Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “quadratic programming”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

Scenario Complexity for Unmanned Aircraft System Traffic

This work introduces an approach to estimate the complexity of a low-altitude air traffic scenario involving multiple UASs using mathematical programming. Given a set of multi-point UAS flight trajectories, vehicle dynamics, and a conflict resolution algorithm, an abstract model is developed such that it can be solved quickly using a mathematical programming optimization software without running high-fidelity simulations that can be computationally expensive and may not suit real-time apA quick and accurate assessment of complexity for a given traffic scenario can help plan and schedule flights to alleviate traffic bottleneck and mitigate operation risks, especially for unmanned aerial system traffic management where high traffic density or complexity is expected. This work introduces a traffic scenario complexity metric that was constructed based on the number of potential conflicts weighted by the conflict resolution cost associated. The cost associated with a conflict is calculated based on the corresponding conflict resolution maneuvers. To obtain the conflict resolution maneuvers, a MILP-based optimization was formulated with the vehicle model and conflict management parameters incorporated. To evaluate the complexity metrics, an approach of using measurements from high-fidelity simulations was proposed. The scenario complexity measurements for 920 random-generated scenarios were obtained through high-fidelity simulations and treated as the ground truth. Two statistics methods: Pearson and Alternative Conditional Expectations were applied for analysis. The results showed that the number of flights has low correlation with the scenario complexity according to the correlation coefficients calculated by both methods. The Alternative Conditional Expectations method shows that the proposed scenario complexity metric has better correlation with the ground truth than the number of potential conflicts.plications. In the abstract model, each vehicle is represented by a time-varied vector associated with position, speed, and heading information. The total extra distance that aircraft need to divert from their original routes to avoid collisions is computed and used to setup a quadratic programming formula. The metrics including the number of conflicts and extra distances travelled by all vehicles are then utilized to estimate the complexity of a given UAS flight scenario. Results and verification against high-fidelity simulations will be provided in the final draft.

traffic complexity↗
NASA NTRS1984

Convex profiles from asteroid lightcurves

A lightcurve inversion method that yields a two-dimensional convex profile is introduced. The number of parameters that characterize the profile is limited only by the number of Fourier harmonics used to represent the parent lightcurve. The implementation of the method is outlined by a recursive quadratic programming algorithm, and its application to photoelectric lightcurves and radar measurements is discussed. Special properties of the lightcurves of geometrically scattering ellipsoids are pointed out, and those properties are used to test the inversion method and obtain a criterion for judging whether any lightcurve could actually be due to such an object. Convex profiles for several asteroids are shown, and the method's validity is discussed from a physical as well as purely statistical point of view.

Ostro, S. J.↗
NASA NTRS1985

Convex-profile Inversion of Asteroid Lightcurves

A lightcurve inversion method that yields a two-dimensional convex profile is introduced. The number of parameters that characterize the profile is limited only by the number of Fourier harmonics used to represent the parent lightcurve. The implementation of the method is outlined by a recursive quadratic programming algorithm, and its application to photoelectric lightcurves and radar measurements is discussed. Special properties of the lightcurves of geometrically scattering ellipsoids are pointed out, and those properties are used to test the inversion method and obtained a criterion for judging whether any lightcurve could actually be due to such an object. Convex profiles for several asteroids are shown, and the method's validity is discussed from a physical as well as purely statistical point of view.

Ostro, S. J.↗
NASA NTRS1987

Single step optimization of manipulator maneuvers with variable structure control

One step ahead optimization has been recently proposed for spacecraft attitude maneuvers as well as for robot manipulator maneuvers. Such a technique yields a discrete time control algorithm implementable as a sequence of state-dependent, quadratic programming problems for acceleration optimization. Its sensitivity to model accuracy, for the required inversion of the system dynamics, is shown in this paper to be alleviated by a fast variable structure control correction, acting between the sampling intervals of the slow one step ahead discrete time acceleration command generation algorithm. The slow and fast looping concept chosen follows that recently proposed for optimal aiming strategies with variable structure control. Accelerations required by the VSC correction are reserved during the slow one step ahead command generation so that the ability to overshoot the sliding surface is guaranteed.

Chen, N.↗
NASA NTRS1988

Performance limits for optimal microburst encounter

An effort has been made to ascertain the envelope-edges for uneventful aircraft penetrations of microburst windshears on the basis of optimal aircraft control strategies. Over 1100 such trajectories have been computed for contemporary airliners and general aviation aircraft, in the case of idealized microbursts, using a successive quadratic program trajectory optimization algorithm able to directly handle inequality constraints. Variations of optimal performance with microburst type, intensity, length scale, and location, define performance limits; these limits fall into short, intermediate, and long microburst length scale regimes. The ability to safely transit a microburst also varies strongly with microburst location.

Psiaki, Mark L.↗
NASA NTRS1988

An investigation of new methods for estimating parameter sensitivities

Parameter sensitivity is defined as the estimation of changes in the modeling functions and the design variables due to small changes in the fixed parameters of the formulation. There are currently several methods for estimating parameter sensitivities requiring either difficult to obtain second order information, or do not return reliable estimates for the derivatives. Additionally, all the methods assume that the set of active constraints does not change in a neighborhood of the estimation point. If the active set does in fact change, than any extrapolations based on these derivatives may be in error. The objective here is to investigate more efficient new methods for estimating parameter sensitivities when the active set changes. The new method is based on the recursive quadratic programming (RQP) method and in conjunction a differencing formula to produce estimates of the sensitivities. This is compared to existing methods and is shown to be very competitive in terms of the number of function evaluations required. In terms of accuracy, the method is shown to be equivalent to a modified version of the Kuhn-Tucker method, where the Hessian of the Lagrangian is estimated using the BFS method employed by the RPQ algorithm. Inital testing on a test set with known sensitivities demonstrates that the method can accurately calculate the parameter sensitivity. To handle changes in the active set, a deflection algorithm is proposed for those cases where the new set of active constraints remains linearly independent. For those cases where dependencies occur, a directional derivative is proposed. A few simple examples are included for the algorithm, but extensive testing has not yet been performed.

Beltracchi, Todd J.↗
NASA NTRS1989

An investigation of new methods for estimating parameter sensitivities

The method proposed for estimating sensitivity derivatives is based on the Recursive Quadratic Programming (RQP) method and in conjunction a differencing formula to produce estimates of the sensitivities. This method is compared to existing methods and is shown to be very competitive in terms of the number of function evaluations required. In terms of accuracy, the method is shown to be equivalent to a modified version of the Kuhn-Tucker method, where the Hessian of the Lagrangian is estimated using the BFS method employed by the RQP algorithm. Initial testing on a test set with known sensitivities demonstrates that the method can accurately calculate the parameter sensitivity.

Beltracchi, Todd J.↗
NASA NTRS1989

Design for steering accuracy in antenna arrays using shared optical phase shifters

Uniform linear phased arrays where many radiating elements share a relatively small number of phase shifters are investigated. Such architectures arise in arrays which derive the time delays in the signal paths from a small group of independent phase shifters. In particular, a true time-delay device which has been suggested recently for optically controlled arrays is used as the basic phase shifter. Different architectures, viz. alternative procedures of deriving the necessary time delay for each antenna in the face of phase-shifter inaccuracies, are examined. The variance of the steered beam's direction is used as the performance criterion. The direction-optimal architecture is obtained by means of quadratic programming, and is shown not to be unique. The nonuniqueness of the optimal architecture is exploited to improve other characteristics of the array's beam shape, and the optimal solution is shown to compare favorably with a suboptimal interleaved solution which is easier to implement.

Kam, Moshe↗
NASA NTRS1990

Robustness, generality and efficiency of optimization algorithms in practical applications

The theoretical foundations of two approaches, sequential quadratic programming (SQP) and optimality criteria (OC), are analyzed and compared, with emphasis on the critical importance of parameters such as accuracy, generality, robustness, efficiency, and ease of use in large scale structural optimization. A simplified fighter wing and active control of space structures are considered with other example problems. When applied to general system identification problems, the OC methods are shown to lose simplicity and demonstrate lack of generality, accuracy and robustness. It is concluded that the SQP method with a potential constraint strategy is a better choice as compared to the currently prevalent mathematical programming and OC approaches.

Thanedar, P. B.↗
NASA NTRS1990

Global optimization methods for engineering design

The problem is to find a global minimum for the Problem P. Necessary and sufficient conditions are available for local optimality. However, global solution can be assured only under the assumption of convexity of the problem. If the constraint set S is compact and the cost function is continuous on it, existence of a global minimum is guaranteed. However, in view of the fact that no global optimality conditions are available, a global solution can be found only by an exhaustive search to satisfy Inequality. The exhaustive search can be organized in such a way that the entire design space need not be searched for the solution. This way the computational burden is reduced somewhat. It is concluded that zooming algorithm for global optimizations appears to be a good alternative to stochastic methods. More testing is needed; a general, robust, and efficient local minimizer is required. IDESIGN was used in all numerical calculations which is based on a sequential quadratic programming algorithm, and since feasible set keeps on shrinking, a good algorithm to find an initial feasible point is required. Such algorithms need to be developed and evaluated.

Arora, Jasbir S.↗
NASA NTRS1990

Trajectory optimization for real-time guidance. I - Time-varying LQR on a parallel processor

A key algorithmic element of a real-time trajectory optimization hardware/software implementation, the quadratic program (QP) solver element, is presented. The purpose of the effort is to make nonlinear trajectory optimization fast enough to provide real-time commands during guidance of a vehicle such as an aeromaneuvering orbiter. Many methods of nonlinear programming require the solution of a QP at each iteration. In the trajectory optimization case the QP has a special dynamic programming structure, a LQR-like structure. QP algorithm speed is increased by taking advantage of this special structure and by parallel implementation.

Psiaki, Mark L.↗
NASA NTRS1990

A computational algorithm for spacecraft control and momentum management

Developments in the area of nonlinear control theory have shown how coordinate changes in the state and input spaces of a dynamical system can be used to transform certain nonlinear differential equations into equivalent linear equations. These techniques are applied to the control of a spacecraft equipped with momentum exchange devices. An optimal control problem is formulated that incorporates a nonlinear spacecraft model. An algorithm is developed for solving the optimization problem using feedback linearization to transform to an equivalent problem involving a linear dynamical constraint and a functional approximation technique to solve for the linear dynamics in terms of the control. The original problem is transformed into an unconstrained nonlinear quadratic program that yields an approximate solution to the original problem. Two examples are presented to illustrate the results.

Dzielski, John↗
NASA NTRS1991

Minimum-fuel rescue trajectories for the Extravehicular Excursion Unit

The problem of determining minimum-fuel trajectories for rescuing astronauts or equipment which become separated from a Space Station is addressed. Using the Clohessy-Wiltshire equations of relative motion and assuming impulsive Delta-Vs, the minimum-fuel rescue problem is shown to be a parameter optimization problem. Minimum-fuel rescue trajectories are found for seventeen test cases using a recursive quadratic programming algorithm. The results are analyzed and general rules for astronaut rescue and equipment retrieval are developed.

Fowler, W. T.↗
NASA NTRS1991

Optimal aircraft performance during microburst encounter

The effects of microburst characteristics on the optimal penetration performance of jet transport and general aviation aircraft are presented. The purpose is to determine the best possible performance that can be achieved in a broad range of microbursts. A secondary goal is to illustrate good strategies for dealing with a range of microbursts during takeoff and landing. Over 1100 optimal trajectories were computed for two aircraft types flying through idealized microbursts using a Successive Quadratic Programs trajectory optimization algorithm. Contours of safety metrics are plotted as functions of the length scales, magnitudes, and locations of horizontal wind shears and vertical downdrafts. These performance contours show three length-scale regimes for optimal microburst penetration. At short length scales, hazards usually associated with gustiness predominate (e.g., high normal load factor, rotational upset). At intermediate length scales, a degraded ability to maintain flight path and/or vertical velocity poses the most serious threat. At very long microburst length scales, excessive touchdown velocities may result. The ability to transit a microburst successfully also varies strongly with microburst location. The results show that both aircraft types could penetrate some very severe microbursts if optimal control histories were followed. Nevertheless, these control strategies assume perfect prior knowledge of the wind, and practical limits to successful encounter with real-time control capabilities would be lower. The optimally controlled jet transport can successfully penetrate higher intensity microbursts than can the general aviation aircraft.

Psiaki, Mark L.↗
NASA NTRS1992

Computation of near-minimum-time maneuvers of flexible structures by parameter optimization

Near-minimum-time attitude maneuvers of space structures as well as ground based test articles are considered. Switching nature of the controls for rigid body maneuvers are illustrated using a control-cube and a critical control axis of rotation. The presence of torque smoothing and where appropriate, gravitational effects and connections to other bodies are explicitly included in the mathematical models of the systems to be optimized. A maximum fuel consumption constraint is included besides the required terminal conditions on attitude and angular velocities. The switch times, maximum thrust magnitudes, and smoothing parameters are determined using the Sequential Quadratic Programming method for parameter optimization. Results indicating attitude and angular velocity histories, thruster forces, and structural vibrations are presented for three, four, and five switch maneuvers, as well as maneuvers that involve large coasting arcs.

Vadali, S. R.↗
NASA NTRS1989

Determination of design and operation parameters for upper atmospheric research instrumentation to yield optimum resolution with deconvolution, appendix 4

The power spectrum for a stationary random process can be defined with the Wiener-Khintchine Theorem, which says that the power spectrum and the auto correlation function are a Fourier transform pair. To implement this theorem for signals that are discrete and of finite length we can use the Blackman-Tukey method. Blackman and Tukey (1958) show that a function w(tau), called a lag window, can be applied to the auto correlation estimates to obtain power spectrum estimates that are statistically stable. The Fourier transform of w(r) is called a spectral window. Typical choices for spectral windows show a distinct trade-off between the main lobe width and side lobe strength. A new idea for designing windows by taking linear combinations of the standard windows to produce hybrid windows was introduced by Smith (1985). We implement Smith's idea to obtain spectral windows with narrow main lobes and smaller (compared with typical windows) near side lobes. One of the main contributions of this thesis is that we show that Smith's problem is equivalent to a Quadratic Programming (QP) problem with linear equality and inequality constraints. A computer program was written to produce hybrid windows by setting up and solving the QP problem. We also developed and solved two variations of the original problem. The two variations involved changing the inequality constraints in both cases from non negativity on the combination coefficients to non negativity on the hybrid lag window itself. For the second variation, the window functions used to construct the hybrid window were changed to a frequency-variable set of truncated cosinusoids. A series of tests was run with the three computer programs to investigate the behavior of the hybrid spectral and lag windows. Emphasis was put on obtaining spectral windows with both relatively narrow main lobes and the lowest possible (for these algorithms) near side lobes. Some success was achieved for this goal. A 10 dB peak side lobe reduction over the rectangular spectral window without significant main lobe broadening was achieved. Also, average side lobe levels of -117 dB were reached at a cost of doubling the main lobe width (at the -3 dB point).

Ioup, George E.↗
NASA NTRS1993

Adjoint methods for aerodynamic wing design

A model inverse design problem is used to investigate the effect of flow discontinuities on the optimization process. The optimization involves finding the cross-sectional area distribution of a duct that produces velocities that closely match a targeted velocity distribution. Quasi-one-dimensional flow theory is used, and the target is chosen to have a shock wave in its distribution. The objective function which quantifies the difference between the targeted and calculated velocity distributions may become non-smooth due to the interaction between the shock and the discretization of the flowfield. This paper offers two techniques to resolve the resulting problems for the optimization algorithms. The first, shock-fitting, involves careful integration of the objective function through the shock wave. The second, coordinate straining with shock penalty, uses a coordinate transformation to align the calculated shock with the target and then adds a penalty proportional to the square of the distance between the shocks. The techniques are tested using several popular sensitivity and optimization methods, including finite-differences, and direct and adjoint discrete sensitivity methods. Two optimization strategies, Gauss-Newton and sequential quadratic programming (SQP), are used to drive the objective function to a minimum.

Grossman, Bernard↗
NASA NTRS1993

Near minimum-time maneuvers of large space structures using parameter optimization

Near minimum-time attitude maneuvers for large, inherently-flexible space structures with finite fuel supplies are investigated. The open loop maneuver is determined with the Sequential Quadratic Programming (SQP) algorithm, which optimizes a bang-off-bang control parameter set for the given maneuver. Torque smoothing is used to prevent discontinuities in the control which would excite the flexible structure. Additional system dynamics such as thruster inefficiency, spring forces and pressure leaks are identified from preliminary experiments on the ASTREX test article.

Carter, M. T.↗