Fast Numerical Methods for Mixed-Integer Nonlinear Model-Predictive Control [electronic resource] /
Kirches, Christian.author.
Current industrial practice knows many optimization tasks that can be cast as mixed-integer optimal control problems. Due to the combinatorial character of these problems, the computation of optimal solutions under real-time constraints is still a demanding challenge. Starting with Bock's direct multiple shooting method for optimal control, 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 rounding. In a sequential quadratic programming framework, extensive exploitation of arising structures in an active set method ultimately brings the developed algorithm towards real-time feasibility.
Description based upon print version of record.
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
Includes bibliographical references.
Current industrial practice knows many optimization tasks that can be cast as mixed-integer optimal control problems. Due to the combinatorial character of these problems, the computation of optimal solutions under real-time constraints is still a demanding challenge. Starting with Bock's direct multiple shooting method for optimal control, 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 rounding. In a sequential quadratic programming framework, extensive exploitation of arising structures in an active set method ultimately brings the developed algorithm towards real-time feasibility.
Computer simulation.
Mathematics.
Simulation and Modeling.
Mathematics, general.