Nonlinear Model Predictive Control

Theory and Algorithms

By: Lars Grune, Jurgen Pannek

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Hardcover | 10 April 2011

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372 Pages

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23.39 x 15.6 x 2.24

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Nonlinear Model Predictive Control is a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. NMPC schemes with and without stabilizing terminal constraints are detailed and intuitive examples illustrate the performance of different NMPC variants. An introduction to nonlinear optimal control algorithms gives insight into how the nonlinear optimisation routine - the core of any NMPC controller - works. An appendix covering NMPC software and accompanying software in MATLAB® and C++(downloadable from www.springer.com/ISBN) enables readers to perform computer experiments exploring the possibilities and limitations of NMPC.

Industry Reviews

"The book provides an excellent and extensive treatment of NMPC from a careful introduction to the underlying theory to advanced results. It can be used for independent reading by applied mathematicians, control theoreticians and engineers who desire a rigorous introduction into the NMPC theory. It can also be used as a textbook for a graduate-level university course in NMPC." (Ilya Kolmanovsky, Mathematical Reviews, April, 2015)

"In the monograph nonlinear, discrete-time, finite-dimensional control systems with constant parameters are considered. ... Each chapter of the monograph contains many numerical examples which illustrate the theoretical considerations, several possible extensions and open problems. Moreover, relationships to results on predictive control published in the literature are pointed out." (Jerzy Klamka, Zentralblatt MATH, Vol. 1220, 2011)

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Introduction	p. 1
What Is Nonlinear Model Predictive Control?	p. 1
Where Did NMPC Come from?	p. 3
How Is This Book Organized?	p. 5
What Is Not Covered in This Book?	p. 9
References	p. 10
Discrete Time and Sampled Data Systems	p. 13
Discrete Time Systems	p. 13
Sampled Data Systems	p. 16
Stability of Discrete Time Systems	p. 28
Stability of Sampled Data Systems	p. 35
Notes and Extensions	p. 39
Problems	p. 39
References	p. 41
Nonlinear Model Predictive Control	p. 43
The Basic NMPC Algorithm	p. 43
Constraints	p. 45
Variants of the Basic NMPC Algorithms	p. 50
The Dynamic Programming Principle	p. 56
Notes and Extensions	p. 62
Problems	p. 64
References	p. 65
Infinite Horizon Optimal Control	p. 67
Definition and Well Posedness of the Problem	p. 67
The Dynamic Programming Principle	p. 70
Relaxed Dynamic Programming	p. 75
Notes and Extensions	p. 81
Problems	p. 83
References	p. 84
Stability and Suboptimality Using Stabilizing Constraints	p. 87
The Relaxed Dynamic Programming Approach	p. 87
Equilibrium Endpoint Constraint	p. 88
Lyapunov Function Terminal Cost	p. 95
Suboptimality and Inverse Optimality	p. 101
Notes and Extensions	p. 109
Problems	p. 110
References	p. 112
Stability and Suboptimality Without Stabilizing Constraints	p. 113
Setting and Preliminaries	p. 113
Asymptotic Controllability with Respect to l	p. 116
Implications of the Controllability Assumption	p. 119
Computation of	p. 121
Main Stability and Performance Results	p. 125
Design of Good Running Costs l	p. 133
Semiglobal and Practical Asymptotic Stability	p. 142
Proof of Proposition 6.17	p. 150
Notes and Extensions	p. 159
Problems	p. 161
References	p. 162
Variants and Extensions	p. 165
Mixed Constrained-Unconstrained Schemes	p. 165
Unconstrained NMPC with Terminal W8	p. 168
Nonpositive Definite Running Cost	p. 170
Multistep NMPC-Feedback Laws	p. 174
Fast Sampling	p. 176
Compensation of Computation Times	p. 180
Online Measurement of	p. 183
Adaptive Optimization Horizon	p. 191
Nonoptimal NMPC	p. 198
Beyond Stabilization and Tracking	p. 207
References	p. 209
Feasibility and Robustness	p. 211
The Feasibility Problem	p. 211
Feasibility of Unconstrained NMPC Using Exit Sets	p. 214
Feasibility of Unconstrained NMPC Using Stability	p. 217
Comparing Terminal Constrained vs. Unconstrained NMPC	p. 222
Robustness: Basic Definition and Concepts	p. 225
Robustness Without State Constraints	p. 227
Examples for Nonrobustness Under State Constraints	p. 232
Robustness with State Constraints via Robust-optimal Feasibility	p. 237
Robustness with State Constraints via Continuity of VN	p. 241
Notes and Extensions	p. 246
Problems	p. 249
References	p. 249
Numerical Discretization	p. 251
Basic Solution Methods	p. 251
Convergence Theory	p. 256
Adaptive Step Size Control	p. 260
Using the Methods Within the NMPC Algorithms	p. 264
Numerical Approximation Errors and Stability	p. 266
Notes and Extensions	p. 269
Problems	p. 271
References	p. 272
Numerical Optimal Control of Nonlinear Systems	p. 275
Discretization of the NMPC Problem	p. 275
Unconstrained Optimization	p. 288
Constrained Optimization	p. 292
Implementation Issues in NMPC	p. 315
Warm Start of the NMPC Optimization	p. 324
Nonoptimal NMPC	p. 331
Notes and Extensions	p. 335
Problems	p. 337
References	p. 337
Appendix NMPC Software Supporting This Book	p. 341
The MATLAB NMPC Routine	p. 341
Additional MATLAB and MAPLE Routines	p. 343
The C++ NMPC Software	p. 345
Glossary	p. 347
Index	p. 353
Table of Contents provided by Ingram. All Rights Reserved.

Nonlinear Model Predictive Control

Theory and Algorithms

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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