Constrained minimization problems in finite- dimensional spaces.
Constrained minimization problems in finite- dimensional spaces in unified approach
OPTIMAL CONTROL↗
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Frequency-domain instability criteria for time- varying and nonlinear systems.
Frequency domain instability criteria generated from stability criteria for time varying and nonlinear feedback problems
LIAPUNOV FUNCTION↗
A nonlinear perturbation theory for estimation and control of time discrete stochastic systems
Nonlinear perturbation theory for optimal estimation and control of time-discrete, stochastic, dynamic systems when measurement data is noisy
Sorenson, H. W.↗
On minimum time and fuel orbital transfer.
The problem of a maneuverable spacecraft, with limited thrust capability, moving between two coplanar circular earth orbits is considered. Thrusting is performed in the plane defined by the circles, so that the nonlinear dynamics and subsequent optimization problem are simplified. The approach used in this paper differs from the approaches of Edelbaum and Goetz in that the equations of motion are not linearized before formulating the optimization problem. An averaging approximation is used to determine the structure of the significant co-state variables.
Stuart G. Greenberg↗
Comparison of several numerical optimization methods.
Numerical optimization methods compared for nonlinear two point boundary value problem associated with optimum spacecraft trajectory
Lewallen, J. M.↗
Differential dynamic programming methods for solving bang-bang control problems.
Nonlinear bang-bang optimal control problems solution based on differential dynamic programming, noting use of Pontryagin adjoint variables
Jacobson, D. H.↗
A separation theorem for nonlinear measurements.
Separation theorem for arbitrary nonlinear measurements to find optimal stochastic control without dynamic programming
Curry, R. E.↗
Estimation and detection of signals in multiplicative noise
A class of detection-estimation problems on matrix Lie groups is defined in which the observation noise is multiplicative in nature. By examining the differential versions of the hypotheses, which are bilinear in nature, it is possible to derive the relevant likelihood ratio formula and the associated optimal estimation equations for the signal given the observations and the assumption that the signal is present. These estimation equations are of interest in their own right, in that they represent a finite dimensional optimal solution to a nonlinear estimation problem and can be viewed as consisting of a Kalman-Bucy filter along with the on-line computation of the solution of the associated Riccati equation, which is driven by the observations. The usefulness of these results is illustrated via an example concerning the detection of an actuator failure in a rigid body rotational control system.
Willsky, A. S.↗
Management of analytical redundancy in digital flight control systems for aircraft
This paper presents a design method for optimal redundancy management for nonlinear systems with application to highly maneuvering aircraft. The approach taken is based on selecting the failure states to be covered by the system design and constructing a cost function that represents the cost of making an incorrect decision. The decision logic which minimizes the cost requires a bank of extended Kalman filters running in parallel. This produces a severe computational requirement. To reduce this requirement, a suboptimal logic is developed based on using a nonlinear single-stage prediction algorithm in the filters with filter gains and decision logic selected using steady-state results obtained from a linearization of the vehicle and sensor dynamics. The design process is then applied to designing a redundancy management system for the F8-C aircraft. Results indicate that the system is superior in failure detection to a system using the same structure but using a linear single-stage prediction algorithm in the filters.
Montgomery, R. C.↗
Chain pooling to minimize prediction errors in subset regression
The existing theory of subset regression is examined, taking into account optimality criteria, small experiments, nonlinear models, colinearities, and special techniques. Approaches based on chain pooling coupled with principal components regression are discussed, giving attention to a comparison of half-normal plotting with chain pooling, a procedure based on prior ordering, deletion under the F-test, the largest of a set of chi-square variates, and principal components regression and model deletion. The choice of a true (population) model for simulations is considered along with the evaluation of the decision procedure and suitable computer programs.
Holms, A. G.↗
Estimation and detection of signals in multiplicative noise
We define a class of detection-estimation problems on matrix Lie groups in which the observation noise is multiplicative in nature. By examining the differential versions of the hypotheses, which are bilinear, we are able to derive the relevant likelihood ratio formula and the associated optimal estimation equations for the signal given the observations and the assumption that the signal is present. These estimation equations are of interest in their own right, in that they represent a finite-dimensional optimal solution to a nonlinear estimation problem and consist of a Kalman-Bucy filter along with the on-line computation of the solution of the associated Riccati equation, which is driven by the observations. The usefulness of these results is illustrated via an example concerning the detection of an actuator failure in a rigid-body rotational control system.
Willsky, A. S.↗
On minimal surfaces, membranes and compressible flows
The theory, variational formulation and finite element analysis of a class of nonlinear problems arising in optimization, thin membrane deflection and compressible flows are developed. Error estimates are summarized, and representative numerical results are presented. Particular theoretical questions pertaining to the existence and uniqueness of solutions are addressed, and their implications for such applications of finite element analysis as the study of compressible flows indicated.
Carey, G. F.↗
Parallel and vector computation for stochastic optimal control applications
A general method for parallel and vector numerical solutions of stochastic dynamic programming problems is described for optimal control of general nonlinear, continuous time, multibody dynamical systems, perturbed by Poisson as well as Gaussian random white noise. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random atmospheric fluctuations. The numerical formulation is highly suitable for a vector multiprocessor or vectorizing supercomputer, and results exhibit high processor efficiency and numerical stability. Advanced computing techniques, data structures, and hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations.
Hanson, F. B.↗
Polarization studies of Zeeman affected spectral lines using the MSFC magnetograph
The Marshall Space Flight Center (MSFC) vector magnetograph records polarization images of absorption lines that are sensitive to magnetic fields. A method is presented for analyzing the Stokes spectral-line profiles of a photospheric Fe I absorption line (5250.2 A) which is influenced by the Zeeman effect. Using nonlinear least-square optimization, the observed Stokes profiles are compared with those generated from the theoretical solution of the polarized radiative transfer equations. The optimization process accounts for the spectral convolution of the source and the MSFC vector magnetograph. The resulting physical properties of the active region producing the polarized light are discussed.
Balasubramaniam, K. S.↗
Function approximations
A development status evaluation is presented for applications of main approximation concepts in nonlinear programming for structural optimization requiring local, midrange, and global approximations. It is noted that there is not yet a sufficient basis for a comprehensive evaluation of relative effectiveness among approximation concepts. Attention is presently given to the careful selection of intermediate-variable and response quantity, and improvements in the traditional Taylor-series expansion by inclusion of either some higher-order terms or information at various points in the design space.
Barthelemy, J.-F. M.↗
Motion Cueing Algorithm Development: New Motion Cueing Program Implementation and Tuning
A computer program has been developed for the purpose of driving the NASA Langley Research Center Visual Motion Simulator (VMS). This program includes two new motion cueing algorithms, the optimal algorithm and the nonlinear algorithm. A general description of the program is given along with a description and flowcharts for each cueing algorithm, and also descriptions and flowcharts for subroutines used with the algorithms. Common block variable listings and a program listing are also provided. The new cueing algorithms have a nonlinear gain algorithm implemented that scales each aircraft degree-of-freedom input with a third-order polynomial. A description of the nonlinear gain algorithm is given along with past tuning experience and procedures for tuning the gain coefficient sets for each degree-of-freedom to produce the desired piloted performance. This algorithm tuning will be needed when the nonlinear motion cueing algorithm is implemented on a new motion system in the Cockpit Motion Facility (CMF) at the NASA Langley Research Center.
Houck, Jacob A.↗
Improving Magnetosphere In Situ Observations Using Solar Sails
Past and current magnetosphere missions employ conventional spacecraft formations for in situ observations of the geomagnetic tail. Conventional spacecraft flying in inertially fixed Keplerian orbits are only aligned with the geomagnetic tail once per year, since the geomagnetic tail is always aligned with the Earth-Sun line, and therefore, rotates annually. Solar sails are able to artificially create sunsynchronous orbits such that the orbit apse line remains aligned with the geomagnetic tail line throughout the entire year. This continuous presence in the geomagnetic tail can significantly increase the science phase for magnetosphere missions. In this paper, the problem of solar sail formation design is explored using nonlinear programming to design optimal two-craft, triangle, and tetrahedron solar sail formations, in terms of formation quality and formation stability. The designed formations are directly compared to the formations used in NASA's Magnetospheric Multi-Scale mission.
Sails↗
Modern Aerocapture Guidance to Enable Reduced-Lift Vehicles at Neptune
Aerocapture is covered extensively in the literature as means of achieving orbital insertion with dramatic mass-saving results compared to fully-propulsive systems. One of the primary obstacles facing aerocapture is the inherent uncertainty associated with passing through a planet’s upper atmosphere. In-flight dispersions due to delivery errors, environment variables, and aerodynamic performance impose a large flight envelope. System studies for aerocapture often select high lift-to-drag ratios to compensate for these uncertainties. However, modern predictor-corrector guidance strategies have shown promise in recent years to provide robust control schemes in-situ. These algorithms do not rely on a pre-calculated reference trajectory and instead employ a numerical optimizer to continuously solve nonlinear equations of motion each guidance cycle. Numerical predictor-corrector strategies may provide considerable accuracy over heritage guidance schemes. The goal of this study is reproduce a landmark study of Neptune aerocapture and apply modern guidance to illustrate relative performance improvements and cost-saving potential. Capture constraints based on the theoretical corridor width are considered. Results indicate that heritage vehicles with moderate lift-to-drag ratios, lower than previous studies have indicated, may prove viable for aerocapture at Neptune.
Heidrich, C. R.↗