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Results for “Second-order optimization”

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.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

The linear quadratic optimal control problem for infinite dimensional systems over an infinite horizon - Survey and examples

Available published results are surveyed for a special class of infinite-dimensional control systems whose evolution is characterized by a semigroup of operators of class C subscript zero. Emphasis is placed on an approach that clarifies the system-theoretic relationship among controllability, stabilizability, stability, and the existence of a solution to an associated operator equation of the Riccati type. Formulation of the optimal control problem is reviewed along with the asymptotic behavior of solutions to a general system of equations and several theorems concerning L2 stability. Examples are briefly discussed which involve second-order parabolic systems, first-order hyperbolic systems, and distributed boundary control.

Bensoussan, A.↗
NASA NTRS1972

On higher order discrete phase-locked loops.

An exact mathematical model is developed for a discrete loop of a general order particularly suitable for digital computation. The deterministic response of the loop to the phase step and the frequency step is investigated. The design of the digital filter for the second-order loop is considered. Use is made of the incremental phase plane to study the phase error behavior of the loop. The model of the noisy loop is derived and the optimization of the loop filter for minimum mean-square error is considered.

Gill, G. S.↗
NASA NTRS1978

Second order approximation of natural frequency constraints in structural synthesis

The paper is concerned with structural optimization problems in which the constraints consist of limits imposed on the natural frequencies of the structure. Improvements in the quality of approximations for the frequency constraints are sought by considering second-order Taylor series expansions. Analysis of the second-order sensitivity of natural frequencies is carried out. As an example, the design of a midplane symmetric aluminum beam of constant depth supporting three nonstructural masses is considered. Web thickness and chord member areas were determined so as to achieve minimum structural mass while maintaining the fundamental frequency at or above 30 Hz.

Miura, H.↗
NASA NTRS1972

Application of multivariable search techniques to structural design optimization

Multivariable optimization techniques are applied to a particular class of minimum weight structural design problems: the design of an axially loaded, pressurized, stiffened cylinder. Minimum weight designs are obtained by a variety of search algorithms: first- and second-order, elemental perturbation, and randomized techniques. An exterior penalty function approach to constrained minimization is employed. Some comparisons are made with solutions obtained by an interior penalty function procedure. In general, it would appear that an interior penalty function approach may not be as well suited to the class of design problems considered as the exterior penalty function approach. It is also shown that a combination of search algorithms will tend to arrive at an extremal design in a more reliable manner than a single algorithm. The effect of incorporating realistic geometrical constraints on stiffener cross-sections is investigated. A limited comparison is made between minimum weight cylinders designed on the basis of a linear stability analysis and cylinders designed on the basis of empirical buckling data. Finally, a technique for locating more than one extremal is demonstrated.

Jones, R. T.↗
NASA NTRS1990

Dissipative compensators for flexible spacecraft control

The problem of controller design for flexible spacecraft is addressed. Model-based compensators, which rely on the knowledge of the system parameters to tune the state estimator, are considered. The instability mechanisms resulting from high sensitivity to parameter uncertainties are investigated. Dissipative controllers, which use collocated actuators and sensors, are also considered, and the robustness properties of constant-gain dissipative controllers in the presence of unmodeled elastic-mode dynamics, sensor/actuator nonlinearities, and actuator dynamics are summarized. In order to improve the performance without sacrificing robustness, a class of dissipative dynamic compensators is proposed and is shown to retain robust stability in the presence of second-order actuator dynamics if acceleration feedback is employed. A class of dissipative dynamic controllers is proposed which consists of a low-authority, constant-gain controller and a high-authority dynamic compensator. A procedure for designing an optimal dissipative dynamic compensator is given which minimizes a quadratic performance criterion. Such compensators offer the promise of better performance while still retaining robust stability.

Joshi, S. M.↗
NASA NTRS1971

Analytical methods for performance evaluation of nonlinear filters.

In the investigation, the filtering problem is considered in the continuous time domain. The postulated simple suboptimal nonlinear filter structure closely parallels the structure of the Kalman-Bucy optimal linear filter algorithm. Two filter performance evaluation methods are developed based on the Kolmogorov equations for the transition density of Markov processes. The expansions in the approximations for the nonlinear system and observation functions are in effect carried out up to second-order terms in both methods. The description of the filter's performance is sought in terms of second-order statistics in both methods.

Bejczy, A. K.↗
NASA NTRS1979

Analysis and design of an adaptive multi-loop controlled two winding buck/boost regulator

Small signal low frequency linear average model is derived for a multi-loop controlled two-winding buck/boost converter employing average techniques and the describing function method. The model reveals that a well-designed multi-loop control can provide a second-order zero adaptive to output filter parameter changes due to component tolerances, temperature changes, aging, and the effect of duty cycle modulation. It also can provide stabilization effect by shifting the positive zero to the left-half S-plane. Design guidelines are formulated to optimize regulator-loop dependent characteristics.

Mahmoud, M. F.↗
NASA NTRS1972

Criteria for the optimal design of experimental tests

Some of the basic concepts are unified that were developed for the problem of finding optimal approximating functions which relate a set of controlled variables to a measurable response. The techniques have the potential for reducing the amount of testing required in experimental investigations. Specifically, two low-order polynomial models are considered as approximations to unknown functionships. For each model, optimal means of designing experimental tests are presented which, for a modest number of measurements, yield prediction equations that minimize the error of an estimated response anywhere inside a selected region of experimentation. Moreover, examples are provided for both models to illustrate their use. Finally, an analysis of a second-order prediction equation is given to illustrate ways of determining maximum or minimum responses inside the experimentation region.

Canavos, G. C.↗
NASA NTRS1989

Algorithm For Optimal Control Of Large Structures

Cost of computation appears competitive with other methods. Problem to compute optimal control of forced response of structure with n degrees of freedom identified in terms of smaller number, r, of vibrational modes. Article begins with Hamilton-Jacobi formulation of mechanics and use of quadratic cost functional. Complexity reduced by alternative approach in which quadratic cost functional expressed in terms of control variables only. Leads to iterative solution of second-order time-integral matrix Volterra equation of second kind containing optimal control vector. Cost of algorithm, measured in terms of number of computations required, is of order of, or less than, cost of prior algoritms applied to similar problems.

Salama, Moktar A.↗
NASA NTRS1988

Helicopter trajectory planning using optimal control theory

A methodology for optimal trajectory planning, useful in the nap-of-the-earth guidance of helicopters, is presented. This approach uses an adjoint-control transformation along with a one-dimensional search scheme for generating the optimal trajectories. In addition to being useful for helicopter nap-of-the-earth guidance, the trajectory planning solution is of interest in several other contexts, such as robotic vehicle guidance and terrain-following guidance for cruise missiles and aircraft. A distinguishing feature of the present research is that the terrain constraint and the threat envelopes are incorporated in the equations of motion. Second-order necessary conditions are examined.

Menon, P. K. A.↗
NASA NTRS1972

On optimizing the treatment of exchange perturbations.

Most theories of exchange perturbations would give the exact energy and wave function if carried out to an infinite order. However, the different methods give different values for the second-order energy, and different values for E(1), the expectation value of the Hamiltonian corresponding to the zeroth- plus first-order wave function. In the presented paper, it is shown that the zeroth- plus first-order wave function obtained by optimizing the basic equation which is used in most exchange perturbation treatments is the exact wave function for the perturbation system and E(1) is the exact energy.

Hirschfelder, J. O.↗
NASA NTRS1977

Optimal estimation and attitude control of a solar electric propulsion spacecraft

Established procedures of linear, quadratic, Gaussian optimal estimation and control are developed and interpreted for their application to the problem of attitude control of spacecraft with dynamically significant elastic appendages. Results are presented both in general terms and for specific application to a solar electric spacecraft. Comparisons are made between alternative coordinate systems, and a realistic range of design parameters is considered. For single axis control, system evaluation is accomplished by simulation of a fifteenth-order spacecraft plant with alternative second-order, fourth-order, and sixth-order constant gain estimators. Results point out the importance of modeling errors.

Larson, V.↗
NASA NTRS1983

Optimum sensitivity derivatives of objective functions in nonlinear programming

The feasibility of eliminating second derivatives from the input of optimum sensitivity analyses of optimization problems is demonstrated. This elimination restricts the sensitivity analysis to the first-order sensitivity derivatives of the objective function. It is also shown that when a complete first-order sensitivity analysis is performed, second-order sensitivity derivatives of the objective function are available at little additional cost. An expression is derived whose application to linear programming is presented.

Barthelemy, J.-F. M.↗
NASA NTRS1984

Efficient calculation of optimum design sensitivity

Two methods for obtaining the sensitivity of an optimized design to changes in problem parameters are presented. The first-order method uses gradient information to estimate the required sensitivity. The second-order method uses second derivatives of the design objective and constraint functions to provide a quadratic approximation to the new design which results from changing the specified parameter. It is shown that the sensitivity of the optimized design may be discontinuous with respect to the new parameter. This discontinuity is accounted for in the present methods. These methods are compared to a previous approach based on the Kuhn-Tucker necessary conditions for optimality. It is shown that the present methods provide the appropriate sensitivity information in an efficient manner. The methods are demonstrated by a structural synthesis example.

Vanderplaats, G. N.↗
NASA NTRS1985

A method to stabilize linear systems using eigenvalue gradient information

Formal optimization methods and eigenvalue gradient information are used to develop a stabilizing control law for a closed loop linear system that is initially unstable. The method was originally formulated by using direct, constrained optimization methods with the constraints being the real parts of the eigenvalues. However, because of problems in trying to achieve stabilizing control laws, the problem was reformulated to be solved differently. The method described uses the Davidon-Fletcher-Powell minimization technique to solve an indirect, constrained minimization problem in which the performance index is the Kreisselmeier-Steinhauser function of the real parts of all the eigenvalues. The method is applied successfully to solve two different problems: the determination of a fourth-order control law stabilizes a single-input single-output active flutter suppression system and the determination of a second-order control law for a multi-input multi-output lateral-directional flight control system. Various sets of design variables and initial starting points were chosen to show the robustness of the method.

Wieseman, C. D.↗