- Lecture 1: (Linear time-varying control systems and linearization)
- Lecture 2: (Review: complete metric spaces)
- Lecture 3: (Banach fixed point theorem)
- Lecture 4: (Existence and uniqueness of solutions in general case)
- Lecture 5: (Picard-Lindelöf theorem)
- Lecture 6: (Existence and uniqueness of solutions for linear time-varying systems)
- Lecture 7: (Transition matrices and Peano-Baker series)
- Lecture 8: (Properties of transition matrices)
- Lecture 9: (Controllability of linear time-varying systems I)
- Lecture 10: (Controllability of linear time-varying systems II)
- Lecture 11: (Controllability of linear time-invariant systems)
- Lecture 12: (Observability of linear time-varying systems)
- Lecture 13: (Weighting patterns, Weiss-Kalman-Youla I)
- Lecture 14: (Weighting patterns, Weiss-Kalman-Youla II)
- Lecture 15: (Minimal realization for LTI control systems I)
- Lecture 16: (Minimal realization for LTI control systems II)
- Lecture 17: (Characterization of LTI transfer functions)
- Lecture 18: (Realization of LTI transfer functions)
- Lecture 19: (Feedbacks I)
- Lecture 20: (Feedbacks II)
- Lecture 21: (Pole placement for multi-input LTI control systems)
- Lecture 22: (Detectability and stabilizability)
- Lecture 23: (Luenberger observer and observer-based controllers)
- Lecture 24: (Optimal control and calculus of variations)
- Lecture 25: (History of calculus of variations: Form Dido's isoperimetric problem to Euler-Lagrange)
- Lecture 26: (Optimal control with quadratic costs)
- Lecture 27: (Free endpoint problem)
- Lecture 28: (The Riccati equations)
- Lecture 29: (Fixed endpoint problem)
- Lecture 30: (Infinite horizon optimal control and the Linear Quadratic Regulators I)
- Lecture 31: (Extensions of solutions to the Riccati equation)
- Lecture 32: (The algebraic Riccati equation)
- Lecture 33: (Infinite horizon optimal control and the Linear Quadratic Regulators II)
- Lecture 34: (Dynamic programming and the Hamilton-Jacobi-Bellman equations)
- Lecture 35: (Sufficient conditions for optimality)
- Lecture 36: (The Riccati equations via Hamilton-Jacobi-Bellman)
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