Section outline

  • Continuous-time optimal control – indirect approach via calculus of variations, LQ-optimal control

    • Introduction to calculus of variations
      • Functional, variation of a functional
      • Finite-interval fixed- and free end problems
      • Euler-Lagrange equation as a first-order necessary condition of optimality
    • General continuous-time optimal control problem
      • Control Hamiltonian
      • State, costate and stationarity equations (aka control Hamiltonian canonical equations) and boundary conditions as the necessary condition of optimality.
    • Continuous-time LQ-optimal control problem
      • State, costate and stationarity equations and boundary conditions as the necessary conditions of optimality
      • Free final state case – differential Riccati equation
    • Infinite time-horizon continuous-time LQ optimal control
      • Algebraic Riccati equation (ARE)