Spacecraft Attitude and Orbital Maneuvers: Applied Optimal Control (AERO 623)

Static optimization
     – Necessary and sufficient conditions
     – Problems without constraints
     – Problems with equality constraints
     – Problems with inequality constarints
     – Numrical solution: using MATLAB fmincon

Discrete-time optimal control problem
     – General discrete-time OCP for nonlinear systems
     – Discrete-time LQR: fixed final state and open-loop control, free final state and closed-loop control, cross-weighted regulator
     – Digital control of continous-time systems
     – Steady-state closed loop control and sub-optimal feedback

Continuous-time optimal control problem
     – Calculus of variations
     – General continuous-time OCP for nonlinear systems
     – Continuous-time LQR: fixed final state and open-loop control, free final state and closed-loop control, cross-weighted regulator
     – Steady-state optimal control and sub-optimal feedback

Tracking problem
     – Continuous-time tracking problem: general approach, regulator with function of final state fixed (fixed final state LQR: closed loop and open loop)
     – Discrete-time tracking problem: general approach, regulator with function of final state fixed (fixed final state LQR: closed loop and open loop)

Some important considerations in optimal control problem
     – Path constraints
     – Switching control: jump formula
     – Different types of discontinuities in OCP
     – Control constraints and Pontryagin's principle
     – Minimum time problems
     – Bang-bang and bang-off-bang control
     – Guidance problem and perturabation control, HJB equation, method of characteristics
     – Conjugate points, singular OCP
     – Primer vector and impulsive trajectory optimization

Numerical methods
     – Direct methods: pseudospectral collocation, GPOPS
     – Indirect methods: shooting method, multiple-shooting
     – Implementing direct and indirect methods for OCP with singular arcs, OCP with path and control constraints

Output feedback and observer
     – LQR with output feedbaack
     – Structured control
     – Estimator problem