Syllabus
Basic mathematical concepts: Finite dimensional optimization, Infinite dimensional optimization, Conditions for optimality, Performance measures for optimal control problems.
Calculus of variations: Examples of variational problems, Basic calculus of variations problem, Weak and strong extrema, Variable end point problems, Hamiltonian formalism and mechanics: Hamilton’s canonical equations. From Calculus of variations to Optimal control: Necessary conditions for strong extrema, Calculus of variations versus optimal control, optimal control problem formulation and assumptions, variational approach to the fixed time, free end point problem.
The Pontryagin’s Minimum principle: Statement of Minimum principle for basic fixed end point and variable end point control problems, Proof of the minimum principle, Properties of the Hamiltonian, Time optimal control problems.
The Linear Quadratic Regulator: Finite horizon LQR problem‐ Candidate optimal feedback law, Ricatti differential equations (RDE), Global existence of solution for the RDE. Infinite horizon LQR problem‐ Existence and properties of the limit, solution, closed loop stability. Examples: Minimum energy control of a DC motor, Active suspension with optimal linear state feedback, Frequency shaped LQ Control. LQR using output feedback: Output feedback LQR design equations, Closed loop stability, Solution of design equations, example.
Linear Quadratic tracking control: Tracking a reference input with compensators of known structure, tracking by regulator redesign, Command generator tracker, and Explicit model following design.
Text Books
Same as Reference
References
1. Optimal Control Theory‐ An Introduction, D.E.Kirk, Dover Publications, New York, 2004.
2. Linear Systems‐ Optimal and Robust Controls, Alok Sinha, CRC Press, 2007.
3. Calculus of variations and Optimal control theory, Daniel Liberzone, Princeton University Press, 2012.
4. Applied optimal control & Estimation‐ Digital design and implementation, Frank L. Lewis, Prentice Hall and Digital Signal Processing Series, Texas Instruments, 1992.
5. Primer on Optimal Control Theory, Jason L. Speyer, David H. Jacobson, SIAM, 2010.
6. Optimal Control Theory with Aerospace Applications, Ben‐Asher, Joseph Z, American Institute of Aeronautics and Astronautics, 2010.
7. Optimal control: linear quadratic methods, Brian D. O. Anderson, John Barratt Moore, Dover, 2007.
8. Optimal filtering, Brian D. O. Anderson, John Barratt Moore, Dover, 2005.
Course Outcomes (COs):
CO1: Evaluate performance measures for optimal control problems, understanding their significance in practical applications.
CO2: Solve variational problems using basic calculus of variations principles.
CO3: Compare and contrast calculus of variations with optimal control methodologies, emphasizing problem formulation and underlying assumptions.
CO4: Solve the Optimal control problem using the parameterization approach and compare its formulation with the standard calculus of variations