**Course No.****：**S070105ZJ009

**Course Category****：**Professional Basic Course

**Period/Credits****：**40/2

**Prerequisites****：**Mathematical analysis, linear algebra, ordinary differential equations, real function introduction.

**Aims & Requirements****：**

This course is a professional basic course for Ph.D and master student of mathematics, systems science major, and it’s also a elective course for students from operations research and cybernetics, systems theory and engineering control. System optimization has a wide range of application, which relate to many practical systems such as guidance, navigation, industry, communication, information, economy, society, resource, environment. It’s a important interdisciplinary between mathematics and engineering sciences. On one hand, this course introduces the classic optimization algorithms, Pontryagim maximum principle from optimal control theory and Hamilton-Jacobi-Bellman equation from dynamic programming methods. On the other hand, it introduces the application of the above algorithms and theories, as well as how to use them to solve problems, for example, quadratic optimal control, a variety of search algorithms.

Through this course, students can understand system optimization from basic concepts to research frontier, grasp the basic concepts of system optimization and basic skills in problem-analyzing, problem-solving, lay the foundation for research in the field of system control.

**Primary Coverage****：**

Section 1:System optimization introduction

Theoretical background, theory formation, theory application, theory development prospects and review of the classic system optimization methods.

Section 2:Necessary conditions for optimal control problems and optimal control

Pontryagim maximum principle.

Section 3: Minimum control problem for linear systems with quadratic performance index

The form, existence, uniqueness of the linear quadratic optimal control, and linear systems with quadratic optimal regulator problem.

Section 4: Sufficient conditions for optimal control problems and optimal control

Dynamic programming method and the basic theory of the Hamilton-Jacobi-Bellman equation .

Section 5: control problem of system with external disturbances

State feedback and output feedback control problem.

Section 6: Classic search algorithm

Unconstrained optimization, Equality Constrained Optimization and Lagrange function method, random search methods.

**Author****：**Zairong Xi, Yanlong Zhao, Bo Qi (Academy of Mathematics and Systems Science)

**Date****：**October, 2009