## Modern Control TheoryBack JP / EN

Numbering Code Year/Term U-ENG29 39058 LJ72U-ENG29 39058 LJ10 2022 ・ First semester 2 Lecture Japanese Tue.2 KASHIMA KENJI (Graduate School of Informatics Associate Professor) This course provides the fundamentals in modern control theory - centered around the so-called state space methods - as a continuation of classical control theory taught in Linear Control Theory. Emphasis is placed on the treatment of such concepts as controllability and observability, pole allocation, the realization problem, observers, and linear quadratic optimal regulators. The objective is to study controllability and observability that are the basis of modern control theory, and also understand design methods such as optimal regulators. It is hoped that the course provides a basis for a more advanced topic such as robust control theory. Introduction to modern control,1time,We give real examples for which the modern control theory are applied. We also give a state-space formulation for modeling dynamical systems. Mathematics for modern control,1time,We discuss some fundamental properties of mathematics, in particular, vectors and matrices. Controllability and observability,2times,We introduce the fundamental notions of controllability and observability for linear dynamical systems, and also discuss their basic properties and their criteria. Canonical decomposition,2times,We give the canonical decomposition for linear systems. Realization problem,2times,We introduce the realization problem that constructs state space representations from transfer functions for single-input and single-output systems. Stability,2times,We discuss the stability of dynamical systems described by state-space equations. We also give mathematical tools for checking if a system is stable or not. State feedback and dynamic compensators,2times,We introduce the construction of dynamic compensators via state feedback, pole allocation and observers. The relationships with controllability and observablity are also discussed. Opimal regulators,2times,We give the basic construction of optimal regulators, in particular, the introduction of the matrix Riccati equation, its solvability, relationship to stability and observability, and root loci. Overall summary, 1time The grading is based on the evaluation of reports and final examination. It is desirable that the student has studied classical control theory (linear control theory). Fundamental knowledge on linear algebra is assumed, e.g., matrices, determinants, rank of a matrix, dimension of a vector space, isomorphism. Fundamental knowledge of linear algebra such as matrix manipulation is assumed. None specified. Linear Algebra, K. Jaenich, translation by M. Nagata, Gendai-suugakusha, isbn{}{4768703194} Mathematics for Systems and Control, Y. Yamamoto, Asakura, isbn{}{4254209762}