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An adaptive approach to cost reduction in nonlinear uncertain systems using Lyapunov design

A time-varying/dynamic compensation strategy for nonlinear uncertain systems is proposed, which adaptively selects one controller from a parametrized family of Lyapunov-based stabilizing controllers. The purpose of the adaptation is to choose the controller that reduces the value of a given cost functional, but stability is guaranteed regardless of whether or not parameter errors prevent cost reduction. This method is potentially applicable to the control of slowly varying nonlinear systems, where it is possible to numerically solve optimal control problems online. The potential of this method is demonstrated in simulation.