Spacecraft Attitude and Orbital Maneuvers: Applied Optimal Control (AERO 623)
by Dr. Srinivas R. Vadali
Static optimization
– Necessary and sufficient conditions
– Problems without constraints
– Problems with equality constraints
– Problems with inequality constarints
– Numrical solution: using MATLAB fmincon
Discretetime optimal control problem
– General discretetime OCP for nonlinear systems
– Discretetime LQR: fixed final state and openloop control, free final state and closedloop control, crossweighted regulator
– Digital control of continoustime systems
– Steadystate closed loop control and suboptimal feedback
Continuoustime optimal control problem
– Calculus of variations
– General continuoustime OCP for nonlinear systems
– Continuoustime LQR: fixed final state and openloop control, free final state and closedloop control, crossweighted regulator
– Steadystate optimal control and suboptimal feedback
Tracking problem
– Continuoustime tracking problem: general approach, regulator with function of final state fixed (fixed final state LQR: closed loop and open loop)
– Discretetime 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
– Bangbang and bangoffbang 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, multipleshooting
– 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
