| List of Symbols and Abbreviations | p. xxvii |
| Discrete-time MPC for Beginners | p. 1 |
| Introduction | p. 1 |
| Day-to-day Application Example of Predictive Control | p. 1 |
| Models Used in the Design | p. 3 |
| State-space Models with Embedded Integrator | p. 4 |
| Single-input and Single-output System | p. 4 |
| MATLAB Tutorial: Augmented Design Model | p. 6 |
| Predictive Control within One Optimization Window | p. 7 |
| Prediction of State and Output Variables | p. 7 |
| Optimization | p. 9 |
| MATLAB Tutorial: Computation of MPC Gains | p. 13 |
| Receding Horizon Control | p. 15 |
| Closed-loop Control System | p. 16 |
| MATLAB Tutorial: Implementation of Receding Horizon Control | p. 20 |
| Predictive Control of MIMO Systems | p. 22 |
| General Formulation of the Model | p. 22 |
| Solution of Predictive Control of MIMO Systems | p. 26 |
| State Estimation | p. 27 |
| Basic Ideas About an Observer | p. 28 |
| Basic Results About Observability | p. 30 |
| Kalman Filter | p. 33 |
| Tuning Observer Dynamics | p. 34 |
| State Estimate Predictive Control | p. 34 |
| Summary | p. 37 |
| Problems | p. 39 |
| Discrete-time MPC with Constraints | p. 43 |
| Introduction | p. 43 |
| Motivational Examples | p. 43 |
| Formulation of Constrained Control Problems | p. 47 |
| Frequently Used Operational Constraints | p. 47 |
| Constraints as Part of the Optimal Solution | p. 50 |
| Numerical Solutions Using Quadratic Programming | p. 53 |
| Quadratic Programming for Equality Constraints | p. 53 |
| Minimization with Inequality Constraints | p. 58 |
| Primal-Dual Method | p. 62 |
| Hildreth's Quadratic Programming Procedure | p. 63 |
| MATLAB Tutorial: Hildreth's Quadratic Programming | p. 67 |
| Closed-form Solution of $$ | p. 68 |
| Predictive Control with Constraints on Input Variables | p. 69 |
| Constraints on Rate of Change | p. 70 |
| Constraints on Amplitude of the Control | p. 73 |
| Constraints on Amplitude and Rate of Change | p. 77 |
| Constraints on the Output Variable | p. 78 |
| Summary | p. 81 |
| Problems | p. 83 |
| Discrete-time MPC Using Laguerre Functions | p. 85 |
| Introduction | p. 85 |
| Laguerre Functions and DMPC | p. 85 |
| Discrete-time Laguerre Networks | p. 86 |
| Use of Laguerre Networks in System Description | p. 90 |
| MATLAB Tutorial: Use of Laguerre Functions in System Modelling | p. 90 |
| Use of Laguerre Functions in DMPC Design | p. 92 |
| Design Framework | p. 93 |
| Cost Functions | p. 94 |
| Minimization of the Objective Function | p. 97 |
| Convolution Sum | p. 98 |
| Receding Horizon Control | p. 98 |
| The Optimal Trajectory of Incremental Control | p. 99 |
| Extension to MIMO Systems | p. 106 |
| MATLAB Tutorial Notes | p. 108 |
| DMPC Computation | p. 108 |
| Predictive Control System Simulation | p. 115 |
| Constrained Control Using Laguerre Functions | p. 118 |
| Constraints on the Difference of the Control Variable | p. 118 |
| Constraints on the Amplitudes of the Control Signal | p. 121 |
| Stability Analysis | p. 127 |
| Stability with Terminal-State Constraints | p. 127 |
| Stability with Large Prediction Horizon | p. 129 |
| Closed-form Solution of Constrained Control for SISO Systems | p. 131 |
| MATLAB Tutorial: Constrained Control of DC Motor | p. 135 |
| Summary | p. 143 |
| Problems | p. 144 |
| Discrete-time MPC with Prescribed Degree of Stability | p. 149 |
| Introduction | p. 149 |
| Finite Prediction Horizon: Re-visited | p. 149 |
| Motivational Example | p. 150 |
| Origin of the Numerical Conditioning Problem | p. 150 |
| Use of Exponential Data Weighting | p. 152 |
| The Cost Function | p. 152 |
| Optimization of Exponentially Weighted Cost Function | p. 153 |
| Interpretation of Results from Exponential Weighting | p. 156 |
| Asymptotic Closed-loop Stability with Exponential Weighting | p. 158 |
| Modification of Q and R Matrices | p. 158 |
| Interpretation of the Results | p. 160 |
| Discrete-time MPC with Prescribed Degree of Stability | p. 165 |
| Tuning Parameters for Closed-loop Performance | p. 170 |
| The Relationship Between P$$ and Jmin | p. 171 |
| Tuning Procedure Once More | p. 176 |
| Exponentially Weighted Constrained Control | p. 179 |
| Additional Benefit | p. 182 |
| Summary | p. 186 |
| Problems | p. 188 |
| Continuous-time Orthonormal Basis Functions | p. 193 |
| Introduction | p. 193 |
| Orthonormal Expansion | p. 193 |
| Laguerre Functions | p. 194 |
| Approximating Impulse Responses | p. 197 |
| Kautz Functions | p. 202 |
| Kautz Functions in the Time Domain | p. 204 |
| Modelling the System Impulse Response | p. 205 |
| Summary | p. 206 |
| Problems | p. 207 |
| Continuous-time MPC | p. 209 |
| Introduction | p. 209 |
| Model Structures for CMPC Design | p. 209 |
| Model Structure | p. 211 |
| Controllability and Observability of the Model | p. 215 |
| Model Predictive Control Using Finite Prediction Horizon | p. 216 |
| Modelling the Control Trajectory | p. 217 |
| Predicted Plant Response | p. 218 |
| Analytical Solution of the Predicted Response | p. 219 |
| The Recursive Solution | p. 221 |
| Optimal Control Strategy | p. 224 |
| Receding Horizon Control | p. 227 |
| Implementation of the Control Law in Digital Environment | p. 234 |
| Estimation of the States | p. 234 |
| MATLAB Tutorial: Closed-loop Simulation | p. 237 |
| Model Predictive Control Using Kautz Functions | p. 240 |
| Summary | p. 244 |
| Problems | p. 245 |
| Continuous-time MPC with Constraints | p. 249 |
| Introduction | p. 249 |
| Formulation of the Constraints | p. 249 |
| Frequently Used Constraints | p. 249 |
| Constraints as Part of the Optimal Solution | p. 251 |
| Numerical Solutions for the Constrained Control Problem | p. 257 |
| Real-time Implementation of Continuous-time MPC | p. 262 |
| Summary | p. 266 |
| Problems | p. 267 |
| Continuous-time MPC with Prescribed Degree of Stability | p. 271 |
| Introduction | p. 271 |
| Motivating Example | p. 271 |
| CMPC Design Using Exponential Data Weighting | p. 274 |
| CMPC with Asymptotic Stability | p. 277 |
| Continuous-time MPC with Prescribed Degree of Stability | p. 283 |
| The Original Anderson and Moore's Results | p. 283 |
| CMPC with a Prescribed Degree of Stability | p. 284 |
| Tuning Parameters and Design Procedure | p. 286 |
| Constrained Control with Exponential Data Weighting | p. 288 |
| Summary | p. 291 |
| Problems | p. 293 |
| Classical MPC Systems in State-space Formulation | p. 297 |
| Introduction | p. 297 |
| Generalized Predictive Control in State-space Formulation | p. 298 |
| Special Class of Discrete-time State-space Structures | p. 298 |
| General NMSS Structure for GPC Design | p. 301 |
| Generalized Predictive Control in State-space Formulation | p. 302 |
| Alternative Formulation to GPC | p. 305 |
| Alternative Formulation for SISO Systems | p. 305 |
| Closed-loop Poles of the Predictive Control System | p. 307 |
| Transfer Function Interpretation | p. 310 |
| Extension to MIMO Systems | p. 313 |
| MNSS Model for MIMO Systems | p. 314 |
| Case Study of NMSS Predictive Control System | p. 315 |
| Continuous-time NMSS model | p. 320 |
| Case Studies for Continuous-time MPC | p. 323 |
| Predictive Control Using Impulse Response Models | p. 326 |
| Summary | p. 329 |
| Problems | p. 330 |
| Implementation of Predictive Control Systems | p. 333 |
| Introduction | p. 333 |
| Predictive Control of DC Motor Using a Micro-controller | p. 333 |
| Hardware Configuration | p. 334 |
| Model Development | p. 336 |
| DMPC Tuning | p. 337 |
| DMPC Implementation | p. 338 |
| Experimental Results | p. 339 |
| Implementation of Predictive Control Using xPC Target | p. 340 |
| Overview | p. 340 |
| Creating a Simulink Embedded Function | p. 342 |
| Constrained Control of DC Motor Using xPC Target | p. 347 |
| Control of Magnetic Bearing Systems | p. 349 |
| System Identification | p. 351 |
| Experimental Results | p. 352 |
| Continuous-time Predictive Control of Food Extruder | p. 353 |
| Experimental Setup | p. 355 |
| Mathematical Models | p. 357 |
| Operation of the Model Predictive Controller | p. 358 |
| Controller Tuning Parameters | p. 359 |
| On-line Control Experiments | p. 360 |
| Summary | p. 365 |
| References | p. 367 |
| Index | p. 373 |
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