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1 | (12) |
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4 | (1) |
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5 | (2) |
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7 | (2) |
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1.4 Concluding Remarks and Comments on the Intended Readership |
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9 | (4) |
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9 | (4) |
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2 MPC with No Model Uncertainty |
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13 | (54) |
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13 | (2) |
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2.2 The Unconstrained Optimum |
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15 | (3) |
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2.3 The Dual-Mode Prediction Paradigm |
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18 | (3) |
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21 | (3) |
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2.5 Controlled Invariant Sets and Recursive Feasibility |
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24 | (5) |
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2.6 Stability and Convergence |
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29 | (3) |
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2.7 Autonomous Prediction Dynamics |
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32 | (10) |
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2.7.1 Polytopic and Ellipsoidal Constraint Sets |
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33 | (3) |
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2.7.2 The Predicted Cost and MPC Algorithm |
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36 | (2) |
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2.7.3 Offline Computation of Ellipsoidal Invariant Sets |
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38 | (4) |
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42 | (4) |
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2.9 Optimized Prediction Dynamics |
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46 | (5) |
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2.10 Early MPC Algorithms |
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51 | (6) |
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57 | (10) |
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62 | (5) |
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3 Open-Loop Optimization Strategies for Additive Uncertainty |
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67 | (54) |
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68 | (3) |
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3.2 State Decomposition and Constraint Handling |
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71 | (12) |
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3.2.1 Robustly Invariant Sets and Recursive Feasibility |
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73 | (3) |
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3.2.2 Interpretation in Terms of Tubes |
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76 | (7) |
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3.3 Nominal Predicted Cost: Stability and Convergence |
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83 | (3) |
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3.4 A Game Theoretic Approach |
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86 | (9) |
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3.5 Rigid and Homothetic Tubes |
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95 | (10) |
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96 | (5) |
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3.5.2 Homothetic Tube MPC |
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101 | (4) |
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3.6 Early Robust MPC for Additive Uncertainty |
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105 | (7) |
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3.6.1 Constraint Tightening |
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105 | (3) |
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108 | (4) |
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112 | (9) |
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119 | (2) |
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4 Closed-Loop Optimization Strategies for Additive Uncertainty |
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121 | (54) |
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4.1 General Feedback Strategies |
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122 | (23) |
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4.1.1 Active Set Dynamic Programming for Min-Max Receding Horizon Control |
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130 | (7) |
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4.1.2 MPC with General Feedback Laws |
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137 | (8) |
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4.2 Parameterized Feedback Strategies |
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145 | (30) |
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4.2.1 Disturbance-Affine Robust MPC |
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146 | (7) |
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4.2.2 Parameterized Tube MPC |
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153 | (11) |
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4.2.3 Parameterized Tube MPC Extension with Striped Structure |
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164 | (8) |
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172 | (3) |
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5 Robust MPC for Multiplicative and Mixed Uncertainty |
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175 | (68) |
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176 | (2) |
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5.2 Linear Matrix Inequalities in Robust MPC |
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178 | (9) |
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5.2.1 Dual Mode Predictions |
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184 | (3) |
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5.3 Prediction Dynamics in Robust MPC |
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187 | (15) |
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5.3.1 Prediction Dynamics Optimized to Maximize the Feasible Set |
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192 | (6) |
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5.3.2 Prediction Dynamics Optimized to Improve Worst-Case Performance |
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198 | (4) |
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5.4 Low-Complexity Poly topes in Robust MPC |
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202 | (11) |
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5.4.1 Robust Invariant Low-Complexity Polytopic Sets |
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202 | (5) |
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5.4.2 Recursive State Bounding and Low-Complexity Polytopic Tubes |
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207 | (6) |
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5.5 Tubes with General Complexity Polytopic Cross Sections |
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213 | (10) |
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5.6 Mixed Additive and Multiplicative Uncertainty |
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223 | (10) |
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233 | (10) |
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238 | (5) |
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6 Introduction to Stochastic MPC |
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243 | (28) |
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245 | (6) |
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6.2 Predicted Cost and Unconstrained Optimal Control Law |
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251 | (6) |
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6.3 Mean-Variance Predicted Cost |
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257 | (3) |
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6.4 Early Stochastic MPC Algorithms |
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260 | (4) |
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6.4.1 Auto-Regressive Moving Average Models |
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260 | (3) |
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6.4.2 Moving Average Models |
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263 | (1) |
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6.5 Application to a Sustainable Development Problem |
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264 | (7) |
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268 | (3) |
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7 Feasibility, Stability, Convergence and Markov Chains |
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271 | (32) |
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7.1 Recursive Feasibility |
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272 | (6) |
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7.2 Prototype SMPC Algorithm: Stability and Convergence |
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278 | (8) |
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278 | (3) |
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281 | (3) |
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7.2.3 Supermartingale Convergence Analysis |
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284 | (2) |
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7.3 Probabilistically Invariant Ellipsoids |
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286 | (6) |
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7.4 Markov Chain Models Based on Tubes with Polytopic Cross Sections |
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292 | (11) |
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301 | (2) |
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8 Explicit Use of Probability Distributions in SMPC |
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303 | (40) |
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8.1 Polytopic Tubes for Additive Disturbances |
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304 | (7) |
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8.2 Striped Prediction Structure with Disturbance Compensation in Mode 2 |
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311 | (5) |
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8.3 SMPC with Bounds on Average Numbers of Constraint Violations |
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316 | (3) |
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8.4 Stochastic Quadratic Bounds for Additive Disturbances |
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319 | (9) |
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8.5 Polytopic Tubes for Additive and Multiplicative Uncertainty |
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328 | (15) |
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340 | (3) |
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343 | (4) |
Solutions to Exercises |
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347 | (30) |
Index |
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377 | |