Optimal Control and Game Theory in Flight Mechanics (IIND-01/C, 6 CFU) [1056505]
Special Master of Aerospace Engineering (Year: 2, Semester: 2)
The course provides theoretical and practical knowledge on optimization techniques for trajectory design, guidance and control of aerospace vehicles. Relevant case studies are simulated numerically (Matlab, GMAT) and the implementation of optimal control algorithms on real flight hardware (FPGA) is proposed as optional lab exercises.
Module 1: Optimal guidance and control
(1) Review of calculus of variations, introduction to optimal control theory and derivation of optimality conditions.
(2) Maximization of the range of a rocket: (a) flat Earth and drag-free analytical solution; (b) numerical solution using unconstrained nonlinear optimization in Matlab.
(3) Time optimal launch: (a) analytical solution assuming flat Earth, single stage and drag free problem; (b) setup of the numerical solver for the TPBVP; (c) numerical solution with mass variation and staging; (d) numerical solution including the effects of aerodynamic force; (e) time optimal landing formulation.
(4) Primer vector theory: (a) minimum-fuel orbital rendezvous with a passive target (introduction of inequality constraints); (b) minimum torque single-axis control of a spacecraft; (c) implementation of bang-bang and bang-off-bang solutions; (d) optimal control with singular arcs (Legendre-Clebsch condition).
(5) Minimum-fuel transfer with low-thrust propulsion with applications on: (a) LEO-GEO/GTO transfer; (b) in-orbit servicing far range; (c) solution using direct/indirect trasncript.
Module 2: Optimal control and actuation
(1) The Linear Quadratic Regulator: (a) continuous and discrete time formulation; (b) exogenous terms; (c) implementation and HiL testing on FPGA.
(2) Linear Quadratic Traking: (a) continuous and discrete time formulation; (b) application on in-orbit servicing homing manevuers; (c) actuation of commanded (optimal) attitude control.
(3) Linear Quadratic Gaussian controller: (a) review of the Kalman filter; (b) determination of covariance and observation noise from experimental data; (c) LQG implementation and HiL testing on FPGA.
(5) Convex optimization.
(6) Tensor-based formulation of the LQG: (a) introduction to tensor algebra and multilinear dynamical systems; (b) application of the Tensor Kalman Filter for orbit determination of a debris cloud; (c) application of the Tensor LQG for the centralized control of a swarm of satellites.
(7) Interplanetary transfers: (a) minimum-energy internal capture conditions; (b) minimum-fuel transfer from high- to low-energy trajectories through L1/L2; (c) minimum-fuel station-keeping in LPO.
(8) Proportional navigation: (a) optimality conditions, (b) homing guidance, (c) adaptive solutions.
Module 3: Differential game theory
(1) Introduction to game theory and zero sum games.
(2) Pursuer-Evader games in flight mechanics: (a) cooperative and (b) competitive rendezvous between spacecraft.
(3) 2- and 3-player games with quadratic cost function: (a) 2-party intercept problem in the atmosphere and (b) 3-party intercept problem in the atmosphere.
(4) Modeling zero sum games using the Tensor LQR.
NOTE: All the software used is free or available free of charge for Sapienza students. FPGA development boards can be provided to students for Hardware-in-the-Loop implementation and testing.