Robust and Adaptive Model Predictive Control of Nonlinear Systems

by Martin Guay, Veronica Adetola, Darryl DeHaan

Overview

Most physical systems possess parametric uncertainties or unmeasurable parameters and, since parametric uncertainty may degrade the performance of model predictive control (MPC), mechanisms to update the unknown or uncertain parameters are desirable in application. One possibility is to apply adaptive extensions of MPC in which parameter estimation and control are performed online. This book proposes such an approach, with a design methodology for adaptive robust nonlinear MPC (NMPC) systems in the presence of disturbances and parametric uncertainties. One of the key concepts pursued is the concept of set-based adaptive parameter estimation, which provides a mechanism to estimate the unknown parameters as well as an estimate of the parameter uncertainty set. The knowledge of non-conservative uncertain set estimates is exploited in the design of robust adaptive NMPC algorithms that guarantee robustness of the NMPC system to parameter uncertainty.

Topics covered include: a review of nonlinear MPC; extensions for performance improvement; introduction to adaptive robust MPC; computational aspects of robust adaptive MPC; finite-time parameter estimation in adaptive control; performance improvement in adaptive control; adaptive MPC for constrained nonlinear systems; adaptive MPC with disturbance attenuation; robust adaptive economic MPC; setbased estimation in discrete-time systems; and robust adaptive MPC for discrete-time systems.

Product Details

ISBN-13:	9781849195522
Publisher:	The Institution of Engineering and Technology
Publication date:	11/13/2015
Series:	Control, Robotics and Sensors
Pages:	272
Product dimensions:	9.40(w) x 6.40(h) x 0.80(d)

About the Author

Martin Guay is a Professor at the Faculty of Engineering and Applied Science at Queens University, Canada, where his research interests include process control, statistical modeling of dynamical systems, extremum seeking control, observation and adaptation in nonlinear systems, and supervisory control design for flexible manufacturing systems. He is Deputy Editor-in-Chief of the Journal of Process Control, and Associate Editor of Automatica, IEEE Transactions on Control Systems Technology and Canadian Journal of Chemical Engineering.

Veronica Adetola is a Research Engineer at the United Technologies Research Centre, USA. Her research interests include model-based design and control of complex dynamical systems, model predictive control of constrained uncertain systems, real-time optimization, adaptive control, parameter estimation and system identification.

Darryl DeHaan is currently a Senior Process Control Engineer with LyondellBasell and has been engaged in both industrial controller implementation and research since 2006. He has a Ph.D. in Chemical Engineering from Queens University, Canada, where his research efforts focused on model predictive control techniques for nonlinear uncertain systems.

Table of Contents

List of figures x

List of tables xiv

Acknowledgments xv

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

Bibliography 237

Index 249