Model Predictive Control

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192 10 Constrained Optimal Control x 2 (0) x 2 (2) x 2 (4) 10 5 0 −5 −10 −10 −5 0 5 10 x (0) 1 (a) Partition of the state space for the affine control law u∗ (0)(Nr 0 = 26) 10 5 0 −5 −10 −10 −5 0 5 10 x (2) 1 (c) Partition of the state space for the affine control law u∗ (2) (Nr 2 = 26) 10 5 0 −5 −10 −10 −5 0 5 10 x (4) 1 (e) Partition of the state space for the affine control law u∗ (4) (Nr 4 = 12) x 2 (1) x 2 (3) x 2 (5) 10 5 0 −5 −10 −10 −5 0 5 10 x (1) 1 (b) Partition of the state space for the affine control law u∗ (1) (Nr 1 = 28) 10 5 0 −5 −10 −10 −5 0 5 10 x (3) 1 (d) Partition of the state space for the affine control law u∗ (3) (Nr 3 = 12) 10 5 0 −5 −10 −10 −5 0 5 10 x (5) 1 (f) Partition of the state space for the affine control law u∗ (5) (Nr 5 = 8) Figure 10.11 Example 10.9: Partition of the state space for optimal control law
10.6 State-Feedback Solution, Minimum-Time Control 193 x 2 10 8 6 4 2 0 −2 −4 −6 −8 −10 −10 −8 −6 −4 −2 0 x 1 2 4 6 8 10 (a) Minimum-Time State Space Partition (b) Minimum-Time Control Law Figure 10.12 Example 10.10: Minimum-Time Partition of the State Space and Control Law
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Predictive Control for linear and h
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ii Preface Dynamic optimization has
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iv book, in Chapter 3 we introduce
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vi Acknowledgements Large part of t
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viii Contents III Optimal Control 1
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x Contents Symbols and Acronyms Log
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xii Contents Dynamical Systems x(k)
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Chapter 1 Main Concepts In this Cha
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1.1 Optimization Problems 5 Active,
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1.2 Convexity 7 Operations preservi
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Chapter 2 Optimality Conditions 2.1
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2.2 Lagrange Duality Theory 11 wher
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2.3 Complementary Slackness 13 Note
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2.4 Karush-Kuhn-Tucker Conditions 1
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2.4 Karush-Kuhn-Tucker Conditions 1
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Chapter 3 Polyhedra, Polytopes and
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3.2 Polyhedra Definitions and Repre
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3.2 Polyhedra Definitions and Repre
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3.3 Polytopal Complexes 25 Definiti
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3.4 Basic Operations on Polytopes 2
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3.5 Operations on P-collections 37
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Chapter 4 Linear and Quadratic Opti
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4.1 Linear Programming 47 4.1.2 Dua
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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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8.2 Solution via Recursive Approach
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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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Page 165: Part IV Constrained Optimal Control
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Page 248 and 249: 234 12 Constrained Robust Optimal C
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242 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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