Hybrid Systems, Optimal Control and Hybrid Vehicles : Theory, Methods and Applications.

Intro -- Series Editors' Foreword -- Preface -- Intended Readership -- What are the Contributions of This Book -- What is Not Covered in This Book -- Structure of the Book -- Acknowledgements -- Contents -- Abbreviations and Symbols -- 1 Introduction -- 1.1 Motivation, Challenges, and Objectives -- 1.2 Vehicle Design Aspects -- 1.2.1 Stages of Energy Conversion -- 1.2.2 Real-World Driving Profile, Consumption, and Emissions -- 1.3 Process Model, Control Strategy, and Optimization -- 1.3.1 General Problem Statement -- 1.3.2 Energy Management -- 1.3.3 Numerical Solutions -- 1.4 Bibliographical Notes -- References -- Part I Theory and Formulations -- 2 Introduction to Nonlinear Programming -- 2.1 Introduction -- 2.2 Unconstrained Nonlinear Optimization -- 2.2.1 Necessary and Sufficient Conditions for Optimality -- 2.2.2 Newton--Raphson Method -- 2.2.3 Globalization of the Newton--Raphson Method -- 2.2.4 Quasi-Newton Method -- 2.3 Constrained Nonlinear Optimization -- 2.3.1 Necessary and Sufficient Conditions for Optimality -- 2.3.2 Projected Hessian -- 2.3.3 Sequential Quadratic Programming -- 2.4 Sensitivity Analysis -- 2.4.1 Sensitivity Analysis of the Objective Function and Constraints -- 2.4.2 Linear Perturbations -- 2.4.3 Approximation of the Perturbed Solution -- 2.4.4 Approximation of the Confidence Region -- 2.5 Multi-Objective Optimization -- 2.5.1 Elitist Multi-Objective Evolutionary Algorithm -- 2.5.2 Remarks for MOGAs -- 2.6 Bibliographical Notes -- References -- 3 Hybrid Systems and Hybrid Optimal Control -- 3.1 Introduction -- 3.2 System Definition -- 3.2.1 Continuous Systems -- 3.2.2 Hybrid Systems -- 3.2.3 Controlled Hybrid Systems and Switched Systems -- 3.2.4 Existence and Uniqueness of Admissible States and Controls -- 3.2.5 Control and State Constraints, Admissible Sets, and Admissible Function Spaces.

3.2.6 Reformulation of Switched Systems -- 3.3 Optimal Control Problem Formulations -- 3.3.1 Functionals -- 3.3.2 Boundary Conditions -- 3.3.3 Continuous Optimal Control Problem -- 3.3.4 Hybrid Optimal Control Problem -- 3.3.5 Switched Optimal Control Problem -- 3.3.6 Binary Switched Optimal Control Problem -- 3.3.7 Transformations of Optimal Control Problems -- 3.4 Bibliographical Notes -- References -- 4 The Minimum Principle and Hamilton--Jacobi--Bellman Equation -- 4.1 Introduction -- 4.1.1 The Calculus of Variations -- 4.1.2 Deriving First-Order Necessary Conditions for an Extremum of an Optimal Control Problem -- 4.2 Minimum Principle -- 4.2.1 Necessary Conditions for Optimal Control Problems with Control Restraints -- 4.2.2 Necessary Conditions for Optimal Control Problems with State Constraints -- 4.2.3 Necessary Conditions for Optimal Control Problems with Affine Controls -- 4.3 Hamilton--Jacobi--Bellman Equation -- 4.4 Hybrid Minimum Principle -- 4.4.1 Necessary Conditions for Switched Optimal Control Problems Without State Jumps -- 4.4.2 Necessary Conditions for Switched Optimal Control Problems with State Jumps -- 4.4.3 Revisited: Necessary Conditions for a State Constrained Optimal Control Problem -- 4.5 Existence -- 4.6 Bibliography -- References -- Part II Methods for Optimal Control -- 5 Discretization and Integration Schemes for Hybrid Optimal Control Problems -- 5.1 Introduction -- 5.2 Discretization of the Initial Value Problem -- 5.3 Runge--Kutta Integration Scheme -- 5.4 Consistence Order of Runge--Kutta Methods -- 5.5 Stability -- 5.6 Some Lower-Order Runge--Kutta Integration Schemes -- 5.6.1 Explicit Runge--Kutta Schemes -- 5.6.2 Implicit Runge--Kutta Schemes -- 5.7 Remarks for Integration Schemes for Switched System with Discontinuities -- 5.8 Consequences of the Discretization to Optimal Control Problems.

5.9 Bibliographical Notes -- References -- 6 Dynamic Programming -- 6.1 Introduction -- 6.2 Optimal Control for Continuous Systems -- 6.3 Optimal Control of Hybrid Systems -- 6.4 Discussion -- 6.5 Bibliography -- References -- 7 Indirect Methods for Optimal Control -- 7.1 Introduction -- 7.2 Optimal Control for Continuous Systems -- 7.2.1 Indirect Shooting Method -- 7.2.2 Indirect Multiple Shooting Method -- 7.3 Optimal Control for Hybrid Systems -- 7.4 Discussion -- 7.5 Bibliography -- References -- 8 Direct Methods for Optimal Control -- 8.1 Introduction -- 8.2 Optimal Control for Continuous Systems -- 8.2.1 Direct Shooting -- 8.2.2 Direct Collocation -- 8.2.3 Comparison of Direct Shooting and Direct Collocation -- 8.2.4 Recovering the Costates from a Direct Shooting and Direct Collocation -- 8.3 Optimal Control for Switched Systems -- 8.3.1 Embedded Optimal Control Problem -- 8.3.2 Two-Stage Algorithm -- 8.3.3 Switching Time Optimization with Parameterized Switching Intervals -- 8.4 Numerical Methods for Obtaining Binary Feasible Control Functions -- 8.5 Discussion -- 8.6 Bibliography -- References -- Part III Numerical Implementations -- 9 Practical Implementation Aspects of Large-Scale Optimal Control Solvers -- 9.1 Sparse Linear Algebra -- 9.1.1 Sparse Matrix Formats -- 9.1.2 Numerical Solution of Large-Scale Linear Systems -- 9.1.3 Checking the Positive Definiteness of Large-Scale Matrices -- 9.2 Calculating Derivatives -- 9.2.1 Computational Graphs -- 9.2.2 Sparsity Pattern Determination -- 9.2.3 Compressed Derivative Calculation -- 9.2.4 Finite Differences -- 9.3 Sparse Quasi-Newton Updates -- 9.3.1 Quasi-Newton Update for Partially Separable Function -- 9.3.2 Simple Quasi-Newton Update for Chordal Sparsity Structures -- 9.3.3 Quasi-Newton Update for Chordal Sparsity Structures -- 9.3.4 Modifications of the Quasi-Newton Update.

9.3.5 Quasi-Newton Updates for Discretized Optimal Control Problems -- 9.4 Bibliographical Notes -- References -- Part IV Modeling of Hybrid Vehicles for Control -- 10 Modeling Hybrid Vehicles as Switched Systems -- 10.1 Introduction -- 10.2 Vehicle Dynamics -- 10.3 Mechatronic Systems -- 10.3.1 Internal Combustion Engine -- 10.3.2 Electric Machine -- 10.3.3 Gearbox -- 10.3.4 Clutch -- 10.3.5 Battery -- 10.4 Hybrid Vehicle Configurations -- 10.4.1 Parallel Hybrids -- 10.4.2 Power-Split Hybrids -- 10.4.3 Serial Hybrids -- 10.4.4 Combined Hybrids -- 10.4.5 Plug-In Hybrids -- 10.4.6 Battery Electric Vehicles -- 10.5 Hybrid Vehicle Models -- 10.5.1 Quasi-static Model for Parallel Hybrids -- 10.5.2 Thermodynamic Model for Parallel Hybrids Using Spark Ignition Engines -- 10.5.3 Quasi-static Model for Power-Split Hybrids -- 10.5.4 Extended Quasi-static Model for Parallel Hybrids -- 10.6 Drive Cycles -- 10.7 Static Function Representation -- 10.8 Switching Costs -- 10.9 Bibliographical Notes -- References -- Part V Applications -- 11 Advanced Vehicle Calibration -- 11.1 Introduction -- 11.2 Offline Solution of Switched Optimal Control Problems ƒ -- 11.3 Analytical Calibration for Rule-Based Energy Managements -- 11.3.1 Constant Costate Assumption -- 11.3.2 Influence of Switching Costs -- 11.3.3 Lookup Table Calculation -- 11.4 Rule-Based Strategies for Choosing the Costate -- 11.4.1 Rule-Based Selection Using Costate Maps -- 11.4.2 Costate for Optimal CO2 Emissions -- 11.5 Implementation Issues -- 11.6 Bibliography -- References -- 12 Predictive Real-Time Energy Management -- 12.1 Introduction -- 12.2 Real-World Benchmark-Cycles -- 12.3 Intelligent Traffic System -- 12.3.1 Time-Based Driver Model -- 12.3.2 Spatial-Based Driver Model -- 12.3.3 Estimation of Stop Events -- 12.4 Predictive Energy Management for Battery Electric Vehicles -- 12.4.1 Vehicle Model.

12.4.2 Dynamic Programming for the Maximal Speed Limit -- 12.4.3 Instantaneous Speed Limit Corrections -- 12.4.4 Experimental Results -- 12.5 Predictive Energy Management for Hybrid Vehicles -- 12.5.1 Event-Triggered Predictive Energy Management -- 12.5.2 Predictive Energy Management with Long Prediction Horizon -- 12.6 Bibliographical Notes -- References -- 13 Optimal Design of Hybrid Powertrain Configurations -- 13.1 Introduction -- 13.2 Process Description -- 13.2.1 Drivability Performance Index -- 13.2.2 Design Parameters -- 13.2.3 Powertrain Dynamics -- 13.3 Multi-objective Powertrain Design -- 13.3.1 Master Problem -- 13.3.2 Map Scaling for Powertrain Components -- 13.3.3 Batched Optimal Control Subproblems -- 13.4 P2-Hybrid Design Study -- 13.5 Post Optimal Parametric Sensitivity Analysis -- 13.6 Further Work -- 13.6.1 Speedup of the Algorithm -- 13.6.2 Increase of Model Complexity -- 13.7 Bibliographical Notes -- References -- Part VI Appendix -- 14 Graph Theoretical Fundamentals for Sparse Matrices -- References -- Index.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.