Cargando…

Adaptive Dynamic Programming for Control: Algorithms and Stability

There are many methods of stable controller design for nonlinear systems. In seeking to go beyond the minimum requirement of stability, Adaptive Dynamic Programming for Control approaches the challenging topic of optimal control for nonlinear systems using the tools of  adaptive dynamic programming...

Descripción completa

Detalles Bibliográficos
Autores principales: Zhang, Huaguang, Liu, Derong, Luo, Yanhong, Wang, Ding
Lenguaje:eng
Publicado: Springer 2013
Materias:
Acceso en línea:https://dx.doi.org/10.1007/978-1-4471-4757-2
http://cds.cern.ch/record/1512951
_version_ 1780928152051122176
author Zhang, Huaguang
Liu, Derong
Luo, Yanhong
Wang, Ding
author_facet Zhang, Huaguang
Liu, Derong
Luo, Yanhong
Wang, Ding
author_sort Zhang, Huaguang
collection CERN
description There are many methods of stable controller design for nonlinear systems. In seeking to go beyond the minimum requirement of stability, Adaptive Dynamic Programming for Control approaches the challenging topic of optimal control for nonlinear systems using the tools of  adaptive dynamic programming (ADP). The range of systems treated is extensive; affine, switched, singularly perturbed and time-delay nonlinear systems are discussed as are the uses of neural networks and techniques of value and policy iteration. The text features three main aspects of ADP in which the methods proposed for stabilization and for tracking and games benefit from the incorporation of optimal control methods: • infinite-horizon control for which the difficulty of solving partial differential Hamilton–Jacobi–Bellman equations directly is overcome, and  proof provided that the iterative value function updating sequence converges to the infimum of all the value functions obtained by admissible control law sequences; • finite-horizon control, implemented in discrete-time nonlinear systems showing the reader how to obtain suboptimal control solutions within a fixed number of control steps and with results more easily applied in real systems than those usually gained from infinte-horizon control; • nonlinear games for which  a pair of mixed optimal policies are derived for solving games both when the saddle point does not exist, and, when it does, avoiding the existence conditions of the saddle point. Non-zero-sum games are studied in the context of a single network scheme in which policies are obtained guaranteeing system stability and minimizing the individual performance function yielding a Nash equilibrium. In order to make the coverage suitable for the student as well as for the expert reader, Adaptive Dynamic Programming for Control: • establishes the fundamental theory involved clearly with each chapter devoted to a clearly identifiable control paradigm; • demonstrates convergence proofs of the ADP algorithms to deepen undertstanding of the derivation of stability and convergence with the iterative computational methods used; and • shows how ADP methods can be put to use both in simulation and in real applications. This text will be of considerable interest to researchers interested in optimal control and its applications in operations research, applied mathematics computational intelligence and engineering. Graduate students working in control and operations research will also find the ideas presented here to be a source of powerful methods for furthering their study. The Communications and Control Engineering series reports major technological advances which have potential for great impact in the fields of communication and control. It reflects research in industrial and academic institutions around the world so that the readership can exploit new possibilities as they become available.
id cern-1512951
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 2013
publisher Springer
record_format invenio
spelling cern-15129512021-04-21T23:27:29Zdoi:10.1007/978-1-4471-4757-2http://cds.cern.ch/record/1512951engZhang, HuaguangLiu, DerongLuo, YanhongWang, DingAdaptive Dynamic Programming for Control: Algorithms and StabilityEngineeringThere are many methods of stable controller design for nonlinear systems. In seeking to go beyond the minimum requirement of stability, Adaptive Dynamic Programming for Control approaches the challenging topic of optimal control for nonlinear systems using the tools of  adaptive dynamic programming (ADP). The range of systems treated is extensive; affine, switched, singularly perturbed and time-delay nonlinear systems are discussed as are the uses of neural networks and techniques of value and policy iteration. The text features three main aspects of ADP in which the methods proposed for stabilization and for tracking and games benefit from the incorporation of optimal control methods: • infinite-horizon control for which the difficulty of solving partial differential Hamilton–Jacobi–Bellman equations directly is overcome, and  proof provided that the iterative value function updating sequence converges to the infimum of all the value functions obtained by admissible control law sequences; • finite-horizon control, implemented in discrete-time nonlinear systems showing the reader how to obtain suboptimal control solutions within a fixed number of control steps and with results more easily applied in real systems than those usually gained from infinte-horizon control; • nonlinear games for which  a pair of mixed optimal policies are derived for solving games both when the saddle point does not exist, and, when it does, avoiding the existence conditions of the saddle point. Non-zero-sum games are studied in the context of a single network scheme in which policies are obtained guaranteeing system stability and minimizing the individual performance function yielding a Nash equilibrium. In order to make the coverage suitable for the student as well as for the expert reader, Adaptive Dynamic Programming for Control: • establishes the fundamental theory involved clearly with each chapter devoted to a clearly identifiable control paradigm; • demonstrates convergence proofs of the ADP algorithms to deepen undertstanding of the derivation of stability and convergence with the iterative computational methods used; and • shows how ADP methods can be put to use both in simulation and in real applications. This text will be of considerable interest to researchers interested in optimal control and its applications in operations research, applied mathematics computational intelligence and engineering. Graduate students working in control and operations research will also find the ideas presented here to be a source of powerful methods for furthering their study. The Communications and Control Engineering series reports major technological advances which have potential for great impact in the fields of communication and control. It reflects research in industrial and academic institutions around the world so that the readership can exploit new possibilities as they become available.Springeroai:cds.cern.ch:15129512013
spellingShingle Engineering
Zhang, Huaguang
Liu, Derong
Luo, Yanhong
Wang, Ding
Adaptive Dynamic Programming for Control: Algorithms and Stability
title Adaptive Dynamic Programming for Control: Algorithms and Stability
title_full Adaptive Dynamic Programming for Control: Algorithms and Stability
title_fullStr Adaptive Dynamic Programming for Control: Algorithms and Stability
title_full_unstemmed Adaptive Dynamic Programming for Control: Algorithms and Stability
title_short Adaptive Dynamic Programming for Control: Algorithms and Stability
title_sort adaptive dynamic programming for control: algorithms and stability
topic Engineering
url https://dx.doi.org/10.1007/978-1-4471-4757-2
http://cds.cern.ch/record/1512951
work_keys_str_mv AT zhanghuaguang adaptivedynamicprogrammingforcontrolalgorithmsandstability
AT liuderong adaptivedynamicprogrammingforcontrolalgorithmsandstability
AT luoyanhong adaptivedynamicprogrammingforcontrolalgorithmsandstability
AT wangding adaptivedynamicprogrammingforcontrolalgorithmsandstability