Introduction to optimization: maximization/minimization of static systems, optimization with equality constraints and use of Lagrange multipliers; Dynamic systems: basics of dynamic systems and state variable representation, state feedback control, controllability, observability, canonical forms, pole placement for controller/observer design; Optimal control discrete time systems; Solution to general discrete optimization problem, open loop system and Lyapunov equation, discrete time LQR, discrete time control of continuous time system, steady state closed loop control and sub-optimal state feedback. Control: Optimal control of continuous time system: The calculus of variations, solution to general continuous optimization problem, continuous time LQR, steady state sub-optimal control; Optimal tracking problem, final time free and constrained input control, dynamic programming for optimal solution, optimal control for polynomial systems; Output feedback and structured control: LQR with output feedback, tracking a reference input, tracking by regulator redesign, command generator tracker
Robustness and multivariable frequency domain analysis.
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