{"title":"部分信息下具有跳变的平均场随机线性二次最优控制问题","authors":"Yiyun Yang, M. Tang, Qingxin Meng","doi":"10.1051/cocv/2022039","DOIUrl":null,"url":null,"abstract":"In this article, the stochastic linear-quadratic optimal control problem of mean-field type with jumps under partial information is discussed. The state equation contains affine terms is a SDE with jumps driven by a multidimensional Brownian motion and a Poisson random martingale measure, the cost function containing cross terms is quadratic, in addition, the state and the control as well as their expectations are contained both in the state equation and the cost functional. Firstly, we prove the existence and uniqueness of the optimal control, and by using Pontryagin’s maximum principle we get the dual characterization of optimal control; Secondly, by introducing the adjoint processes of the state equation, establishing a stochastic Hamiltonian system and using decoupling technology, we deduce two integro-differential Riccati equations and get the feedback representation of the optimal control under partial information; Thirdly, the existence and uniqueness of the solutions of the two associated integro-differential Riccati equations are proved; Finally, we discuss a special case, and by means of filtering technique, establish the corresponding the filtering state feedback representation of the optimal control.","PeriodicalId":50500,"journal":{"name":"Esaim-Control Optimisation and Calculus of Variations","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2022-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A mean-field stochastic linear-quadratic optimal control problem with jumps under partial information\",\"authors\":\"Yiyun Yang, M. Tang, Qingxin Meng\",\"doi\":\"10.1051/cocv/2022039\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this article, the stochastic linear-quadratic optimal control problem of mean-field type with jumps under partial information is discussed. The state equation contains affine terms is a SDE with jumps driven by a multidimensional Brownian motion and a Poisson random martingale measure, the cost function containing cross terms is quadratic, in addition, the state and the control as well as their expectations are contained both in the state equation and the cost functional. Firstly, we prove the existence and uniqueness of the optimal control, and by using Pontryagin’s maximum principle we get the dual characterization of optimal control; Secondly, by introducing the adjoint processes of the state equation, establishing a stochastic Hamiltonian system and using decoupling technology, we deduce two integro-differential Riccati equations and get the feedback representation of the optimal control under partial information; Thirdly, the existence and uniqueness of the solutions of the two associated integro-differential Riccati equations are proved; Finally, we discuss a special case, and by means of filtering technique, establish the corresponding the filtering state feedback representation of the optimal control.\",\"PeriodicalId\":50500,\"journal\":{\"name\":\"Esaim-Control Optimisation and Calculus of Variations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2022-05-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Control Optimisation and Calculus of Variations\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/cocv/2022039\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Control Optimisation and Calculus of Variations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/cocv/2022039","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
A mean-field stochastic linear-quadratic optimal control problem with jumps under partial information
In this article, the stochastic linear-quadratic optimal control problem of mean-field type with jumps under partial information is discussed. The state equation contains affine terms is a SDE with jumps driven by a multidimensional Brownian motion and a Poisson random martingale measure, the cost function containing cross terms is quadratic, in addition, the state and the control as well as their expectations are contained both in the state equation and the cost functional. Firstly, we prove the existence and uniqueness of the optimal control, and by using Pontryagin’s maximum principle we get the dual characterization of optimal control; Secondly, by introducing the adjoint processes of the state equation, establishing a stochastic Hamiltonian system and using decoupling technology, we deduce two integro-differential Riccati equations and get the feedback representation of the optimal control under partial information; Thirdly, the existence and uniqueness of the solutions of the two associated integro-differential Riccati equations are proved; Finally, we discuss a special case, and by means of filtering technique, establish the corresponding the filtering state feedback representation of the optimal control.
期刊介绍:
ESAIM: COCV strives to publish rapidly and efficiently papers and surveys in the areas of Control, Optimisation and Calculus of Variations.
Articles may be theoretical, computational, or both, and they will cover contemporary subjects with impact in forefront technology, biosciences, materials science, computer vision, continuum physics, decision sciences and other allied disciplines.
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in control: modeling, controllability, optimal control, stabilization, control design, hybrid control, robustness analysis, numerical and computational methods for control, stochastic or deterministic, continuous or discrete control systems, finite-dimensional or infinite-dimensional control systems, geometric control, quantum control, game theory;
in optimisation: mathematical programming, large scale systems, stochastic optimisation, combinatorial optimisation, shape optimisation, convex or nonsmooth optimisation, inverse problems, interior point methods, duality methods, numerical methods, convergence and complexity, global optimisation, optimisation and dynamical systems, optimal transport, machine learning, image or signal analysis;
in calculus of variations: variational methods for differential equations and Hamiltonian systems, variational inequalities; semicontinuity and convergence, existence and regularity of minimizers and critical points of functionals, relaxation; geometric problems and the use and development of geometric measure theory tools; problems involving randomness; viscosity solutions; numerical methods; homogenization, multiscale and singular perturbation problems.