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

:	Thomas J. Böhme, Benjamin Frank
:	Hybrid Systems, Optimal Control and Hybrid Vehicles Theory, Methods and Applications
:	Springer-Verlag
:	9783319513171
:	Advances in Industrial Control
:	1
:	CHF 113.90
:

:	Elektronik, Elektrotechnik, Nachrichtentechnik
:	English

:	549
:	Wasserzeichen/DRM
:	PC/MAC/eReader/Tablet
:	PDF

Thi book assembles new methods showing the automotive engineer for the first time how hybrid vehicle configurations can be modeled as systems with discrete and continuous controls. These hybrid systems describe naturally and compactly the networks of embedded systems which use elements such as integrators, hysteresis, state-machines and logical rules to describe the evolution of continuous and discrete dynamics and arise inevitably when modeling hybrid electric vehicles. They can throw light on systems which may otherwise be too complex or recondite.
Hybrid Systems, Optimal Control and Hybrid Vehicles shows the reader how to formulate and solve control problems which satisfy multiple objectives which may be arbitrary and complex with contradictory influences on fuel consumption, emissions and drivability. The text introduces industrial engineers, postgraduates and researchers to the theory of hybrid optimal control problems. A series of novel algorithmic developments provides tools for solving engineering problems of growing complexity in the field of hybrid vehicles.
Important topics of real relevance rarely found in text books and research publications-switching costs, sensitivity of discrete decisions and there impact on fuel savings, etc.-are discussed and supported with practical applications. These demonstrate the contribution of optimal hybrid control in predictive energy management, advanced powertrain calibration, and the optimization of vehicle configuration with respect to fuel economy, lowest emissions and smoothest drivability. Numerical issues such as computing resources, simplifications and stability are treated to enable readers to assess such complex systems. To help industrial engineers and managers with project decision-making, solutions for many important problems in hybrid vehicle control are provided in terms of requirements, benefits and risks.

Dr.Thomas Böhme is currently working as a technical consultant at the iav automotive engineering company. He has over 15 years industrial experience in modeling and control of chemical processes and embedded systems. His research interests are vehicle control and optimal control of hybrid systems. He published over 30 peer-reviewed papers, journal contributions and patents.
Benjamin Frank is mathematician and working at the iav automotive engineering company. He published several papers and contributions in the field of control and optimizations.

	Series Editors’ Foreword	6
	Preface	8
	Intended Readership	8
	What are the Contributions of This Book	9
	What is Not Covered in This Book	10
	Structure of the Book	10
	Acknowledgements	14
	Contents	15
	Abbreviations and Symbols	22
	1 Introduction	33
	1.1 Motivation, Challenges, and Objectives	33
	1.2 Vehicle Design Aspects	35
	1.2.1 Stages of Energy Conversion	36
	1.2.2 Real-World Driving Profile, Consumption, and Emissions	40
	1.3 Process Model, Control Strategy, and Optimization	42
	1.3.1 General Problem Statement	42
	1.3.2 Energy Management	44
	1.3.3 Numerical Solutions	48
	1.4 Bibliographical Notes	51
	References	52
	Part I Theory and Formulations	56
	2 Introduction to Nonlinear Programming	57
	2.1 Introduction	57
	2.2 Unconstrained Nonlinear Optimization	60
	2.2.1 Necessary and Sufficient Conditions for Optimality	61
	2.2.2 Newton--Raphson Method	61
	2.2.3 Globalization of the Newton--Raphson Method	64
	2.2.4 Quasi-Newton Method	67
	2.3 Constrained Nonlinear Optimization	69
	2.3.1 Necessary and Sufficient Conditions for Optimality	71
	2.3.2 Projected Hessian	74
	2.3.3 Sequential Quadratic Programming	76
	2.4 Sensitivity Analysis	84
	2.4.1 Sensitivity Analysis of the Objective Function and Constraints	88
	2.4.2 Linear Perturbations	93
	2.4.3 Approximation of the Perturbed Solution	94
	2.4.4 Approximation of the Confidence Region	96
	2.5 Multi-Objective Optimization	97
	2.5.1 Elitist Multi-Objective Evolutionary Algorithm	98
	2.5.2 Remarks for MOGAs	102
	2.6 Bibliographical Notes	103
	References	104
	3 Hybrid Systems and Hybrid Optimal Control	108
	3.1 Introduction	108
	3.2 System Definition	109
	3.2.1 Continuous Systems	109
	3.2.2 Hybrid Systems	112
	3.2.3 Controlled Hybrid Systems and Switched Systems	115
	3.2.4 Existence and Uniqueness of Admissible States and Controls	117
	3.2.5 Control and State Constraints, Admissible Sets, and Admissible Function Spaces	120
	3.2.6 Reformulation of Switched Systems	123
	3.3 Optimal Control Problem Formulations	125
	3.3.1 Functionals	125
	3.3.2 Boundary Conditions	126
	3.3.3 Continuous Optimal Control Problem	127
	3.3.4 Hybrid Optimal Control Problem	129
	3.3.5 Switched Optimal Control Problem	130
	3.3.6 Binary Switched Optimal Control Problem	131
	3.3.7 Transformations of Optimal Control Problems	132
	3.4 Bibliographical Notes	139
	References	141
	4 The Minimum Principle and Hamilton--Jacobi--Bellman Equation	145
	4.1 Introduction	145
	4.1.1 The Calculus of Variations	145
	4.1.2 Deriving First-Order Necessary Conditions for an Extremum of an Optimal Control Problem	148
	4.2 Minimum Principle	153
	4.2.1 Necessary Conditions for Optimal Control Problems with Control Restraints	156
	4.2.2 Necessary Conditions for Optimal Control Problems with State Constraints	159
	4.2.3 Necessary Conditions for Optimal Control Problems with Affine Controls	165
	4.3 Hamilton--Jacobi--Bellman Equation	168
	4.4 Hybrid Minimum Principle	174
	4.4.1 Necessary Conditions for Switched Optimal Control Problems Without State Jumps	179
	4.4.2 Necessary Conditions for Switched Optimal Control Problems with State Jumps	180
	4.4.3 Revisited: Necessary Conditions for a State Constrained Optimal Control Problem	181
	4.5 Existence	184
	4.6 Bibliography	187
	References	189
	Part II Methods for Optimal Control	192
	5 Discretization and Integration Schemes