Feedback Solution and Receding Horizon Control Synthesis for a Class of Quantum Control Problems
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Control of quantum systems described by the linear Schrödinger equation are considered. Control inputs enter through coupling operators and results in a bilinear control system. Feedback control laws are developed for the orbit tracking and the performance of the feedback control laws is demonstrated by the stable and accurate numerical integrations of the closed-loop system. The receding horizon control synthesis is applied to improve the performance of the feedback law. The second order accurate numerical integrations via time-splitting and the monotone convergent iterative scheme are combined to solve the optimality system, i.e., the two-pint boundary value problem on a given time horizon. The feasibility of the proposed synthesis is demonstrated by numerical tests and the performance is greatly improved if we apply the receding horizon control.
KeywordsOrbit Tracking Recede Horizon Control Monotone Scheme Asymptotic Tracking Strang Splitting
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