Model Predictive Control

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xii Contents Dynamical Systems x(k) Measurement/Estimation of state x at time k Predicted value of state x at time k, given a measurement x(0) xk x + Successor of vector x, i.e. if x = x(k) then x + = x(k + 1) F∞ O∞ C∞ K∞ OLQR ∞ Minimal robust positively invariant set Maximal robust positively invariant set Maximal robust control invariant set Maximal robust stabilizable set Maximal positively invariant set O∞ for LTI system under LQR feedback
Part I Basics on Optimization
Page 1: Predictive Control for linear and h
Page 4 and 5: ii Preface Dynamic optimization has
Page 6 and 7: iv book, in Chapter 3 we introduce
Page 8 and 9: vi Acknowledgements Large part of t
Page 10 and 11: viii Contents III Optimal Control 1
Page 12 and 13: x Contents Symbols and Acronyms Log
Page 17 and 18: Chapter 1 Main Concepts In this Cha
Page 19 and 20: 1.1 Optimization Problems 5 Active,
Page 21 and 22: 1.2 Convexity 7 Operations preservi
Page 23 and 24: Chapter 2 Optimality Conditions 2.1
Page 25 and 26: 2.2 Lagrange Duality Theory 11 wher
Page 27 and 28: 2.3 Complementary Slackness 13 Note
Page 29 and 30: 2.4 Karush-Kuhn-Tucker Conditions 1
Page 31 and 32: 2.4 Karush-Kuhn-Tucker Conditions 1
Page 33 and 34: Chapter 3 Polyhedra, Polytopes and
Page 35 and 36: 3.2 Polyhedra Definitions and Repre
Page 37 and 38: 3.2 Polyhedra Definitions and Repre
Page 39 and 40: 3.3 Polytopal Complexes 25 Definiti
Page 41 and 42: 3.4 Basic Operations on Polytopes 2
Page 51 and 52: 3.5 Operations on P-collections 37
Page 59 and 60: Chapter 4 Linear and Quadratic Opti
Page 61 and 62: 4.1 Linear Programming 47 4.1.2 Dua
Page 63 and 64: 4.1 Linear Programming 49 x2 c =
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4.1 Linear Programming 51 J(z) 6 5
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4.2 Quadratic Programming 53 0.5z
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4.3 Mixed-Integer Optimization 55 A
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4.3 Mixed-Integer Optimization 57 4
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Part II Multiparametric Programming
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62 5 General Results for Multiparam
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74 6 Multiparametric Programming: a
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100 6 Multiparametric Programming:
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Chapter 7 General Formulation and D
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7.2 Solution via Batch Approach 119
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7.3 Solution via Recursive Approach
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7.4 Optimal Control Problem with In
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7.4 Optimal Control Problem with In
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7.5 Lyapunov Stability 127 - asympt
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7.5 Lyapunov Stability 129 where x(
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7.5 Lyapunov Stability 131 An effec
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Chapter 8 Linear Quadratic Optimal
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8.4 Infinite Horizon Problem 137 As
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8.5 Stability of the Infinite Horiz
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Chapter 9 1/∞ Norm Optimal Contro
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9.1 Solution via Batch Approach 143
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9.4 Infinite Horizon Problem 147 wh
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9.4 Infinite Horizon Problem 149 wi
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Part IV Constrained Optimal Control
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154 10 Constrained Optimal Control
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196 11 Receding Horizon Control Mod
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228 11 Receding Horizon Control x 2
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230 11 Receding Horizon Control x 2
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232 11 Receding Horizon Control
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234 12 Constrained Robust Optimal C
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268 13 On-line Control Computation
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Chapter 14 Models of Hybrid Systems
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14.2 Piecewise Affine Systems 285 X
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14.2 Piecewise Affine Systems 287 x
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14.2 Piecewise Affine Systems 289 k
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14.3 Discrete Hybrid Automata 291 A
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14.3 Discrete Hybrid Automata 293 e
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14.3 Discrete Hybrid Automata 295
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14.4 Logic and Mixed-Integer Inequa
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14.5 Mixed Logical Dynamical System
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14.7 The HYSDEL Modeling Language 3
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14.8 Literature Review 307 systems
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14.8 Literature Review 309 and allo
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Chapter 15 Optimal Control of Hybri
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15.1 Problem Formulation 313 Consid
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15.2 Properties of the State Feedba
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15.4 Computation of the Optimal Con
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15.6 State Feedback Solution via Re
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15.8 Receding Horizon Control 335 U
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15.8 Receding Horizon Control 337 x
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15.8 Receding Horizon Control 339 x
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References [1] L. Chisci A. Bempora
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References 343 [25] A. Bemporad. Re
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References 345 [52] F. Blanchini an
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References 347 [81] B. De Schutter
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References 349 [110] E. G. Gilbert
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References 351 [138] J.N. Hooker. L
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References 353 [164] M. Lazar, D. M
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References 355 [194] K. R. Muske an
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References 357 [222] M. Schechter.
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References 359 [249] R. Vidal, S. S
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