OPTIMAL FEEDBACK CONTROL DESIGN FOR A HYPERSONIC REENTRY VEHICLE
Open Access
- Author:
- Mirzaei, Mehrdad
- Graduate Program:
- Aerospace Engineering
- Degree:
- Master of Science
- Document Type:
- Master Thesis
- Date of Defense:
- May 16, 2019
- Committee Members:
- Puneet Singla, Thesis Advisor/Co-Advisor
Robert Graham Melton, Committee Member
Amy Ruth Pritchett, Committee Member - Keywords:
- Optimal Control
Hamilton-Jacobi-Bellman Equation
Optimal Feedback Control
Trajectory Optimization
Hypersonic Reentry Vehicle
Sparse Collocation Method
Convex Optimization - Abstract:
- The study of hypersonic flight is of utmost importance for commercial as well as military missions involving orbital and near orbital speeds. Hypersonic trajectory optimization is considered a challenging problem due to its highly nonlinear dynamic equations of motion, and different constraints which must be satisfied during the mission. Although open-loop optimal trajectory planning and feedback control laws for hypersonic flight have been studied in detail separately, to our best knowledge, very little attention has been devoted to the design of optimal feedback control laws. Designing the optimal feedback control law is a difficult task because it requires the solution of a nonlinear partial differential equation (PDE) called the Hamilton Jacobi Bellman (HJB) equation which is a multivariate function of system states and time. The main challenge in providing a numerical solution for the governing PDE is the curse of dimensionality. In this thesis, the recently developed sparse collocation method is used for deriving optimal feedback control laws for the hypersonic flight trajectory guidance problem. The sparse collocation method exploits a non-product quadrature rule known as the Conjugate Unscented Transformation (CUT) in conjunction with l 1 -norm optimization to derive the optimal feedback control laws. The CUT method provides the minimal number of initial conditions for open-loop solutions corresponding to domain of interest. The l 1 -norm based sparse approximation provides an interpolating surface for value function through these CUT provided open-loop solutions. The main advantage of this approach is that it does not require any a-priori information or assumption about the optimal control profile. A test hypersonic re-entry case corresponding to maximum energy impact at a known target location is considered to show the efficacy of the developed methodology. Finally, the performance of interpolating surface representing the optimal feedback control law is demonstrated for random initial conditions.