Robust and adaptive model predictive control of non-linear systems /

Most physical systems possess parameter uncertainties or unmeasurable parameters and since parametric uncertainty may degrade the performance of model predictive control (MPC), mechanism to update the unknown or uncertain parameters are desirable in application. One possibility is to apply adaptive...

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Bibliographic Details
Main Authors:	Guay, Martin, 1966- (Author), Adetola, Veronica (Author), DeHaan, Darryl (Author)
Corporate Author:	Alumni and Friends Memorial Book Fund
Format:	Book
Language:	English
Published:	Stevenage, United Kingdom : The Institution of Engineering and Technology, 2015
Series:	IET control, robotics and sensors series ; 83
Subjects:	Adaptive control systems Predictive control

Table of Contents:

1 Introduction 1
2 Optimal control 3
2.1 Emergence of optimal control 3
2.2 MPC as receding-horizon optimization 4
2.3 Current limitations in MPC 4
2.4 Notational and mathematical preliminaries 5
2.5 Brief review of optimal control 6
2.5.1 Variational approach: Euler, Lagrange & Pontryagin 6
2.5.2 Dynamic programming: Hamilton, Jacobi, & Bellman 8
2.5.3 Inverse-optimal control Lyapunov functions 9
3 Review of nonlinear MPC 11
3.1 Sufficient conditions for stability 12
3.2 Sampled-data framework 12
3.2.1 General nonlinear sampled-data feedback 12
3.2.2 Sampled-data MPC 13
3.2.3 Computational delay and forward compensation 14
3.3 Computational techniques 14
3.3.1 Single-step SQP with initial-value embedding 16
3.3.2 Continuation methods 17
3.3.3 Continuous-time adaptation for L2-stabilized systems 19
3.4 Robustness considerations 20
4 A real-time nonlinear MPC technique 23
4.1 Introduction 23
4.2 Problem statement and assumptions 24
4.3 Preliminary results 27
4.3.1 Incorporation of state constraints 27
4.3.2 Parameterization of the input trajectory 28
4.4 Genera] framework for real-time MPC 29
4.4.1 Description of algorithm 29
4.4.2 A notion of closed-loop "solutions" 31
4.4.3 Main result 32
4.5 Flow and jump mappings 33
4.5.1 Improvement by γ: the SD approach 33
4.5.2 Improvement by Ψ: a real-time approach 34
4.5.3 Other possible definitions for Ψ and γ 36
4.6 Computing the real-time update law 36
4.6.1 Calculating gradients 36
4.6.2 Selecting the descent metric 37
4.7 Simulation examples 38
4.7.1 Example 4.1 38
4.7.2 Example 4.2 39
4.8 Summary 41
4.9 Proofs for Chapter 4 42
4.9.1 Proof of Claim 4.2.2 42
4.9.2 Proof of Lemma 4.3.2 43
4.9.3 Proof of Corollary 4.3.6 43
4.9.4 Proof of Theorem 4.4.4 44
5 Extensions for performance improvement 47
5.1 General input parameterizations, and optimizing time support 47
5.1.1 Revised problem setup 48
5.1.2 General input parameterizations 49
5.1.3 Requirements for the local stabilizer 49
5.1.4 Closed-loop hybrid dynamics 52
5.1.5 Stability results 54
5.1.6 Simulation Example 5.1 55
5.1.7 Simulation Example 5.2 56
5.2 Robustness properties in overcoming locality 62
5.2.1 Robustness properties of the real-time approach 62
5.2.2 Robustly incorporating global optimization methods 65
5.2.3 Simulation Example 5.3 67
6 Introduction to adaptive robust MPC 71
6.1 Review of NMPC for uncertain systems 71
6.1.1 Explicit robust MPC using open-loop models 72
6.1.2 Explicit robust MPC using feedback models 73
6.1.3 Adaptive approaches to MPC 75
6.2 An adaptive approach to robust MPC 76
6.3 Minimally conservative approach 78
6.3.1 Problem description 78
6.4 Adaptive robust controller design framework 80
6.4.1 Adaptation of parametric uncertainty sets 80
6.4.2 Feedback-MPC framework 81
6.4.3 Generalized terminal conditions 82
6.4.4 Closed-loop stability 83
6.5 Computation and performance issues 84
6.5.1 Excitation of the closed-loop trajectories 84
6.5.2 A practical design approach for W and X, 84
6.6 Robustness issues 85
6.7 Example problem 88
6.8 Conclusions 89
6.9 Proofs for Chapter 6 89
6.9.1 Proof of Theorem 6.4.6 89
6.9.2 Proof of Proposition 6.5.1 91
6.9.3 Proof of Claim 6.6.1 92
6.9.4 Proof of Proposition 6.6.2 93
7 Computational aspects of robust adaptive MPC 97
7.1 Problem description 97
7.2 Adaptive robust design framework 98
7.2.1 Method for of closed-loop adaptive control 98
7.2.2 Finite-horizon robust MPC design 102
7.2.3 Stability of the underlying robust MPC 105
7.3 Internal model of the identifier 107
7.4 Incorporating asymptotic filters 110
7.5 Simulation example 111
7.5.1 System description 112
7.5.2 Terminal penalty 112
7.5.3 Simulation results 114
7.5.4 Discussion 116
7.6 Summary 117
7.7 Proofs for Chapter 7 117
7.7.1 Proof of Proposition 7.2.2 117
7.7.2 Proof of Theorem 7.2.8 119
7.7.3 Proof of Claim 7.3.5 122
7.7.4 Proof of Proposition 7.3.6 123
7.7.5 Proof of Corollary 7.3.8 125
8 Finite-time parameter estimation in adaptive control 127
8.1 Introduction 127
8.2 Problem description and assumptions 128
8.3 FT parameter identification 129
8.3.1 Absence of PE 131
8.4 Robustness property 132
8.5 Dither signal design 134
8.5.1 Dither signal removal 135
8.6 Simulation examples 135
8.6.1 Example 1 135
5.6.1 Example 2 135
8.7 Summary 138
9 Performance improvement in adaptive control 139
9.1 Introduction 139
9.2 Adaptive compensation design 139
9.3 Incorporating adaptive compensator for performance improvement 141
9.4 Dither signal update 142
9.5 Simulation example 143
9.6 Summary 146
10 Adaptive MPC for constrained nonlinear systems 147
10.1 Introduction 147
10.2 Problem description 148
10.3 Estimation of uncertainty 148
10.3.1 Parameter adaptation ]48
10.3.2 Set adaptation 149
10.4 Robust adaptive MPC-a min-max approach 15)
10.4.1 Implementation algorithm 151
10.4.2 Closed-loop robust stability 152
10.5 Robust adaptive MPC-a Lipschitz-based approach 153
10.5.1 Prediction of state error bound 154
10.5.2 Lipschitz-based finite horizon optimal control problem 154
10.5.3 Implementation algorithm 155
10.6 Incorporating FTI 155
10.6.1 FTI-based min-max approach 156
10.6.2 FTI-based Lipshitz-bound approach 157
10.7 Simulation example 159
10.8 Conclusions 160
10.9 Proofs of main results 160
10.9.1 Proof of Theorem 10.4.4 160
10.9.2 Proof of Theorem 10.5.3 163
11 Adaptive MPC with disturbance attenuation 165
11.1 Introduction 165
11.2 Revised problem set-up 165
11.3 Parameter and uncertainty set estimation 166
11.3.1 Preamble 155
11.3.2 Parameter adaptation 166
11.3.3 Set adaptation 168
11.4 Robust adaptive MPC 169
11.4.1 Min-max approach 169
11.4.2 Lipschitz-based approach 170
11.5 Closed-loop robust stability 171
11.5.1 Main results 172
11.6 Simulation example 172
11.7 Conclusions 173
12 Robust adaptive economic MPC 177
12.1 Introduction 177
12.2 Problem description 179
12.3 Set-based parameter estimation routine 180
12.3.1 Adaptive parameter estimation 180
12.3.2 Set adaptation 181
12.4 Robust adaptive economic MPC implementation 183
12.4.1 Alternative stage cost in economic MPC 183
12.4.2 A min-max approach 186
12.4.3 Main result 188
12.4.4 Lipschitz-based approach 190
12.5 Simulation example 192
12.5.1 Terminal penalty and terminal set design 193
12.6 Conclusions 199
13 Set-based estimation in discrete-time systems 201
13.1 Introduction 201
13.2 Problem description 202
13.3 FT parameter identification 203
13.4 Adaptive compensation design 204
13.5 Parameter uncertainty set estimation 205
13.5.1 Parameter update 205
13.5.2 Set update 208
13.6 Simulation examples 210
13.6.1 FT parameter identification 211
13.6.2 Adaptive compensation design 211
13.6.3 Parameter uncertainty set estimation 213
13.7 Summary 213
14 Robust adaptive MPC for discrete-time systems 215
14.1 Introduction 215
14.2 Problem description 215
14.3 Parameter and uncertainty set estimation 216
14.3.1 Parameter adaptation 216
14.3.2 Set update 217
14.4 Robust adaptive MPC 218
14.4.1 A min-max approach 218
14.4.2 Lipschitz-based approach 219
14.5 Closed-loop robust stability 221
14.5.1 Main results 221
14.6 Simulation example 223
14.6.1 Open-loop tests of the parameter estimation routine 225
14.6.2 Closed-loop simulations 228
14.6.3 Closed-loop simulations with disturbances 231
14.7 Summary 235

Robust and adaptive model predictive control of non-linear systems /

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