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At least 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
NASA NTRS2025

Robust Trajectory Optimization for NRHO Rendezvous Using SPICE Kernel Relative Motion

In this paper, robust optimization is performed on trajectory correction maneuvers during the lunar lander return phase of an Artemis mission, treating the trajectory from one hour after low lunar orbit departure to arrival in the vicinity of the lunar Gateway as a relative motion problem. To enable rapid stochastic optimization techniques requiring many candidate trajectories, SPICE kernel relative motion as implemented by the Quadratic Interpolated State Transition (QIST) system is used as the underlying dynamics propagation. The optimization is performed with a genetic optimizer using linear covariance (LinCov) software in a simplified operational context, taking into account the availability of navigation sensors with varying measurement models, ranges, and accuracies. No numerical integration is used, since the relative motion around Gateway is fully characterized with the a priori computation of the QIST coefficients. Maneuver placements are computed to optimize the minimum 3σ delta-v of the trajectory, the position dispersion at a target point, and a convex combination of these two metrics. An order of magnitude runtime improvement is provided over legacy methods with less than 10% error introduced. All QIST results are shown to be in-family with legacy methods. The tradespace for optimal delta-v design is found to range from 77.0 to 93.9 m/s, while the range of optimal dispersion is between 1.4 and 11.7 km.

Relative Motion↗
NASA NTRS1993

Hodograph analysis in aircraft trajectory optimization

An account is given of key geometrical concepts involved in the use of a hodograph as an optimal control theory resource which furnishes a framework for geometrical interpretation of the minimum principle. Attention is given to the effects of different convexity properties on the hodograph, which bear on the existence of solutions and such types of controls as chattering controls, 'bang-bang' control, and/or singular control. Illustrative aircraft trajectory optimization problems are examined in view of this use of the hodograph.

Cliff, Eugene M.↗
NASA NTRS2006

A Convex Guidance Algorithm for Formation Reconfiguration

In this paper, a reconfiguration guidance algorithm for formation flying spacecraft is presented. The formation reconfiguration guidance problem is first formulated as a continuous-time minimum-fuel or minimum-energy optimal control problem with collision avoidance and control constraints. The optimal control problem is then discretized to obtain a finite dimensional parameter optimization problem. In this formulation, the collision avoidance constraints are imposed via separating planes between each pair of spacecraft. A heuristic is introduced to choose these separating planes that leads to the convexification of the collision avoidance constraints. Additionally, convex constraints are imposed to guarantee that no collisions occur between discrete time samples. The resulting finite dimensional optimization problem is a second order cone program, for which standard algorithms can compute the global optimum with deterministic convergence and a prescribed level of accuracy. Consequently, the formation reconfiguration algorithm can be implemented onboard a spacecraft for real-time operations.

formation reconfiguration↗
DOE OSTI2025

Data-Driven Compositional Optimization in Misspecified Regimes

With a manifold growth in the scale and intricacy of systems, the challenges of parametric misspecification become pronounced. These concerns are further exacerbated in compositional settings, which emerge in problems complicated by modeling risk and robustness. In “Data-Driven Compositional Optimization in Misspecified Regimes,” the authors consider the resolution of compositional stochastic optimization problems, plagued by parametric misspecification. In considering settings where such misspecification may be resolved via a parallel learning process, the authors develop schemes that can contend with diverse forms of risk, dynamics, and nonconvexity. They provide asymptotic and rate guarantees for unaccelerated and accelerated schemes for convex, strongly convex, and nonconvex problems in a two-level regime with extensions to the multilevel setting. Surprisingly, the nonasymptotic rate guarantees show no degradation from the rate statements obtained in a correctly specified regime and the schemes achieve optimal (or near-optimal) sample complexities for general T-level strongly convex and nonconvex compositional problems.

Business & Economics↗
NASA NTRS1991

New displacement-based methods for optimal truss topology design

Two alternate methods for maximum stiffness truss topology design are presented. The ground structure approach is used, and the problem is formulated in terms of displacements and bar areas. This large, nonconvex optimization problem can be solved by a simultaneous analysis and design approach. Alternatively, an equivalent, unconstrained, and convex problem in the displacements only can be formulated, and this problem can be solved by a nonsmooth, steepest descent algorithm. In both methods, the explicit solving of the equilibrium equations and the assembly of the global stiffness matrix are circumvented. A large number of examples have been studied, showing the attractive features of topology design as well as exposing interesting features of optimal topologies.

Bendsoe, Martin P.↗
NASA NTRS1993

On convexity of H-infinity Riccati solutions and its applications

The celebrated two-Riccati-equation solution to a standard H-infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H-infinity controllers if the optimal H-infinity norm or gamma, an upper bound of a suboptimal H-infinity norm, is given. In this note, some properties of these H-infinity Riccati solutions are revealed. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma on the domain of interest. Based on these properties, a quadratically convergent algorithm is developed to compute the optimal H-infinity norm.

Li, X. P.↗
NASA NTRS1991

Robust control of systems with real parameter uncertainty and unmodelled dynamics

During this research period we have made significant progress in the four proposed areas: (1) design of robust controllers via H infinity optimization; (2) design of robust controllers via mixed H2/H infinity optimization; (3) M-delta structure and robust stability analysis for structured uncertainties; and (4) a study on controllability and observability of perturbed plant. It is well known now that the two-Riccati-equation solution to the H infinity control problem can be used to characterize all possible stabilizing optimal or suboptimal H infinity controllers if the optimal H infinity norm or gamma, an upper bound of a suboptimal H infinity norm, is given. In this research, we discovered some useful properties of these H infinity Riccati solutions. Among them, the most prominent one is that the spectral radius of the product of these two Riccati solutions is a continuous, nonincreasing, convex function of gamma in the domain of interest. Based on these properties, quadratically convergent algorithms are developed to compute the optimal H infinity norm. We also set up a detailed procedure for applying the H infinity theory to robust control systems design. The desire to design controllers with H infinity robustness but H(exp 2) performance has recently resulted in mixed H(exp 2) and H infinity control problem formulation. The mixed H(exp 2)/H infinity problem have drawn the attention of many investigators. However, solution is only available for special cases of this problem. We formulated a relatively realistic control problem with H(exp 2) performance index and H infinity robustness constraint into a more general mixed H(exp 2)/H infinity problem. No optimal solution yet is available for this more general mixed H(exp 2)/H infinity problem. Although the optimal solution for this mixed H(exp 2)/H infinity control has not yet been found, we proposed a design approach which can be used through proper choice of the available design parameters to influence both robustness and performance. For a large class of linear time-invariant systems with real parametric perturbations, the coefficient vector of the characteristic polynomial is a multilinear function of the real parameter vector. Based on this multilinear mapping relationship together with the recent developments for polytopic polynomials and parameter domain partition technique, we proposed an iterative algorithm for coupling the real structured singular value.

Chang, Bor-Chin↗
NASA NTRS2004

A Study of Penalty Function Methods for Constraint Handling with Genetic Algorithm

COMETBOARDS (Comparative Evaluation Testbed of Optimization and Analysis Routines for Design of Structures) is a design optimization test bed that can evaluate the performance of several different optimization algorithms. A few of these optimization algorithms are the sequence of unconstrained minimization techniques (SUMT), sequential linear programming (SLP) and the sequential quadratic programming techniques (SQP). A genetic algorithm (GA) is a search technique that is based on the principles of natural selection or "survival of the fittest". Instead of using gradient information, the GA uses the objective function directly in the search. The GA searches the solution space by maintaining a population of potential solutions. Then, using evolving operations such as recombination, mutation and selection, the GA creates successive generations of solutions that will evolve and take on the positive characteristics of their parents and thus gradually approach optimal or near-optimal solutions. By using the objective function directly in the search, genetic algorithms can be effectively applied in non-convex, highly nonlinear, complex problems. The genetic algorithm is not guaranteed to find the global optimum, but it is less likely to get trapped at a local optimum than traditional gradient-based search methods when the objective function is not smooth and generally well behaved. The purpose of this research is to assist in the integration of genetic algorithm (GA) into COMETBOARDS. COMETBOARDS cast the design of structures as a constrained nonlinear optimization problem. One method used to solve constrained optimization problem with a GA to convert the constrained optimization problem into an unconstrained optimization problem by developing a penalty function that penalizes infeasible solutions. There have been several suggested penalty function in the literature each with there own strengths and weaknesses. A statistical analysis of some suggested penalty functions is performed in this study. Also, a response surface approach to robust design is used to develop a new penalty function approach. This new penalty function approach is then compared with the other existing penalty functions.

Ortiz, Francisco↗
NASA NTRS1989

Trajectory optimization and guidance for an aerospace plane

The first step in the approach to developing guidance laws for a horizontal take-off, air breathing single-stage-to-orbit vehicle is to characterize the minimum-fuel ascent trajectories. The capability to generate constrained, minimum fuel ascent trajectories for a single-stage-to-orbit vehicle was developed. A key component of this capability is the general purpose trajectory optimization program OTIS. The pre-production version, OTIS 0.96 was installed and run on a Convex C-1. A propulsion model was developed covering the entire flight envelope of a single-stage-to-orbit vehicle. Three separate propulsion modes, corresponding to an after burning turbojet, a ramjet and a scramjet, are used in the air breathing propulsion phase. The Generic Hypersonic Aerodynamic Model Example aerodynamic model of a hypersonic air breathing single-stage-to-orbit vehicle was obtained and implemented. Preliminary results pertaining to the effects of variations in acceleration constraints, available thrust level and fuel specific impulse on the shape of the minimum-fuel ascent trajectories were obtained. The results show that, if the air breathing engines are sized for acceleration to orbital velocity, it is the acceleration constraint rather than the dynamic pressure constraint that is active during ascent.

Mease, Kenneth D.↗
NASA NTRS1990

The shape of Eros

Monte Carlo simulations are presently used to optimize estimation, ascertain associated errors, and guide bias-correction procedures, for the Eros polar silhouette convex hull that has been estimated from radar echo spectra. This hull is trapezoidal; this nonaxisymmetric shape may account for odd harmonics in Eros' echo spectral signature as a function of rotation phase. Additional constraints have been obtained for the figure of Eros through the inversion of the optical lightcurve to estimate the asteroid's two-dimensional average of the three-dimensional shape. This 'mean cross-section' and the polar silhouette exhibit similar elongations.

Ostro, S. J.↗
NASA NTRS1990

Global nonlinear optimization of spacecraft protective structures design

The global optimization of protective structural designs for spacecraft subject to hypervelocity meteoroid and space debris impacts is presented. This nonlinear problem is first formulated for weight minimization of the space station core module configuration using the Nysmith impact predictor. Next, the equivalence and uniqueness of local and global optima is shown using properties of convexity. This analysis results in a new feasibility condition for this problem. The solution existence is then shown, followed by a comparison of optimization techniques. Finally, a sensitivity analysis is presented to determine the effects of variations in the systemic parameters on optimal design. The results show that global optimization of this problem is unique and may be achieved by a number of methods, provided the feasibility condition is satisfied. Furthermore, module structural design thicknesses and weight increase with increasing projectile velocity and diameter and decrease with increasing separation between bumper and wall for the Nysmith predictor.

Mog, R. A.↗
DOE OSTI2025

Data-Conforming Data-Driven Control: Avoiding Premature Generalizations Beyond Data

Data-driven and adaptive control approaches face the problem of introducing sudden distributional shifts beyond the distribution of data encountered during learning. Therefore, they are prone to invalidating the very assumptions used in their own construction. This is due to the linearity of the underlying system, inherently assumed and formulated in most data-driven control approaches, which may falsely generalize the behavior of the system beyond the behavior experienced in the data. This article seeks to mitigate these problems by enforcing consistency of the newly designed closed-loop systems with data and slowing down any distributional shifts in the joint state-input space. This is achieved through incorporating affine regularization terms and linear matrix inequality constraints to data-driven approaches, resulting in convex semi-definite programs that can be efficiently solved by standard software packages. We discuss the optimality conditions of these programs and then conclude this article with a numerical example that further highlights the problem of premature generalization beyond data and shows the effectiveness of our proposed approaches in enhancing the safety of data-driven control methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1990

Large scale nonlinear numerical optimal control for finite element models of flexible structures

This paper discusses the development of large scale numerical optimal control algorithms for nonlinear systems and their application to finite element models of structures. This work is based on our expansion of the optimal control algorithm (DDP) in the following steps: improvement of convergence for initial policies in non-convex regions, development of a numerically accurate penalty function method approach for constrained DDP problems, and parallel processing on supercomputers. The expanded constrained DDP algorithm was applied to the control of a four-bay, two dimensional truss with 12 soft members, which generates geometric nonlinearities. Using an explicit finite element model to describe the structural system requires 32 state variables and 10,000 time steps. Our numerical results indicate that for constrained or unconstrained structural problems with nonlinear dynamics, the results obtained by our expanded constrained DDP are significantly better than those obtained using linear-quadratic feedback control.

Shoemaker, Christine A.↗
DOE OSTI2025

A method for bounding high-order finite element functions: Applications to mesh validity and bounds-preserving limiters

We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be used to locally bound any combination of these basis functions. This approach can be applied to any element/basis type at any approximation order, can provide local (i.e., subcell) extremum bounds to a desired level of accuracy, and can be evaluated efficiently on-the-fly in simulations. Furthermore, we show that this approach generally yields more accurate bounds in comparison to traditional methods based on convex hull properties (e.g., Bernstein polynomials). Furthermore, the efficacy of this technique is shown in applications such as mesh validity checks and optimization for high-order curved meshes, where positivity of the element Jacobian determinant can be ensured throughout the entire element, and continuously bounds-preserving limiters for hyperbolic systems, which can enforce maximum principle bounds across the entire solution polynomial.

Bounding box↗
NASA NTRS2000

Robust Control of Uncertain Systems via Dissipative LQG-Type Controllers

Optimal controller design is addressed for a class of linear, time-invariant systems which are dissipative with respect to a quadratic power function. The system matrices are assumed to be affine functions of uncertain parameters confined to a convex polytopic region in the parameter space. For such systems, a method is developed for designing a controller which is dissipative with respect to a given power function, and is simultaneously optimal in the linear-quadratic-Gaussian (LQG) sense. The resulting controller provides robust stability as well as optimal performance. Three important special cases, namely, passive, norm-bounded, and sector-bounded controllers, which are also LQG-optimal, are presented. The results give new methods for robust controller design in the presence of parametric uncertainties.

Joshi, Suresh M.↗
NASA NTRS1992

Fuel consumption in optimal control

A method has been developed for comparing three optimal control strategies based on fuel consumption. A general cost function minimization procedure was developed by applying two theorems associated with convex sets. Three cost functions associated with control saturation, pseudofuel, and absolute fuel are introduced and minimized. The first two cost functions led to the bang-bang and continuous control strategies, and the minimization of absolute fuel led to an impulsive strategy. The three control strategies were implemented on two elementary systems and a comparison of fuel consumption was made. The impulse control strategy consumes significantly less fuel than the continuous and bang-bang control strategies. This comparison suggests a potential for fuel savings in higher-order systems using impulsive control strategies. However, since exact solutions to fuel-optimal control for large-order systems are difficult if not impossible to achieve, the alternative is to develop near-optimal control strategies.

Redmond, Jim↗
NASA NTRS2001

Cryogenic Tank Structure Sizing With Structural Optimization Method

Structural optimization methods in MSC/NASTRAN are used to size substructures and to reduce the weight of a composite sandwich cryogenic tank for future launch vehicles. Because the feasible design space of this problem is non-convex, many local minima are found. This non-convex problem is investigated in detail by conducting a series of' analyses along a design line connecting two feasible designs. Strain constraint violations occur for some design points along the design line. Since MSC/NASTRAN uses gradient based optimization procedures, it does not guarantee that the lowest weight design can be found. In this study, a simple procedure is introduced to create a new starting point based on design variable values from previous optimization analyses. Optimization analysis using this new starting point can produce a lower weight design. Detailed inputs for setting up the MSC/NASTRAN optimization analysis and final tank design results are presented in this paper. Approaches for obtaining further weight reductions are also discussed.

Wang, J. T.↗
NASA NTRS1988

Asteroid shapes from radar echo spectra - A new theoretical approach

Asteroid shape determinations are presently made by means of a novel technique based on the geometric relation between spectral edge frequencies and the shape of a rotating, rigid radar target. By employing the echo spectra obtained at many rotational phases, the asteroid's convex polar silhouette hull is obtained; noise content is treated as a problem in weighted-least-squares optimization, subject to inequality constraints. The performance of this estimation method is assessed in a series of simulated data giving attention to spectral noise propagation into hull error; sensitivity to echo strength and spectral resolution are also evaluated.

Ostro, Steven J.↗