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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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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

The Stochastic Gause Predator-Prey model: Noise-induced extinctions and invariance

We consider the Gause predator-prey with general bounded or sub‑linear functional responses, – which includes those of Holling types Ⅰ–Ⅳ. – and multiplicative Gaussian noise. In contrast to previous studies, the prey in our model follows logistic dynamics while the predator's population is solely regulated by consumption of the prey. To ensure well-posedeness, we derive explicit Lyapunov‐type criteria ensuring global positivity and moment boundedness of solutions. We find conditions for noise‑induced extinctions, proving that stochasticity can drive either population to collapse even when the deterministic analogue predicts stable coexistence. In the case when the predator becomes extinct, we establish a limiting distribution for the predator's population. Last, for functional responses of Holling type Ⅰ, we provide sufficient conditions on the intensity of the noise for the existence and uniqueness of a stationary distribution.

Gause model↗
NASA NTRS1972

An algorithm for control system design via parameter optimization

An algorithm for design via parameter optimization has been developed for linear-time-invariant control systems based on the model reference adaptive control concept. A cost functional is defined to evaluate the system response relative to nominal, which involves in general the error between the system and nominal response, its derivatives and the control signals. A program for the practical implementation of this algorithm has been developed, with the computational scheme for the evaluation of the performance index based on Lyapunov's theorem for stability of linear invariant systems.

Sinha, P. K.↗
NASA NTRS1972

Nutational stability of a dual-spin satellite under the influence of applied reaction torques.

The nutational stability of a dual-spin satellite under the influence of an applied reaction torque is analyzed. It is assumed that since the solar paddle attachments to the hub of the spacecraft are not rigidly locked, the effect of the solar panels can be replaced by a constant reaction torque acting on the hub of the spacecraft. This could result in the satellite having an equilibrium motion about an axis displaced from the nominal axis of symmetry. The variational equations of motion are developed about such an equilibrium position using the SAS-A spacecraft as a model. Energy dissipation on the rotor as well as the main body is included. This nonautonomous set of differential equations are linearized and transformed to an autonomous set using the Lyapunov Reducibility Theorem. The stability of the kinematically similar system is examined numerically using representative SAS-A parameters for the case when either pair of solar panels is assumed to be loosely attached. Stability is verified for small system nutation angles (0.1 degree) although the time constant associated with the least damped mode is approximately one order of magnitude larger than that for the SAS-A system without the influence of the reaction torques.

Bainum, P. M.↗
NASA NTRS1972

Computation of optimal output-feedback compensators for linear time-invariant systems

The control of linear time-invariant systems with respect to a quadratic performance criterion was considered, subject to the constraint that the control vector be a constant linear transformation of the output vector. The optimal feedback matrix, f*, was selected to optimize the expected performance, given the covariance of the initial state. It is first shown that the expected performance criterion can be expressed as the ratio of two multinomials in the element of f. This expression provides the basis for a feasible method of determining f* in the case of single-input single-output systems. A number of iterative algorithms are then proposed for the calculation of f* for multiple input-output systems. For two of these, monotone convergence is proved, but they involve the solution of nonlinear matrix equations at each iteration. Another is proposed involving the solution of Lyapunov equations at each iteration, and the gradual increase of the magnitude of a penalty function. Experience with this algorithm will be needed to determine whether or not it does, indeed, possess desirable convergence properties, and whether it can be used to determine the globally optimal f*.

Platzman, L. K.↗
NASA NTRS1971

Stability of uncertain systems

The asymptotic properties of feedback systems are discussed, containing uncertain parameters and subjected to stochastic perturbations. The approach is functional analytic in flavor and thereby avoids the use of Markov techniques and auxiliary Lyapunov functionals characteristic of the existing work in this area. The results are given for the probability distributions of the accessible signals in the system and are proved using the Prohorov theory of the convergence of measures. For general nonlinear systems, a result similar to the small loop-gain theorem of deterministic stability theory is given. Boundedness is a property of the induced distributions of the signals and not the usual notion of boundedness in norm. For the special class of feedback systems formed by the cascade of a white noise, a sector nonlinearity and convolution operator conditions are given to insure the total boundedness of the overall feedback system.

Blankenship, G. L.↗
NASA NTRS1972

Stability of large-scale systems under structural perturbations.

A large-scale system is considered as a system constituted of subsystems which may be connected or disconnected from each other during operation. A new concept of connective stability is introduced by which a large-scale system is regarded as stable if it remains stable (in the sense of Lyapunov) under structural perturbations produced by the on-off participation of the subsystems. Algebraic conditions are developed that guarantee exponential connective stability of large-scale systems which may be composed of linear and nonlinear time-varying subsystems coupled by linear or nonlinear connections.

Siljak, D. D.↗
NASA NTRS1972

Invariance and stability for bounded uncertain systems.

The positive limit sets of the solutions of a contingent differential equation are shown to possess an invariance property. In this connection the 'invariance principle' in the theory of Lyapunov stability is extended to systems with unknown, bounded, time-varying parameters, and thus to a large and important class of nonautonomous systems. Asymptotic stability criteria are obtained and applied to guaranteed cost control problems.

Peng, T. K. C.↗
NASA NTRS1972

An approximate method for the synthesis of optimal control of distributed systems.

An approximate method is presented for the synthesis of an optimal control of distributed parameter systems, based on a combination of the ideas of Lyapunov's direct method and those of Bellman's successive approximation in policy space. The method is such that the approximate equation is improved after each iteration in the sense of the performance index being used.

Park, K. E.↗
NASA NTRS1973

An adaptive observer for single-input single-output linear systems.

A full order adaptive observer is described for observing the state of a single-input single-output observable continuous differential system with unknown parameters. Convergence of the observer states to those of the system is accomplished by directly changing the parameters of the observer using an adaptive law based upon Lyapunov stability theory. Observer eigenvalues may be freely chosen. Some restriction is placed upon the system input in that it must be sufficiently rich in frequencies in order to insure convergence.

Carroll, R. L.↗
NASA NTRS1973

Design implementation in model-reference adaptive systems

The derivation of an approximate error characteristic equation describing the transient system error response is given, along with a procedure for selecting adaptive gain parameters so as to relate to the transient error response. A detailed example of the application and implementation of these methods for a space shuttle type vehicle is included. An extension of the characteristic equation technique is used to provide an estimate of the magnitude of the maximum system error and an estimate of the time of occurrence of this maximum after a plant parameter disturbance. Techniques for relaxing certain stability requirements and the conditions under which this can be done and still guarantee asymptotic stability of the system error are discussed. Such conditions are possible because the Lyapunov methods used in the stability derivation allow for overconstraining a problem in the process of insuring stability.

Boland, J. S., III↗
NASA NTRS1975

Prediction of axial-flow instabilities in a turbojet engine by use of a multistage compressor simulation on the digital computer

A method of estimating the undistorted stall line for an axial-flow compressor by using the digital computer is presented. The method involves linearization of nonlinear dynamic equations about an operating point on a speed line, and then application of the first method of Lyapunov to determine the stability of the nonlinear system from the stability of the linear system. The method is applied to a simulation of the J85 compressor, which utilizes stage stacking and lumped volume techniques for the interstage regions to simulate steady-state and dynamic compressor performance. The stability boundary predicted by the digital simulation compares quite well with the stall line predicted by a dynamic simulation of the J85 compressor programmed on the analog computer. Since previous studies have shown that the analog-predicted stall line agrees well with the stall line of the compressor, the digital method presented is also a good means of estimating the stall line.

Daniele, C. J.↗
NASA NTRS1974

Model reference adaptive control with an augmented error signal

It is shown how globally stable model reference adaptive control systems may be designed when one has access to only the plant's input and output signals. Controllers for single input-single output, nonlinear, nonautonomous plants are developed based on Lyapunov's direct method and the Meyer-Kalman-Yacubovich lemma. Derivatives of the plant output are not required, but are replaced by filtered derivative signals. An augmented error signal replaces the error normally used, which is defined as the difference between the model and plant outputs. However, global stability is assured in the sense that the normally used error signal approaches zero asymptotically.

Monopoli, R. V.↗
NASA NTRS1975

Control optimization, stabilization and computer algorithms for aircraft applications

Research related to reliable aircraft design is summarized. Topics discussed include systems reliability optimization, failure detection algorithms, analysis of nonlinear filters, design of compensators incorporating time delays, digital compensator design, estimation for systems with echoes, low-order compensator design, descent-phase controller for 4-D navigation, infinite dimensional mathematical programming problems and optimal control problems with constraints, robust compensator design, numerical methods for the Lyapunov equations, and perturbation methods in linear filtering and control.

Source record↗
NASA NTRS1975

Error magnitude estimation in model-reference adaptive systems

A second order approximation is derived from a linearized error characteristic equation for Lyapunov designed model-reference adaptive systems and is used to estimate the maximum error between the model and plant states, and the time to reach this peak following a plant perturbation. The results are applicable in the analysis of plants containing magnitude-dependent nonlinearities.

Colburn, B. K.↗
NASA NTRS1976

Stabilization by modification of the Lagrangian

In order to reduce the error growth during a numerical integration, a method for stabilizing the differential equations of Keplerian motion is offered. It is characterized by the use of the eccentric anomaly as independent variable in such a way that the time transformation is given by a generalized Lagrange formalism. The control terms in the equations of motion obtained by this modified Lagrangian give immediately a completely Lyapunov-stable set of differential equations. The equation of time integration is modified by a control term which leads to an integral which defined the time element for the perturbed Keplerian motion.

Baumgarte, J. W.↗
NASA NTRS1976

Numerical solution of the state dependent noise problem

A numerical technique is given for solving the matrix quadratic equation that arises in the optimal stationary control of linear systems with state (and/or control) dependent noise. The technique exploits fully existing, efficient algorithms for the matrix Lyapunov and Ricatti equations. The computational requirements are discussed, with an associated example.

Kleinman, D. L.↗