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Results for “Stochastic dynamical systems”

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 NTRS1989

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.↗
NASA NTRS1983

Structural considerations for a software life cycle dynamic simulation model

This paper presents the results of a preliminary study into the prospects for simulating the software implementation and maintenance life cycle process, with the aim of producing a computerized tool for use by management and software engineering personnel in project planning, tradeoff studies involving product, environmental, situational, and technological factors, and training. The approach taken is the modular application of a 'flow of resource' concept to the systems dynamics simulation modeling technique. The software life cycle process is represented as a number of stochastic, time-varying, interacting work tasks that each achieves one of the project milestones. Each task is characterized by the item produced, the personnel applied, and the budgetary profile.

Tausworthe, R. C.↗
NASA NTRS1985

Optimal generalized multistep integration formulae for real-time digital simulation

The problem of discretizing a dynamical system for real-time digital simulation is considered. Treating the system and its simulation as stochastic processes leads to a statistical characterization of simulator fidelity. A plant discretization procedure based on an efficient matrix generalization of explicit linear multistep discrete integration formulae is introduced, which minimizes a weighted sum of the mean squared steady-state and transient error between the system and simulator outputs.

Moerder, D. D.↗
NASA NTRS1986

Control design for robust stability in linear regulators: Application to aerospace flight control

Time domain stability robustness analysis and design for linear multivariable uncertain systems with bounded uncertainties is the central theme of the research. After reviewing the recently developed upper bounds on the linear elemental (structured), time varying perturbation of an asymptotically stable linear time invariant regulator, it is shown that it is possible to further improve these bounds by employing state transformations. Then introducing a quantitative measure called the stability robustness index, a state feedback conrol design algorithm is presented for a general linear regulator problem and then specialized to the case of modal systems as well as matched systems. The extension of the algorithm to stochastic systems with Kalman filter as the state estimator is presented. Finally an algorithm for robust dynamic compensator design is presented using Parameter Optimization (PO) procedure. Applications in a aircraft control and flexible structure control are presented along with a comparison with other existing methods.

Yedavalli, R. K.↗
NASA NTRS1987

State-space self-tuning controllers for general multivariable stochastic systems

This paper presents a state-space approach for self-tuning control of a more general class of multivariable stochastic systems having a number of inputs equal or different from the number of outputs. The dynamic system is represented in the state-space innovation form with Luenberger's canonical structures. The model parameters and the Kalman gain are identified via either the extended least-squares algorithm or the least-squares ladder algorithm. The Kalman gain matrix and states can be estimated from the identified parameters without utilizing the standard state estimation algorithm. A long division method is introduced for finding the similarity transformation matrix.

Shieh, L. S.↗
NASA NTRS1990

Advances and trends in computational structures technology

The major goals of computational structures technology (CST) are outlined, and recent advances in CST are examined. These include computational material modeling, stochastic-based modeling, computational methods for articulated structural dynamics, strategies and numerical algorithms for new computing systems, multidisciplinary analysis and optimization. The role of CST in the future development of structures technology and the multidisciplinary design of future flight vehicles is addressed, and the future directions of CST research in the prediction of failures of structural components, the solution of large-scale structural problems, and quality assessment and control of numerical simulations are discussed.

Noor, A. K.↗
NASA NTRS2003

Integration of Online Parameter Identification and Neural Network for In-Flight Adaptive Control

An indirect adaptive system has been constructed for robust control of an aircraft with uncertain aerodynamic characteristics. This system consists of a multilayer perceptron pre-trained neural network, online stability and control derivative identification, a dynamic cell structure online learning neural network, and a model following control system based on the stochastic optimal feedforward and feedback technique. The pre-trained neural network and model following control system have been flight-tested, but the online parameter identification and online learning neural network are new additions used for in-flight adaptation of the control system model. A description of the modification and integration of these two stand-alone software packages into the complete system in preparation for initial flight tests is presented. Open-loop results using both simulation and flight data, as well as closed-loop performance of the complete system in a nonlinear, six-degree-of-freedom, flight validated simulation, are analyzed. Results show that this online learning system, in contrast to the nonlearning system, has the ability to adapt to changes in aerodynamic characteristics in a real-time, closed-loop, piloted simulation, resulting in improved flying qualities.

Hageman, Jacob↗
NASA NTRS2003

Integration of Online Parameter Identification and Neural Network for In-Flight Adaptive Control

An indirect adaptive system has been constructed for robust control of an aircraft with uncertain aerodynamic characteristics. This system consists of a multilayer perceptron pre-trained neural network, online stability and control derivative identification, a dynamic cell structure online learning neural network, and a model following control system based on the stochastic optimal feedforward and feedback technique. The pre-trained neural network and model following control system have been flight-tested, but the online parameter identification and online learning neural network are new additions used for in-flight adaptation of the control system model. A description of the modification and integration of these two stand-alone software packages into the complete system in preparation for initial flight tests is presented. Open-loop results using both simulation and flight data, as well as closed-loop performance of the complete system in a nonlinear, six-degree-of-freedom, flight validated simulation, are analyzed. Results show that this online learning system, in contrast to the nonlearning system, has the ability to adapt to changes in aerodynamic characteristics in a real-time, closed-loop, piloted simulation, resulting in improved flying qualities.

Hageman, Jacob J.↗
NASA NTRS1997

Detection of chaotic determinism in time series from randomly forced maps

Time series from biological system often display fluctuations in the measured variables. Much effort has been directed at determining whether this variability reflects deterministic chaos, or whether it is merely "noise". Despite this effort, it has been difficult to establish the presence of chaos in time series from biological sytems. The output from a biological system is probably the result of both its internal dynamics, and the input to the system from the surroundings. This implies that the system should be viewed as a mixed system with both stochastic and deterministic components. We present a method that appears to be useful in deciding whether determinism is present in a time series, and if this determinism has chaotic attributes, i.e., a positive characteristic exponent that leads to sensitivity to initial conditions. The method relies on fitting a nonlinear autoregressive model to the time series followed by an estimation of the characteristic exponents of the model over the observed probability distribution of states for the system. The method is tested by computer simulations, and applied to heart rate variability data.

Non-NASA Center↗
NASA NTRS1973

Structural Aspects of System Identification

The problem of identifying linear dynamical systems is studied by considering structural and deterministic properties of linear systems that have an impact on stochastic identification algorithms. In particular considered is parametrization of linear systems so that there is a unique solution and all systems in appropriate class can be represented. It is assumed that a parametrization of system matrices has been established from a priori knowledge of the system, and the question is considered of when the unknown parameters of this system can be identified from input/output observations. It is assumed that the transfer function can be asymptotically identified, and the conditions are derived for the local, global and partial identifiability of the parametrization. Then it is shown that, with the right formulation, identifiability in the presence of feedback can be treated in the same way. Similarly the identifiability of parametrizations of systems driven by unobserved white noise is considered using the results from the theory of spectral factorization.

Glover, Keith↗
NASA NTRS1983

Identification of helicopter rotor dynamic models

A recursive, extended Kalman-filter approach is applied to the identifiction of rotor damping levels of representative helicopter dynamic systems. The general formulation of the approach is presented in the context of a typically posed stochastic estimation problem, and the method is analytically applied to determining the damping levels of a coupled rotor-body system. The identified damping covergence characteristics are studied for sensitivity to both constant-coefficient and periodic-coefficient measurement models, process-noise covariance levels, and specified initial estimates of the rotor-system damping. A second application of the method to identifying the plant model for a highly damped, isolated flapping blade with a constant-coefficient state model (hover) and a periodic-coefficient state model (forward flight) is also investigated. The parameter-identification capability is evaluated for the effect of periodicity on the plant model coefficients and the influence of different measurement noise levels.

Molusis, J. A.↗
NASA NTRS2008

Simulation of Stochastic Processes by Coupled ODE-PDE

A document discusses the emergence of randomness in solutions of coupled, fully deterministic ODE-PDE (ordinary differential equations-partial differential equations) due to failure of the Lipschitz condition as a new phenomenon. It is possible to exploit the special properties of ordinary differential equations (represented by an arbitrarily chosen, dynamical system) coupled with the corresponding Liouville equations (used to describe the evolution of initial uncertainties in terms of joint probability distribution) in order to simulate stochastic processes with the proscribed probability distributions. The important advantage of the proposed approach is that the simulation does not require a random-number generator.

Zak, Michail↗
NASA NTRS2005

Stochastic Representation of Chaos using Terminal Attractors

A nonlinear version of the Liouville equation based upon terminal attractors is proposed for describing post-instability motions of dynamical systems with exponential divergence of trajectories such as those leading to chaos and turbulence. As a result, the post-instability motions are represented by expectations, variances, and higher moments of the state variables as functions of time. The proposed approach can be applied to conservative chaos, and in particular, to n-bodies problem, as well as to dissipative systems, and in particular, to chaotic attractors and turbulence.

stochastic processes↗
NASA NTRS1986

Dynamic remapping decisions in multi-phase parallel computations

The effectiveness of any given mapping of workload to processors in a parallel system is dependent on the stochastic behavior of the workload. Program behavior is often characterized by a sequence of phases, with phase changes occurring unpredictably. During a phase, the behavior is fairly stable, but may become quite different during the next phase. Thus a workload assignment generated for one phase may hinder performance during the next phase. We consider the problem of deciding whether to remap a paralled computation in the face of uncertainty in remapping's utility. Fundamentally, it is necessary to balance the expected remapping performance gain against the delay cost of remapping. This paper treats this problem formally by constructing a probabilistic model of a computation with at most two phases. We use stochastic dynamic programming to show that the remapping decision policy which minimizes the expected running time of the computation has an extremely simple structure: the optimal decision at any step is followed by comparing the probability of remapping gain against a threshold. This theoretical result stresses the importance of detecting a phase change, and assessing the possibility of gain from remapping. We also empirically study the sensitivity of optimal performance to imprecise decision threshold. Under a wide range of model parameter values, we find nearly optimal performance if remapping is chosen simply when the gain probability is high. These results strongly suggest that except in extreme cases, the remapping decision problem is essentially that of dynamically determining whether gain can be achieved by remapping after a phase change; precise quantification of the decision model parameters is not necessary.

Nicol, D. M.↗
NASA NTRS1980

Optimal regulation in systems with stochastic time sampling

An optimal control theory that accounts for stochastic variable time sampling in a distributed microprocessor based flight control system is presented. The theory is developed by using a linear process model for the airplane dynamics and the information distribution process is modeled as a variable time increment process where, at the time that information is supplied to the control effectors, the control effectors know the time of the next information update only in a stochastic sense. An optimal control problem is formulated and solved for the control law that minimizes the expected value of a quadratic cost function. The optimal cost obtained with a variable time increment Markov information update process where the control effectors know only the past information update intervals and the Markov transition mechanism is almost identical to that obtained with a known and uniform information update interval.

Montgomery, R. C.↗
NASA NTRS1983

Fixed-order dynamic compensation through optimal projection

This paper reviews a formulation for the design of fixed-order dynamic compensation for flexible mechanical systems which is based upon explicit optimality conditions derived under the minimum data/maximum entropy stochastic modelling approach. The optimality conditions give rise to the novel concept of "optimal projection' which provides significant insight with regard to the compensator structure and permits earlier, more restricted and/or ad hoc design schemes to be seen as special cases of the present formulation.

Hyland, D. C.↗
NASA NTRS2014

CLEANing the Reward: Counterfactual Actions to Remove Exploratory Action Noise in Multiagent Learning

Learning in multiagent systems can be slow because agents must learn both how to behave in a complex environment and how to account for the actions of other agents. The inability of an agent to distinguish between the true environmental dynamics and those caused by the stochastic exploratory actions of other agents creates noise in each agent's reward signal. This learning noise can have unforeseen and often undesirable effects on the resultant system performance. We define such noise as exploratory action noise, demonstrate the critical impact it can have on the learning process in multiagent settings, and introduce a reward structure to effectively remove such noise from each agent's reward signal. In particular, we introduce Coordinated Learning without Exploratory Action Noise (CLEAN) rewards and empirically demonstrate their benefits

Reinforcement Learning↗