The approach based on linear matrix inequality (LMI) is now an important tool in analysis and design of modern control. We
will first review some basic modern control theory, and then learn from convex sets, convex functions and proceed to definition
of LMIs in control theory. Thereafter, we present the system analysis (focusing on stability) and design (focusing on stabilization
and robustness) with LMIs. Numerical simulations are also described and practiced in MATLAB and Simulink.

The approach based on linear matrix inequality (LMI) is now an important tool in analysis and design of modern control. We
will learn from convex sets, convex functions and then proceed to definition of LMIs in control theory. Thereafter, we present
the system analysis (focusing on stability) and design (focusing on stabilization and robustness) with LMIs. Numerical simulations
are also described and practiced in MATLAB and Simulink.

- Students can understand basic modern control theory, master the definition of convex sets, convex functions and apply basic idea of convex programming.
- Students can understand the definition and properties of LMIs, and perform basic simulation for solving LMIs.
- Students can derive and solve LMIs for analysis and design of modern control systems.

Class schedule | HW assignments (Including preparation and review of the class.) | Amount of Time Required | |
---|---|---|---|

1． | Course guidance, history of LMIs in modern control theory |
Comparison between classic and modern control | 190minutes |

2． | State space representation (SSR) of modern control systems |
Review of differential equations together with simple mechanical systems and RCLs | 190minutes |

3． | Solutions of SSR | Review of differential equations and Laplace transform | 190minutes |

4． | Stability of control systems | Eigenvalues of matrices and system responses (trajectories) | 190minutes |

5． | Robustness and robust stability of control systems | Review norm of vectors and matrices | 190minutes |

6． | Review and Report 1 (system modeling, solution and stability) |
Review of Week 1-5 | 190minutes |

7． | Convex sets, convex functions, convex programming |
Review of functions with one or two variables | 190minutes |

8． | Definition and properties of LMIs | Review positive (negative) definite properties of symmetric matrices | 190minutes |

9． | Stability analysis with LMIs | Review stability concept and system behavior | 190minutes |

10． | Robust stability analysis with LMIs | Preview of system uncertainty and its evaluation | 190minutes |

11． | LMI based stabilization via state feedback | Review the basic idea of state feedback in control systems | 190minutes |

12． | LMI based robust stabilization via state feedback (polytopic uncertainties) |
Review of convex functions and the definition of polytopic uncertainties with convex sets |
190minutes |

13． | LMI based robust stabilization via state feedback (norm-bounded uncertainties) |
Preview of the definition of bounded uncertainties with matrix norms | 190minutes |

14． | Review and Report 2 | Review of the whole course | 190minutes |

Total. | - | - | 2660minutes |

Report 1 | Report 2 | Total. | |
---|---|---|---|

1. | 30% | 10% | 40% |

2. | 30% | 30% | |

3. | 30% | 30% | |

Total. | 30% | 70% | - |

Report 1: 30%

Report 2: 70%

-------------------

PASS when reaching 60% of the whole evaluation

Report 2: 70%

-------------------

PASS when reaching 60% of the whole evaluation

ways of feedback | specific contents about "Other" |
---|---|

Feedback in the class |

No text books; Will deliver handouts and suggest several reference books

【1】Katsuhiko Ogata: Modern Control Engineering (5th edition), Prentice Hall, 2010

【2】岩崎徹也︓ＬＭＩと制御，昭晃堂，1997 (ISBN 4785690534)

【3】Boyd, Vandenberghe: Convex Optimization, Cambridge University Press, 2004

(http://www.stanford.edu/~boyd/cvxbook/) (ISBN 978-0-521-83378-3)

【4】Boyd, El Ghaoui, Feron, Balakrishnan: Linear Matrix Inequalities in System and Control Theory, SIAM, 1994

(http://www.stanford.edu/~boyd/lmibook/lmibook.pdf) (ISBN 0-89871-334-X)

【1】Katsuhiko Ogata: Modern Control Engineering (5th edition), Prentice Hall, 2010

【2】岩崎徹也︓ＬＭＩと制御，昭晃堂，1997 (ISBN 4785690534)

【3】Boyd, Vandenberghe: Convex Optimization, Cambridge University Press, 2004

(http://www.stanford.edu/~boyd/cvxbook/) (ISBN 978-0-521-83378-3)

【4】Boyd, El Ghaoui, Feron, Balakrishnan: Linear Matrix Inequalities in System and Control Theory, SIAM, 1994

(http://www.stanford.edu/~boyd/lmibook/lmibook.pdf) (ISBN 0-89871-334-X)

- Course that cultivates an ability for utilizing knowledge
- Course that cultivates a basic problem-solving skills

Work experience | Work experience and relevance to the course content if applicable |
---|---|

Applicable | Used some of the knowledge and theory with simulation in analysis and design of real plants |

- 9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
- 11.SUSTAINABLE CITIES AND COMMUNITIES
- 12.RESPONSIBLE CONSUMPTION & PRODUCTION
- 13.CLIMATE ACTION

Last modified : Sat Sep 09 05:49:23 JST 2023