This thesis discusses optimal trajectories for hypervelocity flight of interest in aeroassisted orbital transfer. Both coplanar orbital transfer and noncoplanar orbital transfer are studied. For these cases, the GEO-to-LEO transfer, the HEO-to-LEO transfer, and the LEO-to-LEO transfer are considered in connection with a spacecraft which is controlled during the atmospheric pass via the angle of attack (coplanar case) or via the angle of attack and the angle of bank (noncoplanar case). For the noncoplanar case, three transfer maneuvers are studied. Type 1 involves four impulses and four space plane changes; Type 2 involves three impulses and three space plane changes; and Type 3 involves three impulses and no space plane change. In Type 1, the initial impulse directs the spacecraft away from Earth, and then is followed by an apogee impulse propelling the spacecraft toward Earth; in Types 2 and 3, the initial impulse directs the spacecraft toward Earth. A common element of these maneuvers is that they all include an atmospheric pass, with velocity depletion coupled with plane change. Within the framework of classical optimal control, the following problems are studied: (P1) minimize the energy required for orbital transfer; (P2) maximize the time of flight during the atmospheric portion of the trajectory; and (P3) minimize the time integral of the square of the path inclination. Within the framework of minimax optimal control, the following problem is studied: (P4) minimize the peak heating rate. Numerical solutions for Problems (P1), (P2), (P3), (P4) are obtained by means of the sequential gradient-restoration algorithm for optimal control problems. The engineering implications of the results obtained are discussed. In particular, it is shown that the nearly-grazing solution (namely, the trajectory solving Problem (P3)) is a useful engineering compromise between energy requirements and aerodynamic heating requirements.

A geometric nonlinear filter (GNF) is designed for application to the problem of tracking a maneuvering aircraft. The aircraft tracking problem is a state estimation problem and a state prediction problem. A nonlinear aircraft maneuver model is proposed for use in the state estimation as well as the state prediction. This nonlinear model is based on the so-called coordinated turn and describes planar trajectories. The GNF design approach involves state transformations with output injection to transform the nonlinear system model to a linear form, known as the observer canonical form. For many nonlinear systems, such as the proposed aircraft maneuver model, this linearizing transformation does not exist. Therefore, for the maneuvering aircraft model, a transformation to an approximate observer canonical form is given. Utilizing a Lyapunov stability approach, sufficient conditions for stability of the GNF estimation error are derived. No such conditions exist for the extended Kalman filter (EKF). The GNF was found to be stable in cases where the EKF was not stable. The tracking performance of the GNF compares favorably with the EKF for various levels of measurement noise. However, the GNF offers a substantial savings in computational time making it more attractive than the EKF for use in a fire control computer.

The application of the sequential gradient-restoration algorithm (SGRA) to the estimation of the windshear along the trajectory of an aircraft is studied. Based on the measured trajectory data obtained from the digital flight data recorder (DFDR) of Flight Delta 191 (August 2, 1985, Dallas-Fort Worth International Airport), a nonlinear least-square problem is formulated. The performance index being minimized measures the deviation of the experimental trajectory (the altitude, the relative velocity, and the pitch attitude angle) from the computed trajectory, obtained by integrating the equations of motion of an aircraft in a vertical plane. Since the thrust and the aerodynamic forces enter directly in this dynamic formulation, a clear picture of the forces acting on the aircraft can be seen. This leads to a good understanding of the behavior of the aircraft during the windshear encounter. The angle of attack is treated as a control, and the power setting is regarded as a known input. By assuming that the manufacturer-supplied aerodynamic and thrust data are dependable, the dynamically estimated vertical wind shows reasonable agreement with that obtained with the kinematic approach. However, the results obtained for the horizontal wind are less satisfactory. Upon modifying the manufacturer-supplied thrust and aerodynamic data with unknown multiplicative factors, a better agreement between the measured and computed trajectory can be achieved. As a consequence, the estimated winds exhibit better accuracy. The inclusion of penalty terms in the performance index being minimized forces the values of the unknown multiplicative factors to be close to unity. The estimation of these factors is important, because it might explain some unusual effects, such as the presence of rain. Upon employing different combinations of the measured trajectory data, the relative importance of each data can be established. The horizontal distance data and the relative velocity data are found to have minor effect on the estimation results. The altitude data affect mostly the vertical wind, and the pitch attitude angle data are crucial to the estimation of both the horizontal and vertical winds.

The problem considered here involves a functional I subject to differential constraints, nondifferential constraints, and general boundary conditions. It consists of finding the state x(t), control u(t), and parameter $\pi$ so that the functional I is minimized, while the differential constraints, nondifferential constraints, and boundary conditions are satisfied to a predetermined accuracy. Here, I is a scalar, x an n-vector, u an m-vector, and $\pi$ a p-vector. Four types of gradient-restoration algorithms are considered, and their relative efficiency in terms of the number of iterations for convergence and CPU time is evaluated. The algorithms considered are as follows: sequential gradient-restoration algorithm, complete restoration (SGRA-CR); sequential gradient-restoration algorithm, incomplete restoration (SGRA-IR); combined gradient-restoration algorithm, no restoration (CGRA-NR); and combined gradient-restoration algorithm, incomplete restoration (CGRA-IR).

Low-altitude windshear is a threat to the safety of aircraft in take-off and landing: over the past 20 years, some 30 aircraft accidents have been attributed to windshear. The Aero-Astronautics Group of Rice University under the direction of Dr. Angelo Miele has determined the optimal capability of an aircraft in take-off under windshear conditions and has developed near-optimal guidance strategies. In this thesis, using the above information, the values of the parameters for different guidance strategies are determined in order to provide the best approximation to the optimal capabilities. The calculation is treated as a mathematical programming problem, solved by the Nelder-Mead simplex algorithm. Then, the optimal parameters data are applied to guidance strategies. The resulting guidance trajectories are presented in graphical form along with the optimal trajectories for comparison.

This thesis deals with the optimization of four classes of combat maneuvers for a next-generation jet fighter aircraft: climb maneuvers, fly-to-point maneuvers, pop-up attack maneuvers, and dive recovery maneuvers. For the first three classes of maneuvers, the optimization criterion is the minimization of the flight time, resulting in a Mayer-Bolza problem of optimal control; for the fourth class, the optimization criterion is the minimization of the maximum altitude loss during dive recovery, resulting in a Chebyshev problem of optimal control. Each class of problems is solved using the sequential gradient-restoration algorithm for optimal control. Among the four classes of combat maneuvers studied, only dive recovery benefits from the ability of a next-generation fighter aircraft to maneuver at extremely high angles of attack. For the other three classes, relatively low angles of attack are required. The optimal climb trajectories are characterized by three distinct segments: a central segment often flown with a load factor of nearly 1 and two terminal segments (dive or zoom) to and from the central segment. The central and final segments are nearly independent of the initial conditions, instead being dominated by the final conditions. The optimal fly-to-point trajectories consist of three segments: turning, characterized by relatively high load factor; level acceleration at maximum thrust; and finally, resumption of steady-state cruising. The effects of the heading change magnitude and the load factor limit are discussed. The optimal pop-up trajectories consist of three segments flown at maximum power: pitch-up, zoom, and pitch-down. The effects of using the afterburner, heading change magnitude, and dive angle magnitude are discussed. The optimal dive recovery trajectories consist of one to three segments, depending on initial speed and flight path angle. All the optimal trajectories conclude with a pitch-up at the maximum available load factor. For very low initial speed, the pitch-up is preceded by a brief supermaneuver segment. For very low initial speed coupled with very high initial flight path angle, the supermaneuver segment is preceded by a dive initiation segment. The optimal trajectories reported here serve two purposes. First, they can benefit aircraft designers by highlighting those flight characteristics that are most beneficial in combat. Second, they can benefit aircraft pilots as the basis for guidance trajectories that approximate the optimal trajectories.

A method that combines experimental airfoil coefficient data with numerical data has been developed to construct airfoil performance tables given limited data sets. This work addresses the problem faced by engineers and aerodynamicists that currently rely on incomplete performance tables when researching airfoil characteristics. The method developed utilizes the Sequential Function Approximation (SFA) neural network tool and employs a simple regularization scheme to fuse multi-dimensional experimental and computational fluid dynamics (CFD) data efficiently. The method is considered an adaptive and robust tool requiring relatively little computational demand and minimal user dependence. An existing performance table for the NACA 0012 airfoil was used as a test case to verify the feasibility of the SFA-fused network. A second test case assesses the method's viability for a more realistic and challenging problem using highly sparse and scattered data sets for the SC1095 airfoil. Results from both studies realize the method's capability to make consistent approximations and smooth interpolations given only limited experimental data. Comparisons are made with other scattered data approximation techniques. The testing conditions, requirements, and limitations of this approach are discussed and future applications and recommendations are made.

In this work, we present a complete study of the Hohmann transfer maneuver between two circular coplanar orbits. After revisiting its known properties, we present a number of supplementary properties which are essential to the qualitative understanding of the maneuver. Specifically, along a Hohmann transfer trajectory, there exists a point where the path inclination is maximum: this point occurs at midradius and is such that the spacecraft velocity equals the local circular velocity. This implies that, in a Hohmann transfer, the spacecraft velocity is equal to the local circular velocity three times: before departure, at midradius, and after arrival. In turn, this allows the subdivision of the Hohmann transfer trajectory into a region where the velocity is subcircular and a region where the velocity is supercircular, with the transition from one region to another occurring at midradius. Also, we present a simple analytical proof of the optimality of the Hohmann transfer and complement it with a numerical study via the sequential gradient-restoration algorithm. Finally, as an application, we present a numerical study of the transfer of a spacecraft from the Earth orbit around the Sun to another planetary orbit around the Sun for both the case of an ascending transfer (orbits of Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto) and the case of a descending transfer (orbits of Mercury and Venus).

In recent years, there has been a growing demand for the autonomous rendezvous and docking capability of a spacecraft. Current guidance methods in existence are based on the human control of the chaser spacecraft and are not suitable nor sufficient for an autonomous vehicle. The optimal solution of the rendezvous problem investigated in this thesis consists of finding an allowable finite control distribution which minimizes some prescribed performance index (i.e. time, fuel, etc) and brings a chaser vehicle into coincidence with a target vehicle. This thesis first derives the well-known Clohessy-Wiltshire (CW) differential equations (Ref. 1) and focuses on the optimal solution of a linearized three-dimensional rendezvous with bounded thrust and limited fuel. To accomplish this, the sequential gradient-restoration algorithm is utilized to optimize several rendezvous trajectories for the case of a target spacecraft in a circular orbit at the International Space Station (ISS) altitude and a chaser spacecraft with typical initial conditions during the terminal phase of the rendezvous with bounded thrust and bounded DeltaV. First, the time-optimal rendezvous is investigated followed by the fuel-optimal rendezvous for three values of the max thrust acceleration via the sequential gradient-restoration algorithm (SGRA). Then, the time-optimal rendezvous for given fuel and the fuel-optimal rendezvous for given time are investigated. There are three controls, two of which determine the thrust direction in space and one which determines the thrust magnitude. The main conclusion is that the optimal control distribution can result in two, three, or four subarcs depending on the performance index and the constraints. The time-optimal case results in a two-subarc solution with max thrust. The fuel-optimal case results in a four subarc solution consisting of an initial coasting period, followed by a maximum thrust phase, followed by another coasting period, followed by another maximum thrust phase. Regardless of the number of resulting subarcs, the optimal thrust distribution requires the thrust magnitude to be either at the maximum value or at zero. The coasting periods are finite in duration and their length increases as the time to rendezvous increases and/or as the max allowable thrust increases. Another finding is that, for the fuel-optimal rendezvous with the time unconstrained, the minimum fuel required is nearly constant and independent of the max available thrust. Based on the above observations, the final potion of this thesis applies the multiple-subarc version of SGRA to solve the guidance problem based on the implementation of constant-control finite-thrust functions during each subarc. (Abstract shortened by UMI.)

This thesis considers both classical and minimax problems of optimal control arising in the study of noncoplanar, aeroassisted orbital transfer. The maneuver considered involves the transfer from a high planetary orbit to a low planetary orbit with a prescribed atmospheric plane change. With reference to the atmospheric part of the maneuver, trajectory control is achieved by modulating the lift coefficient and the angle of bank. The presence of upper and lower bounds on the lift coefficient is considered. Within the framework of classical optimal control, the performance indexes studied are the energy required for orbital transfer and the time integral of the square of the path inclination. Within the framework of minimax optimal control, the performance index studied is the peak heating rate. Numerical solutions are obtained by means of the sequential gradient-restoration algorithm for optimal control problems. Numerical examples are presented, and their engineering implications are discussed.