## TIEE3035 Syllabus - Optimal Control - 2022 Regulation Anna University

TIEE3035

OPTIMAL CONTROL

L T P C

3003

COURSE OBJECTIVES:
• To provide an exposure to different type of optimal control problems such as time- optimal, fuel optimal, energy optimal control problems.
• To impart knowledge and skills needed to design Linear Quadratic Regulator for Time- invariant and Time-varying Linear system (Continuous time and Discrete-time systems).
• To introduce concepts needed to design optimal controller using Dynamic Programming Approach and H-J-B equation.
• To provide an exposure to various types of fault tolerant control schemes such as Passive and active approaches.
• To introduce concepts needed to design optimal controller in the presence of state constraints and time optimal controller.

UNIT I

CALCULUS OF VARIATIONS AND OPTIMAL CONTROL

(7+2 SKILL) 9

Introduction – Performance Index- Constraints – Formal statement of optimal control system – Calculus of variations – Function, Functional, Increment, Differential and variation and optimum of function and functional – The basic variation problem Extrema of functions and functional with conditions – variational approach to optimal control system

UNIT II

(7+2 SKILL) 9

Problem formulation – Finite time Linear Quadratic regulator – Infinite time LQR system: Time Varying case- Time-invariant case – Stability issues of Time-invariant regulator – Linear Quadratic Tracking system: Fine time case and Infinite time case

UNIT III

DISCRETE TIME OPTIMAL CONTROL SYSTEMS

(7+2 SKILL) 9

Variational calculus for Discrete time systems – Discrete time optimal control systems:- Fixedfinal state and open-loop optimal control and Free-final state and open-loop optimal control - Discrete time linear state regulator system – Steady state regulator system

UNIT IV

PONTRYAGIN MINIMUM PRINCIPLE

(7+2 SKILL) 9

Pontryagin Minimum Principle – Dynamic Programming:- Principle of optimality, optimal control using Dynamic Programming – Optimal Control of Continuous time and Discrete-time systems – Hamilton-Jacobi-Bellman Equation – LQR system using H-J-B equation

UNIT V

CONSTRAINED OPTIMAL CONTROL SYSTEMS

(7+2 SKILL) 9

Time optimal control systems – Fuel Optimal Control Systems- Energy Optimal Control Systems – Optimal Control Systems with State Constraints

TOTAL: 45 PERIODS

COURSE OUTCOMES: Students able to
CO1 Explain different type of optimal control problems such as time-optimal, fuel optimal, energy optimal control problems.
CO2 Design Linear Quadratic Regulator for Time-invariant and Time-varying Linear system (Continuous time and Discrete-time systems)
CO3 Design optimal controller using Dynamic Programming Approach and H-J-B equation.
CO4 Explain the Pontryagin Minimum Principle.
CO5 Design optimal controller in the presence of state constraints and time optimal controller.
CO6 Understand the concepts of dynamic programming

TEXT BOOKS:
1. Donald E. Kirk, Optimal Control Theory – An Introduction, Dover Publications, Inc. Mineola, New York, 2012, 10th Edition.

REFERENCES BOOKS
1. D. Subbaram Naidu, Optimal Control Systems, CRC Press, New York, 2003, 1st Edition.
2. Frank L. Lewis, Draguna Vrabie, Vassilis L. Syrmos, Optimal Control, 3rd Edition, Wiley Publication, 2012, 3rd Edition.
3. Yan Wang, Cheng-Lin Liu, Zhi-Cheng Ji, Quantitative Analysis and Optimal Control of Energy Efficiency in Discrete Manufacturing System, Springer, 2020, 1st Edition.