Course Details

Course details of EE6412
Course NoEE6412
Course TitleOptimal Control
Course Content1.Review of state-space representation of systems2. Introduction to Optimization- Unconstrained and constrained optimization, Karush-Kuhn-Tucker (KKT) conditions3. Calculus of variations-Examples of variational problems, Brachistochrone, Catenary etc., Cost functionals, extremals, Weak and strong extrema, First-order necessary conditions for weak extrema--Euler-Lagrange equations, Hamiltonian formalism and mechanics, Variational problems with constraints, Second-order conditions-Legendre's condition, Weierstrass-Erdmann corner conditions, Weierstrass excess function4. Optimal control problem formulations- Variational approach to the fixed-time, free-endpoint problem5. Pontryagin maximum principle- Proof of the maximum principle, Time-optimal control of double integrator, Bang-bang control6. Hamiltonian-Jacobi Bellman (HJB) equation-principle of optimality, Sufficient condition for optimality7. Linear quadratic regulator (LQR) problem- candidate optimal feedback law, Riccati differential equation, proof of sufficiency using HJB equation8. Numerical methods for optimal control problems- Evaluation of parameter-dependent functionals and their gradients, Indirect methods, Direct methods, 9. Applications- Time-optimal control of linear systems, Singular control, Optimal control to target curves
Course Offered this semesterYes
Faculty NameDr. Rachel