The optimization techniques can be used in different ways depending on the approach (algebraic or geometric), the interest (single or multiple), the nature of the signals (deterministic or stochastic), and the stage (single or multiple). The main objective of optimal control is to determine control signals that will cause a process (plant) to satisfy some physical constraints and at the same time extremize (maximize or minimize) a chosen performance criterion (performance index or cost function).

INTENDED AUDIENCE : It is an Elective Course forPG, Research Engineers, Scientists, Non Ph.D Faculties.

PRE-REQUISITES : Advanced Control System.

INDUSTRIES SUPPORT : DRDO, ISRO and Engineering Institutions etc.

Week 1 : Introduction and Performance Index

Basic Concept of calculus of variation

The basic variational problem

Fixed end point problem

Free end point problem

Week 2 : Free end point problem (Continued)

Free end point problem (Continued)

Free end point problem (Continued)

Optimum of a function with conditions

Optimum of Functions with Conditions

(Lagrange Multiplier Method)

Week 3 : Optimum of a functional with conditions

Variational Approach to Optimal Control Systems

Variational Approach to Optimal Control Systems (continued)

Linear Quadratic Optimal Control Systems

Linear Quadratic Optimal Control Systems (Contnued)

Week 4 : Linear Quadratic Optimal Control Systems (Contnued)

Linear Quadratic Optimal Control Systems (Contnued)

Linear Quadratic Optimal Control Systems (Contnued)

Linear Quadratic Optimal Control Systems

(Optimal Value of Performance Index)

Infinite Horizon Regulator Problem

Week 5 : Infinite Horizon Regulator Problem (Continued)

Analytical Solution of Matrix Differential Riccati Equation (State Transition Matrix Approach)

Analytical Solution of Matrix Differential Riccati Equation (Similarity Transformation Approach)

Analytical Solution of Matrix Differential Riccati Equation (Similarity Transformation Approach) (Continued)

Frequency Domain Interpretation of LQR

(Linear Time Invariant System)

Week 6 : Frequency Domain Interpretation of LQR

(Linear Time Invariant System) (Continued)

LQR with a Specified Degree of Stability

Inverse Matrix Riccati Equation

Linear Quadratic Tracking System

Discrete-Time Optimal Control Systems

Week 7 : Discrete-Time Optimal Control Systems (Continued)

Discrete-Time Optimal Control Systems (Continued)

Matrix Discrete Riccati Equation

Analytical Solution of Matrix Difference Riccati Equation

Analytical Solution of Matrix Difference Riccati Equation (Continued)

Week 8 : Optimal Control Using Dynamic Programming

The Hamilton-Jacobi-Bellman (HJB) Equation

LQR System Using H-J-B Equation

Time Optimal Control System

(Constrained Input)

Time Optimal Control System(Continued)

1.D.E.Kirk,OptimalControlTheory:AnIntroduction,PrenticeHall,EnglewoodCliffs,NJ,1970

2.F.L.Lewis,OptimalControl,JohnWiley&Sons,Inc.,NewYork,NY,1986

3.M.Gopal,ModernControlSystemTheory,NewAgeInternational

4.SageA.P.&WhiteC.C.,OptimumSystemsControl,PrenticeHall

Dr. Barjeev Tyagi received the PhD in Electrical Engineering, IIT-Kanpur, 2005 and M. Tech Electrical Engineering (Control System) from IIT-Kharagpur in the year 2000. Prior to these he completed his B. E. Electrical Engineering from IIT-Roorkee (Formally Univ. of Roorkee) in 1987. Presently he is serving as Associate Professor in EED, IIT-Roorkee since 2007. His research interests include Control System Analysis and Design, Control application in Power System, Distributed Generation and Control.

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams:**26 March 2023** Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

**CRITERIA TO GET A CERTIFICATE**

Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

**YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.**

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Roorkee.It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams:

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

Average assignment score = 25% of average of best 6 assignments out of the total 8 assignments given in the course.

Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Roorkee.It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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