Monotonically convergent algorithms for solving quantum optimal control problems of a dynamical system nonlinearly interacting with a control

This paper gives a robust pseudospectral scheme for solving a class of nonlinear optimal control problems (OCPs) governed by differential inclusions. The basic idea includes two major stages. At the first stage, we linearize the nonlinear dynamical system by an interesting technique which is called linear combination property of intervals. After this stage, the linearized dynamical system is transformed into a multi domain dynamical system via computational interval partitioning. Moreover, the integral form of this multidomain dynamical system is considered. Collocating these constraints at the Legendre Gauss Lobatto (LGL) points together with using the Legendre Gauss Lobatto quadrature rule for approximating the involved integrals enables us to transform the basic OCPs into the associated nonlinear programming problems (NLPs). In all parts of this procedure, the associated control and state functions are approximated by piecewise constants and piecewise polynomials, respectively. An illustrative example is provided for confirming the accuracy and applicability of the proposed idea.

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Monotonically convergent algorithms for solving quantum optimal control problems described by an integrodifferential equation of motion

Physical Review A ◽

10.1103/physreva.75.033407 ◽

2007 ◽

Vol 75 (3) ◽

Cited By ~ 26

Author(s):

Yukiyoshi Ohtsuki ◽

Yoshiaki Teranishi ◽

Peter Saalfrank ◽

Gabriel Turinici ◽

Herschel Rabitz

Keyword(s):

Optimal Control ◽

Integrodifferential Equation ◽

Optimal Control Problems ◽

Equation Of Motion ◽

Control Problems ◽

Quantum Optimal Control

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On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

ESAIM Control Optimisation and Calculus of Variations ◽

10.1051/cocv/2019057 ◽

2020 ◽

Vol 26 ◽

pp. 41

Author(s):

Tianxiao Wang

Keyword(s):

Optimal Control ◽

Closed Loop ◽

Optimal Control Problems ◽

Mean Field ◽

Open Loop ◽

Time Inconsistency ◽

Control Problems ◽

Linear Quadratic ◽

Linear Quadratic Optimal Control ◽

Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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