Research in optimization and guidance theory
Trajectory optimization and guidance theory for powered flight vehicles
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Trajectory optimization and guidance theory for powered flight vehicles
Optimal control of linear functional differential equations
We solve a multi-period portfolio optimization problem using D-Wave Systems' quantum annealer. We derive a formulation of the problem, discuss several possible integer encoding schemes, and present numerical examples that show high success rates. The formulation incorporates transaction costs (including permanent and temporary market impact), and, significantly, the solution does not require the inversion of a covariance matrix. The discrete multi-period portfolio optimization problem we solve is significantly harder than the continuous variable problem. We present insight into how results may be improved using suitable software enhancements and why current quantum annealing technology limits the size of problem that can be successfully solved today. Here, the formulation presented is specifically designed to be scalable, with the expectation that as quantum annealing technology improves, larger problems will be solvable using the same techniques.
Optimal control and trajectory optimization in aperiodic discrete time functional systems
Information pertinent to users of the program to optimize simulated trajectories (POST) is presented. The input required and output available is described for each of the trajectory and targeting/optimization options. A sample input listing and resulting output are given.
Solution of trajectory optimization problems by calculus of variations, dynamic programming, and Pontryagin's Principle
Control and trajectory optimization involves the minimization of a performance index (PI) of integral form where some optimal control law exists in a dynamic system. In this paper, a hybrid minicomputer with an adaptive random-search algorithm implements an iterative search for the optimal control. The search assumes that some initial control is randomly perturbed and a fast analog computer generates respective PI from the analog response of the dynamic system. An improved PI informs the digital computer to utilize the perturbed control as a basis for the next iteration; otherwise a new perturbation replaces the old perturbation in the next iteration. The search terminates when no further improvements occur.
A general purpose FORTRAN program for simulating and optimizing point mass trajectories (POST) of aerospace vehicles is described. The equations and the numerical techniques used in the program are documented. Topics discussed include: coordinate systems, planet model, trajectory simulation, auxiliary calculations, and targeting and optimization.
The flight trajectory of abort landing in the presence of windshear is examined with reference to flight in a vertical plane. It is assumed that the only control is the angle of attack. Inequality constraints are imposed on both the angle of attack and its time derivative. Numerical results are obtained for several combinations of windshear intensities and initial altitudes. Guidance trajectories are considered, approximating the optimal trajectories and using local information on the state of the aircraft, the initial altitude, and the total wind velocity difference. Results are presented for optimal trajectories, guidance trajectories, simplified guidance trajectories, constant pitch trajectories, and maximum angle of attack trajectories.
Finite difference Newton-Raphson algorithm extension to solve variational equations for simultaneous optimization of trajectories and associated parameters
Finite difference Newton-Raphson algorithm extension to solve variational equations for simultaneous optimization of trajectories and associated parameters
Optimal transfer trajectories from earth parking orbit to various terminal conic constraints, and ROBOT computer program modifications
No abstract available
The optimization of ballistic planetary trajectories is developed which includes constraints on departure parking orbit inclination and node. This problem is formulated to result in a minimum total Delta V where the entire constrained injection Delta V is included in the optimization. An additional Delta V is also defined to allow for possible optimization of parking orbit inclination when the launch vehicle orbit capability varies as a function of parking orbit inclination. The optimization problem is formulated using primer vector theory to derive partial derivatives of total Delta V with respect to possible free parameters. Minimization of total Delta V is accomplished using a quasi-Newton gradient search routine. The analysis is applied to an Eros rendezvous mission whose transfer trajectories are characterized by high values of launch asymptote declination during particular launch opportunities. Comparisons in performance are made between trajectories where parking orbit constraints are included in the optimization and trajectories where the constraints are not included.
Information pertinent to the programmer and relating to the program to optimize simulated trajectories (POST) is presented. Topics discussed include: program structure and logic, subroutine listings and flow charts, and internal FORTRAN symbols. The POST core requirements are summarized along with program macrologic.
Guidance regime for optimal multistage lunar trajectory derived by applying calculus of variations to generalized Bolza problem
Motivation - Noise management is one of the major barriers to Urban Air Mobility - Approaches to noise mitigation (non-exhaustive) - Vehicle configuration - Directivity control via propeller phase synchronization - Trajectory optimization Objective - Create framework for trajectory generation integrating location-based acoustic metrics and vehicle performance limitations - Multiple trajectory optimization methods and acoustic noise models - Mission-relevant constraints - Mission duration, airspace restrictions, ... - Vehicle dynamic constraints - Aircraft structural limitations, min/max airspeed, ... - Vehicle separation/obstacle avoidance - Acoustic constraints at a number of discrete observer locations
Motivation - Noise management is one of the major barriers to Urban Air Mobility - Approaches to noise mitigation (non-exhaustive) - Vehicle configuration - Directivity control via propeller phase synchronization - Trajectory optimization Objective - Create framework for trajectory generation integrating location-based acoustic metrics and vehicle performance limitations - Multiple trajectory optimization methods and acoustic noise models - Mission-relevant constraints - Mission duration, airspace restrictions, ... - Vehicle dynamic constraints - Aircraft structural limitations, min/max airspeed, ... - Vehicle separation/obstacle avoidance - Acoustic constraints at a number of discrete observer locations