Theory and Numerics

of

Nonlinear Model Predictive Control

James B. Rawlings |

Department of Chemical and Biological Engineering |

University of Wisconsin |

Madison, Wisconsin |

Copyright (C) 2015 James B. Rawlings |

The course overheads are provided below. Clicking on the thumbnail figures displays the code that was used to create the figure. In addition, the complete collection of the CasADi/Python files and Matlab m-files in single zip files are available for download from the links below:

**CasADi/Python**:-
mpc-short-course-casadi-py-files-v1.0.zip

**Octave/Matlab**:-
mpc-short-course-matlab-m-files-v1.0.zip

Monday 11:00-12:00: Exercises:

Monday 13:00-14:30: Tracking, disturbances, and zero offset

Monday 15:00-16:00: Exercises:

Monday 16:30-18:00: Review and exercise solutions

Tuesday 11:00-12:00: Exercises:

Tuesday 13:00-14:30: Nonlinear moving horizon state estimation

Tuesday 15:00-16:00: Exercises:

Tuesday 16:30-18:00: Review and exercise solutions

**Control concepts: **Linear quadratic regulation, stage cost, cost-to-go, linear quadratic estimation, Kalman filter, dynamic programming, recursive least squares, controllability and stabilizability, regulator convergence, infinite horizon regulator, observability and detectability, estimator convergence

**Programming concepts: **Representation with ss(A,B,C,D), c2d(sys, DT), and tf(num, den), anti-reset windup, minimal realization with minreal(sys)

Slides (4up version) |

**Control concepts: **Setpoint tracking, steady-state targets, dynamic regulation, state estimation, disturbance models, zero offset

**Programming concepts: **linear-quadratic regulator/estimator with dlqr(A,B,Q,R)/dlqe(A,C,Q,R), quadratic programming, creating CasADi models with getCasadiFunc, simulation with OneStepSimulator

Slides (4up version) |

**Control concepts: **Equilibrium, positive invariance, K, K-infinty, KL functions, Lyapunov stability, asymptotic stability, exponential stability, Lyapunov function, converse theorems, stability of nonlinear MPC

**Programming concepts: **solving nonlinear OCPs with nmpc

Slides (4up version) |

**Control concepts: **Full information estimation, nonlinear detectability, incremental input/output to state stability , estimator stability, global asymptotic stability (GAS), robust GAS, moving horizon estimation (MHE), arrival cost, stability of MHE

**Programming concepts: **solving nonlinear estimation with nmhe

Slides (4up version) |

Figure 1 (slide 67):Example results for MHE on batch reactor system. |

Research monograph (available for purchase and download) |