible problem when the input signals are excited, and there was thus no need to apply nonconvex optimization for the problem described below.…”

“…A number of techniques have been proposed to overcome the problem. The analysis technique we develop in our paper applies to the nonconvex optimization method developed in [13]. Application of this estimation technique therefore gives global stability and robustness of the adaptive system.…”