Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller.
Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems: The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). The synthesized discrete-time optimal controller can be directly implemented in real-time systems. The book also proposes the use of recurrent neural networks to model discrete-time nonlinear systems. Combined with the inverse optimal control approach, such models constitute a powerful tool to deal with uncertainties such as unmodeled dynamics and disturbances.
Learn from Simulations and an In-Depth Case Study: The authors include a variety of simulations to illustrate the effectiveness of the synthesized controllers for stabilization and trajectory tracking of discrete-time nonlinear systems. An in-depth case study applies the control schemes to glycemic control in patients with type 1 diabetes mellitus, to calculate the adequate insulin delivery rate required to prevent hyperglycemia and hypoglycemia levels.
The discrete-time optimal and robust control techniques proposed can be used in a range of industrial applications, from aerospace and energy to biomedical and electromechanical systems. Highlighting optimal and efficient control algorithms, this is a valuable resource for researchers, engineers, and students working in nonlinear system control.
Author(s): Edgar N. Sanchez, Fernando Ornelas-Tellez
Series: System of Systems Engineering
Publisher: CRC Press
Year: 2013
Language: English
Pages: xxx+238
Discrete-Time Inverse Optimal Control for Nonlinear Systems......Page 4
Contents......Page 8
List of Figures......Page 14
List of Tables......Page 18
Preface......Page 20
Acknowledgments......Page 24
Fernando Ornelas-Tellez......Page 26
Notations and Acronyms......Page 28
1 Introduction......Page 32
1.1 Inverse Optimal Control via Passivity......Page 34
1.2 Inverse Optimal Control via CLF......Page 35
1.3 Neural Inverse Optimal Control......Page 37
1.4 Motivation......Page 38
2.1 Optimal Control......Page 40
2.2 Lyapunov Stability......Page 43
2.3 Robust Stability Analysis......Page 46
2.3.1 Optimal Control for Disturbed Systems......Page 51
2.4 Passivity......Page 52
2.5 Neural Identification......Page 54
2.5.2 Discrete-Time Recurrent High Order Neural Network......Page 55
2.5.2.1 RHONN Models......Page 58
2.5.2.2 On-line Learning Law......Page 59
2.5.3 Discrete-Time Recurrent Multilayer Perceptron......Page 60
3.1 Inverse Optimal Control via Passivity......Page 66
3.1.1 Stabilization of a Nonlinear System......Page 72
3.2 Trajectory Tracking......Page 77
3.2.1 Example: Trajectory Tracking of a Nonlinear System......Page 80
3.2.2 Application to a Planar Robot......Page 81
3.2.2.1 Robot Model......Page 82
3.2.2.2 Robot as an Affine System......Page 85
3.2.2.3 Control Synthesis......Page 86
3.2.2.4 Simulation Results......Page 87
3.3 Passivity-Based Inverse Optimal Control for a Class of Nonlinear
Positive Systems......Page 89
3.4 Conclusions......Page 96
4.1 Inverse Optimal Control via CLF......Page 98
4.1.1 Example......Page 106
4.1.2 Inverse Optimal Control for Linear Systems......Page 110
4.2 Robust Inverse Optimal Control......Page 112
4.3 Trajectory Tracking Inverse Optimal Control......Page 123
4.3.1.1 Boost Converter Model......Page 127
4.3.1.2 Control Synthesis......Page 129
4.3.1.3 Simulation Results......Page 130
4.4 CLF-Based Inverse Optimal Control for a Class of Nonlinear
Positive Systems......Page 131
4.5 Conclusions......Page 138
5.1 Speed-Gradient Algorithm for the Inverse Optimal Control......Page 140
5.1.1 Speed-Gradient Algorithm......Page 141
5.1.2 Summary of the Proposed SG Algorithm to Calculate
Parameter pk......Page 146
5.1.3 SG Inverse Optimal Control......Page 148
5.1.3.1 Example......Page 152
5.1.4 Application to the Inverted Pendulum on a Cart......Page 153
5.1.4.1 Simulation Results......Page 157
5.2 Speed-Gradient Algorithm for Trajectory Tracking......Page 159
5.2.1 Example......Page 164
5.3 Trajectory Tracking for Systems in Block-Control Form......Page 166
5.3.1 Example......Page 171
5.4 Conclusions......Page 173
6 Neural Inverse Optimal Control......Page 174
6.1.1 Stabilization......Page 175
6.1.2 Example......Page 176
6.1.2.2 Control Synthesis......Page 177
6.1.3 Trajectory Tracking......Page 178
6.1.3.1 Example......Page 180
6.1.4 Application to a Synchronous Generator......Page 181
6.1.4.1 Synchronous Generator Model......Page 183
6.1.4.2 Neural Identification for the Synchronous
Generator......Page 185
6.1.4.4 Simulation Results......Page 187
6.1.5 Comparison......Page 189
6.2 Block-Control Form: A Nonlinear Systems Particular Class......Page 191
6.2.1 Block Transformation......Page 192
6.2.3.1 Robot Model Description......Page 195
6.2.3.2 Neural Network Identifier......Page 196
6.2.3.3 Control Synthesis......Page 197
6.2.3.4 Simulation Results......Page 198
6.3 Conclusions......Page 201
7.1 Introduction......Page 204
7.2 Passivity Approach......Page 208
7.2.1 Virtual Patient......Page 209
7.2.2 State Space Representation......Page 215
7.2.3 Control Law Implementation......Page 220
7.3 CLF Approach......Page 221
7.3.1 Simulation Results via CLF......Page 224
7.3.2 Passivity versus CLF......Page 225
7.4 Conclusions......Page 228
8 Conclusions......Page 230
References......Page 234
Index......Page 252
FIGURE 3.7......Page 264
FIGURE 4.6......Page 265
FIGURE 5.10......Page 266
FIGURE 6.7......Page 267
FIGURE 7.1......Page 268
FIGURE 7.5......Page 269
