Lectures

  • Lecture 1: Introduction

  • Lecture 2: Finite-Dimensional Unconstrained Optimization. Book Chapter 1.2.1

  • Lecture 3: Constrained Optimization. Book Chapter 1.2.2

  • Lecture 4: Metric Space and Completeness

  • Lecture 5: Preview of Infinite-Dimensional Optimization. Book Chapter 1.3

  • Lecture 6: Basic Calculus of Variations Problem. Book Chapter 2.2

  • Lecture 7: Euler-Lagrange Equation. Book Chapter 2.3

  • Lecture 8: Hamiltonian Formalism and Mechanics. Book Chapter 2.4

  • Lecture 9: Variational Problems with Constraints. Book Chapter 2.5

  • Lecture 10: Second-order Necessary Conditions for Weak Extrema. Book Chapter 2.6

  • Lecture 11: Second-order Sufficient Conditions for Weak Extrema. Book Chapter 2.6

  • Lecture 12: Necessary Conditions for Strong Extrema. Book Chapter 3.1

  • Lecture 13: Optimal Control Problem. Book Chapter 3.2 and 3.3

  • Lecture 14: Variational Approach to the Fixed-time, Free-endpoint Problem. Book Chapter 3.4

  • Lecture 15: Maximum Principle I. Book Chapter 4.1

  • Lecture 16: Maximum Principle II. Book Chapter 4.2

  • Lecture 17: Maximum Principle, Proof I. Book Chapter 4.2 and 4.3

  • Lecture 18: Maximum Principle, Proof II. Book Chapter 4.2 and 4.3

  • Lecture 19: Maximum Principle, Proof III. Book Chapter 4.2 and 4.3

  • Lecture 20: Time-optimal Control Problem. Book Chapter 4.4

  • Lecture 21: Bang-Bang Control for Double Integrator. Book Chapter 4.4.1

  • Lecture 22: Bang-Bang Control for Linear Systems. Book Chapter 4.4.2

  • Lecture 23: Lie Brackets and Bang-Bang Control for Nonlinear Systems. Book Chapter 4.4.3

  • Lecture 24: Dynamic Programming for Discrete-time Systems. Book Chapter 5.1

  • Lecture 25: Principle of Optimality and HJB Equation. Book Chapter 5.1

  • Lecture 26: HJB Equation, Part II. Book Chapter 5.2

  • Lecture 27: HJB Equation, Part III. Book Chapter 5.3

  • Lecture 28: LQR, Part I. Book Chapter 6.1

  • Lecture 29: LQR, Part II. Book Chapter 6.2