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Fast Numerical Methods for Mixed-Integer Nonlinear Model-Predictive Control / by Christian Kirches
Resource type: Ressourcentyp: Buch (Online)Buch (Online)Sprache: Englisch Reihen: SpringerLink BücherVerlag: Wiesbaden : Vieweg+Teubner Verlag / Springer Fachmedien Wiesbaden GmbH, Wiesbaden, 2011Beschreibung: Online-Ressource (XX, 367p. 64 illus, digital)ISBN:- 9783834882028
- 1283477734
- 9781283477734
- 003.3
- 629.8
- QA76.9.C65
- QA402.35
Inhalte:
Zusammenfassung: Christian KirchesZusammenfassung: Christian Kirches develops a fast numerical algorithm of wide applicability that efficiently solves mixed-integer nonlinear optimal control problems. He uses convexification and relaxation techniques to obtain computationally tractable reformulations for which feasibility and optimality certificates can be given even after discretization and roundingPPN: PPN: 1651069050Package identifier: Produktsigel: ZDB-2-SCS
Acknowledgments; Abstract; Contents; List of Figures; List of Tables; List of Acronyms; 0 Introduction; Optimal Control; Model-Predictive Control; Mixed-Integer Optimal Control; Mixed-Integer Programming; Mixed-Integer Model-Predictive Control; Aims and Contributions of this Thesis; Mixed-Integer Nonlinear Model Predictive Control; Switch Costs; Convexification and Relaxation; A Nonconvex Parametric SQP Method; Block Structured Linear Algebra; Matrix Update Techniques; Analysis of Computational Demand; Software Package; Case Studies; Realtime Predictive Cruise Control; Thesis Overview
Computing Environment1 The Direct Multiple Shooting Method for Optimal Control; 1.1 Problem Formulations; 1.2 Solution Methods for Optimal Control Problems; 1.2.1 Indirect Methods; 1.2.2 Dynamic Programming; 1.2.3 Direct Single Shooting; 1.2.4 Direct Collocation; 1.2.5 Direct Multiple Shooting; 1.3 The Direct Multiple Shooting Method for OptimalControl; 1.3.1 Control Discretization; 1.3.2 State Parameterization; 1.3.3 Constraint Discretization; 1.3.4 The Nonlinear Problem; 1.3.5 Separability; 1.4 Summary; 2 Mixed-Integer Optimal Control; 2.1 Problem Formulations
2.2 Mixed-Integer Nonlinear Programming2.2.1 Discretization to a Mixed-Integer Nonlinear Program; 2.2.2 Enumeration Techniques; 2.2.3 Branching Techniques; 2.2.4 Outer Approximation; 2.2.5 Reformulations; 2.3 Outer Convexification and Relaxation; 2.3.1 Convexified and Relaxed Problems; 2.3.2 The Bang-Bang Principle; 2.3.3 Bounds on the Objective Function; 2.3.4 Bounds on the Infeasibility; 2.4 Rounding Strategies; 2.4.1 The Linear Case; 2.4.2 The Nonlinear Case; 2.4.3 The Discretized Case; 2.5 Switch Costs; 2.5.1 Frequent Switching; 2.5.2 Switch Costs in a MILP Formulation
2.5.3 Switch Costs for Outer Convexification2.5.4 Reformulations; 2.6 Summary; 3 Constrained Nonlinear Programming; 3.1 Constrained Nonlinear Programming; 3.1.1 Definitions; 3.1.2 First Order Necessary Optimality Conditions; 3.1.3 Second Order Conditions; 3.1.4 Stability; 3.2 Sequential Quadratic Programming; 3.2.1 Basic Algorithm; 3.2.2 The Full Step Exact Hessian SQP Method; 3.2.3 The Gauß-Newton Approximation; 3.2.4 BFGS Hessian Approximation; 3.2.5 Local Convergence; 3.2.6 Termination Criterion; 3.2.7 Scaling; 3.3 Derivative Generation; 3.3.1 Analytical Derivatives
3.3.2 Finite Difference Approximations3.3.3 Complex Step Approximation; 3.3.4 Automatic Differentiation; 3.3.5 Second Order Derivatives; 3.4 Initial Value Problems and Sensitivity Generation; 3.4.1 Runge-Kutta Methods for ODE IVPs; 3.4.2 Sensitivities of Initial Value Problems; 3.4.3 Second Order Sensitivities; 3.5 Summary; 4 Mixed-Integer Real-Time Iterations; 4.1 Real-Time Optimal Control; 4.1.1 Conventional NMPC Approach; 4.1.2 The Idea of Real-Time Iterations; 4.2 The Real-Time Iteration Scheme; 4.2.1 Parametric Sequential Quadratic Programming; 4.2.2 Initial Value Embedding
4.2.3 Moving Horizons
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