Abstract
This paper presents a composite control approach to the problem of steering the state of a singularly perturbed system from a given initial state to a given final state, while minimizing a cost functional. The problem is treated for a class of nonlinear systems whose fast dynamics are weakly nonlinear in the fast variables and control inputs. The composite control comprises three components: a reduced control, a feedback boundary-layer stabilizing control and an open-loop right boundary-layer control. It is shown that application of the composite control results in a final state that is O(ϵ) close to the desired state, and a value of the cost that is O(ϵ) close to the optimal cost of the reduced problem.
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