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Adaptive Dynamic Programming with Applications in Optimal Control
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Adaptive Dynamic Programming with Applications in Optimal Control
von: Derong Liu, Qinglai Wei, Ding Wang, Xiong Yang, Hongliang Li
Springer-Verlag, 2017
ISBN: 9783319508153
609 Seiten, Download: 18959 KB
 
Format:  PDF
geeignet für: Apple iPad, Android Tablet PC's Online-Lesen PC, MAC, Laptop

Typ: B (paralleler Zugriff)

 

 
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Inhaltsverzeichnis

  Foreword 6  
  Series Editors’ Foreword 8  
     References 10  
  Preface 11  
  Acknowledgements 16  
  Contents 17  
  Abbreviations 24  
  Symbols 25  
  1 Overview of Adaptive Dynamic Programming 27  
     1.1 Introduction 27  
     1.2 Reinforcement Learning 29  
     1.3 Adaptive Dynamic Programming 33  
        1.3.1 Basic Forms of Adaptive Dynamic Programming 36  
        1.3.2 Iterative Adaptive Dynamic Programming 41  
        1.3.3 ADP for Continuous-Time Systems 44  
        1.3.4 Remarks 47  
     1.4 Related Books 48  
     1.5 About This Book 52  
     References 53  
  Part I Discrete-Time Systems 60  
  2 Value Iteration ADP for Discrete-Time Nonlinear Systems 61  
     2.1 Introduction 61  
     2.2 Optimal Control of Nonlinear Systems Using General Value Iteration 62  
        2.2.1 Convergence Analysis 64  
        2.2.2 Neural Network Implementation 72  
        2.2.3 Generalization to Optimal Tracking Control 76  
        2.2.4 Optimal Control of Systems with Constrained Inputs 80  
        2.2.5 Simulation Studies 83  
     2.3 Iterative ?-Adaptive Dynamic Programming Algorithm for Nonlinear Systems 91  
        2.3.1 Convergence Analysis 93  
        2.3.2 Optimality Analysis 101  
        2.3.3 Summary of Iterative ?-ADP Algorithm 104  
        2.3.4 Simulation Studies 107  
     2.4 Conclusions 111  
     References 111  
  3 Finite Approximation Error-Based Value Iteration ADP 115  
     3.1 Introduction 115  
     3.2 Iterative ?-ADP Algorithm with Finite Approximation Errors 116  
        3.2.1 Properties of the Iterative ADP Algorithm with Finite Approximation Errors 117  
        3.2.2 Neural Network Implementation 124  
        3.2.3 Simulation Study 128  
     3.3 Numerical Iterative ?-Adaptive Dynamic Programming 131  
        3.3.1 Derivation of the Numerical Iterative ?-ADP Algorithm 131  
        3.3.2 Properties of the Numerical Iterative ?-ADP Algorithm 135  
        3.3.3 Summary of the Numerical Iterative ?-ADP Algorithm 144  
        3.3.4 Simulation Study 145  
     3.4 General Value Iteration ADP Algorithm with Finite Approximation Errors 149  
        3.4.1 Derivation and Properties of the GVI Algorithm with Finite Approximation Errors 149  
        3.4.2 Designs of Convergence Criteria with Finite Approximation Errors 157  
        3.4.3 Simulation Study 164  
     3.5 Conclusions 171  
     References 171  
  4 Policy Iteration for Optimal Control of Discrete-Time Nonlinear Systems 174  
     4.1 Introduction 174  
     4.2 Policy Iteration Algorithm 175  
        4.2.1 Derivation of Policy Iteration Algorithm 176  
        4.2.2 Properties of Policy Iteration Algorithm 177  
        4.2.3 Initial Admissible Control Law 183  
        4.2.4 Summary of Policy Iteration ADP Algorithm 185  
     4.3 Numerical Simulation and Analysis 185  
     4.4 Conclusions 196  
     References 197  
  5 Generalized Policy Iteration ADP for Discrete-Time Nonlinear Systems 199  
     5.1 Introduction 199  
     5.2 Generalized Policy Iteration-Based Adaptive Dynamic Programming Algorithm 199  
        5.2.1 Derivation and Properties of the GPI Algorithm 201  
        5.2.2 GPI Algorithm and Relaxation of Initial Conditions 210  
        5.2.3 Simulation Studies 214  
     5.3 Discrete-Time GPI with General Initial Value Functions 221  
        5.3.1 Derivation and Properties of the GPI Algorithm 221  
        5.3.2 Relaxations of the Convergence Criterion and Summary of the GPI Algorithm 233  
        5.3.3 Simulation Studies 237  
     5.4 Conclusions 243  
     References 243  
  6 Error Bounds of Adaptive Dynamic Programming Algorithms 244  
     6.1 Introduction 244  
     6.2 Error Bounds of ADP Algorithms for Undiscounted Optimal Control Problems 245  
        6.2.1 Problem Formulation 245  
        6.2.2 Approximate Value Iteration 247  
        6.2.3 Approximate Policy Iteration 252  
        6.2.4 Approximate Optimistic Policy Iteration 258  
        6.2.5 Neural Network Implementation 262  
        6.2.6 Simulation Study 264  
     6.3 Error Bounds of Q-Function for Discounted Optimal Control Problems 268  
        6.3.1 Problem Formulation 268  
        6.3.2 Policy Iteration Under Ideal Conditions 270  
        6.3.3 Error Bound for Approximate Policy Iteration 275  
        6.3.4 Neural Network Implementation 278  
        6.3.5 Simulation Study 280  
     6.4 Conclusions 283  
     References 284  
  Part II Continuous-Time Systems 286  
  7 Online Optimal Control of Continuous-Time Affine Nonlinear Systems 287  
     7.1 Introduction 287  
     7.2 Online Optimal Control of Partially Unknown Affine Nonlinear Systems 287  
        7.2.1 Identifier--Critic Architecture for Solving HJB Equation 289  
        7.2.2 Stability Analysis of Closed-Loop System 301  
        7.2.3 Simulation Study 306  
     7.3 Online Optimal Control of Affine Nonlinear Systems with Constrained Inputs 311  
        7.3.1 Solving HJB Equation via Critic Architecture 314  
        7.3.2 Stability Analysis of Closed-Loop System with Constrained Inputs 318  
        7.3.3 Simulation Study 322  
     7.4 Conclusions 325  
     References 326  
  8 Optimal Control of Unknown Continuous-Time Nonaffine Nonlinear Systems 328  
     8.1 Introduction 328  
     8.2 Optimal Control of Unknown Nonaffine Nonlinear Systems with Constrained Inputs 329  
        8.2.1 Identifier Design via Dynamic Neural Networks 330  
        8.2.2 Actor--Critic Architecture for Solving HJB Equation 335  
        8.2.3 Stability Analysis of Closed-Loop System 337  
        8.2.4 Simulation Study 342  
     8.3 Optimal Output Regulation of Unknown Nonaffine Nonlinear Systems 346  
        8.3.1 Neural Network Observer 347  
        8.3.2 Observer-Based Optimal Control Scheme Using Critic Network 352  
        8.3.3 Stability Analysis of Closed-Loop System 356  
        8.3.4 Simulation Study 359  
     8.4 Conclusions 362  
     References 362  
  9 Robust and Optimal Guaranteed Cost Control of Continuous-Time Nonlinear Systems 364  
     9.1 Introduction 364  
     9.2 Robust Control of Uncertain Nonlinear Systems 365  
        9.2.1 Equivalence Analysis and Problem Transformation 367  
        9.2.2 Online Algorithm and Neural Network Implementation 369  
        9.2.3 Stability Analysis of Closed-Loop System 372  
        9.2.4 Simulation Study 375  
     9.3 Optimal Guaranteed Cost Control of Uncertain Nonlinear Systems 379  
        9.3.1 Optimal Guaranteed Cost Controller Design 381  
        9.3.2 Online Solution of Transformed Optimal Control Problem 387  
        9.3.3 Stability Analysis of Closed-Loop System 392  
        9.3.4 Simulation Studies 397  
     9.4 Conclusions 402  
     References 403  
  10 Decentralized Control of Continuous-Time Interconnected Nonlinear Systems 406  
     10.1 Introduction 406  
     10.2 Decentralized Control of Interconnected Nonlinear Systems 407  
        10.2.1 Decentralized Stabilization via Optimal Control Approach 408  
        10.2.2 Optimal Controller Design of Isolated Subsystems 413  
        10.2.3 Generalization to Model-Free Decentralized Control 419  
        10.2.4 Simulation Studies 423  
     10.3 Conclusions 433  
     References 433  
  11 Learning Algorithms for Differential Games of Continuous-Time Systems 435  
     11.1 Introduction 435  
     11.2 Integral Policy Iteration for Two-Player Zero-Sum Games 436  
        11.2.1 Derivation of Integral Policy Iteration 438  
        11.2.2 Convergence Analysis 441  
        11.2.3 Neural Network Implementation 443  
        11.2.4 Simulation Studies 446  
     11.3 Iterative Adaptive Dynamic Programming for Multi-player Zero-Sum Games 449  
        11.3.1 Derivation of the Iterative ADP Algorithm 451  
        11.3.2 Properties 456  
        11.3.3 Neural Network Implementation 462  
        11.3.4 Simulation Studies 469  
     11.4 Synchronous Approximate Optimal Learning for Multi-player Nonzero-Sum Games 477  
        11.4.1 Derivation and Convergence Analysis 478  
        11.4.2 Neural Network Implementation 482  
        11.4.3 Simulation Study 491  
     11.5 Conclusions 496  
     References 496  
  Part III Applications 499  
  12 Adaptive Dynamic Programming for Optimal Residential Energy Management 500  
     12.1 Introduction 500  
     12.2 A Self-learning Scheme for Residential Energy System Control and Management 501  
        12.2.1 The ADHDP Method 505  
        12.2.2 A Self-learning Scheme for Residential Energy System 506  
        12.2.3 Simulation Study 509  
     12.3 A Novel Dual Iterative Q-Learning Method for Optimal Battery Management 513  
        12.3.1 Problem Formulation 513  
        12.3.2 Dual Iterative Q-Learning Algorithm 514  
        12.3.3 Neural Network Implementation 520  
        12.3.4 Numerical Analysis 523  
     12.4 Multi-battery Optimal Coordination Control for Residential Energy Systems 530  
        12.4.1 Distributed Iterative ADP Algorithm 532  
        12.4.2 Numerical Analysis 544  
     12.5 Conclusions 550  
     References 550  
  13 Adaptive Dynamic Programming for Optimal Control of Coal Gasification Process 553  
     13.1 Introduction 553  
     13.2 Data-Based Modeling and Properties 554  
        13.2.1 Description of Coal Gasification Process and Control Systems 554  
        13.2.2 Data-Based Process Modeling and Properties 556  
     13.3 Design and Implementation of Optimal Tracking Control 562  
        13.3.1 Optimal Tracking Controller Design by Iterative ADP Algorithm Under System and Iteration Errors 562  
        13.3.2 Neural Network Implementation 570  
     13.4 Numerical Analysis 573  
     13.5 Conclusions 584  
     References 585  
  14 Data-Based Neuro-Optimal Temperature Control of Water Gas Shift Reaction 586  
     14.1 Introduction 586  
     14.2 System Description and Data-Based Modeling 587  
        14.2.1 Water Gas Shift Reaction 587  
        14.2.2 Data-Based Modeling and Properties 588  
     14.3 Design of Neuro-Optimal Temperature Controller 590  
        14.3.1 System Transformation 590  
        14.3.2 Derivation of Stable Iterative ADP Algorithm 591  
        14.3.3 Properties of Stable Iterative ADP Algorithm with Approximation Errors and Disturbances 593  
     14.4 Neural Network Implementation for the Optimal Tracking Control Scheme 597  
     14.5 Numerical Analysis 600  
     14.6 Conclusions 604  
     References 604  
  Index 606  


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