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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 109 records · Page 6
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NASA NTRS1972

Adaptive control of stochastic linear systems with unknown parameters

The problem of optimal control of linear discrete-time stochastic dynamical system with unknown and, possibly, stochastically varying parameters is considered on the basis of noisy measurements. It is desired to minimize the expected value of a quadratic cost functional. Since the simultaneous estimation of the state and plant parameters is a nonlinear filtering problem, the extended Kalman filter algorithm is used. Several qualitative and asymptotic properties of the open loop feedback optimal control and the enforced separation scheme are discussed. Simulation results via Monte Carlo method show that, in terms of the performance measure, for stable systems the open loop feedback optimal control system is slightly better than the enforced separation scheme, while for unstable systems the latter scheme is far better.

Ku, R. T.↗
NASA NTRS1971

A stochastic model for eye movements during fixation on a stationary target.

A stochastic model describing small eye movements occurring during steady fixation on a stationary target is presented. Based on eye movement data for steady gaze, the model has a hierarchical structure; the principal level represents the random motion of the image point within a local area of fixation, while the higher level mimics the jump processes involved in transitions from one local area to another. Target image motion within a local area is described by a Langevin-like stochastic differential equation taking into consideration the microsaccadic jumps pictured as being due to point processes and the high frequency muscle tremor, represented as a white noise. The transform of the probability density function for local area motion is obtained, leading to explicit expressions for their means and moments. Evaluation of these moments based on the model is comparable with experimental results.

Vasudevan, R.↗
NASA NTRS1972

On the application of deterministic optimization methods to stochastic control problems.

A technique is presented by which one can apply the Minimum Principle of Pontryagin to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being essentially deterministic. The technique is applied to systems with quadratic and non-quadratic costs to illustrate its use.

Kramer, L. C.↗
NASA NTRS1973

Solution of the stochastic control problem in unbounded domains.

Bellman's dynamic programming equation for the optimal index and control law for stochastic control problems is a parabolic or elliptic partial differential equation frequently defined in an unbounded domain. Existing methods of solution require bounded domain approximations, the application of singular perturbation techniques or Monte Carlo simulation procedures. In this paper, using the fact that Poisson impulse noise tends to a Gaussian process under certain limiting conditions, a method which achieves an arbitrarily good approximate solution to the stochastic control problem is given. The method uses the two iterative techniques of successive approximation and quasi-linearization and is inherently more efficient than existing methods of solution.

Robinson, P.↗
NASA NTRS1974

Control of Finite-State, Finite Memory Stochastic Systems

A generalized problem of stochastic control is discussed in which multiple controllers with different data bases are present. The vehicle for the investigation is the finite state, finite memory (FSFM) stochastic control problem. Optimality conditions are obtained by deriving an equivalent deterministic optimal control problem. A FSFM minimum principle is obtained via the equivalent deterministic problem. The minimum principle suggests the development of a numerical optimization algorithm, the min-H algorithm. The relationship between the sufficiency of the minimum principle and the informational properties of the problem are investigated. A problem of hypothesis testing with 1-bit memory is investigated to illustrate the application of control theoretic techniques to information processing problems.

Sandell, Nils R.↗
NASA NTRS1974

Sequential decision analysis for nonstationary stochastic processes

A formulation of the problem of making decisions concerning the state of nonstationary stochastic processes is given. An optimal decision rule, for the case in which the stochastic process is independent of the decisions made, is derived. It is shown that this rule is a generalization of the Bayesian likelihood ratio test; and an analog to Wald's sequential likelihood ratio test is given, in which the optimal thresholds may vary with time.

Schaefer, B.↗
NASA NTRS1974

On the application of deterministic optimization methods to stochastic control problems

A technique is presented by which deterministic optimization techniques, for example, the maximum principle of Pontriagin, can be applied to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being deterministic. The use of the technique in treating problems with quadratic and nonquadratic costs is illustrated.

Kramer, L. C.↗
NASA NTRS1973

Open-loop-feedback-optimal adaptive stochastic control of linear systems

This paper considers the suboptimal stochastic control of linear discrete-time dynamical systems with unknown or stochastically varying parameters. The suboptimal scheme is based upon the use of the open-loop-feedback-optimal method. The state and parameter estimates are generated by an extended Kalman filter algorithm. Numerical results for first-order systems are presented.

Ku, R.↗
NASA NTRS1973

An empirical analysis of the distribution of overshoots in a stationary Gaussian stochastic process

The frequency distribution of overshoots in a stationary Gaussian stochastic process is analyzed. The primary processes involved in this analysis are computer simulation and statistical estimation. Computer simulation is used to simulate stationary Gaussian stochastic processes that have selected autocorrelation functions. An analysis of the simulation results reveals a frequency distribution for overshoots with a functional dependence on the mean and variance of the process. Statistical estimation is then used to estimate the mean and variance of a process. It is shown that for an autocorrelation function, the mean and the variance for the number of overshoots, a frequency distribution for overshoots can be estimated.

Carter, M. C.↗
NASA NTRS1973

A linear stochastic model of the human operator

A linear stochastic model of the human operator is developed and applied to the problem of piloted control of an aircraft. The pilot and aircraft are modeled as linear time-invariant systems containing both process and measurement noise. The loop closure by the pilot is determined by formulating the problem as an optimal stochastic control problem. The solution to the optimal control problem yields not only the pilot's optimal control output which he uses to control the vehicle, but also the optimal combination of his observations of the vehicle states upon which the pilot bases his control. A method is presented so that, using experimental pilot vehicle data, the cost functional which is minimized in the optimal control problem will be numerically equal to the pilot rating that the pilot would associate with the given vehicle and task.

Durrett, J. C.↗
NASA NTRS1975

Stochastic model for fatigue crack size and cost effective design decisions

This paper describes a methodology for making cost effective fatigue design decisions. The methodology is based on a probabilistic model for the stochastic process of fatigue crack growth with time. The development of a particular model for the stochastic process is also discussed in the paper. The model is based on the assumption of continuous time and discrete space of crack lengths. Statistical decision theory and the developed probabilistic model are used to develop the procedure for making fatigue design decisions on the basis of minimum expected cost or risk function and reliability bounds. Selections of initial flaw size distribution, NDT, repair threshold crack lengths, and inspection intervals are discussed.

Hanagud, S.↗
NASA NTRS1975

Connective stability of large-scale stochastic systems

The procedure of decomposition-aggregation analysis reported by Siljak (1973) and Grujic and Siljak (1973) has been used in a study of the connective-stability aspects of large-scale stochastic systems. An investigation is conducted of the tolerance of a system of interconnected deterministic subsystems to both deterministic and stochastic interactions. The connective stability in the mean is considered and the connective property of stability is defined. The defined concept is included in a modification of the comparison theorem described by Ladde (1975). Attention is also given to a derivation of the sufficient conditions for the connective stability in the mean.

Ladde, G. S.↗
NASA NTRS1975

Stochastic stability and instability of model ecosystems

In this work, we initiate a stability study of multispecies communities in stochastic environment by using Ito's differential equations as community models. By applying the direct method of Liapunov, we obtain sufficient conditions for stability and instability in the mean of the equilibrium populations. The conditions are expressed in terms of the dominant diagonal property of community matrices, which is a suitable mechanism for resolving the central problem of 'complexity vs stability' in model ecosystems. As a by-product of this analysis we exhibit important structural properties of the stochastic density-dependent models, and establish tolerance of community stability to a broad class of nonlinear time-varying perturbations.

Ladde, G. S.↗
NASA NTRS1975

A note on the consistency of maximum likelihood estimates for finite families of stochastic processes

The note considers families of stochastic processes indexed by a finite number of alternative parameter values. For general classes of stochastic processes, it is shown that maximum-likelihood estimates converge almost surely to the correct parameter value. This is established by use of a submartingale property of the sequence of maximized-likelihood ratios together with a technique first employed by Wald (1949) in the case of independent identically distributed random variables.

Caines, P. E.↗
NASA NTRS1976

Estimation of characteristics and stochastic control of an aircraft flying in atmospheric turbulence

An adaptive control technique to improve the flying qualities of an aircraft in turbulence was investigated. The approach taken was to obtain maximum likelihood estimates of the unknown coefficients of the aircraft system and then, using these estimates along with the separation principle, to define the stochastic optimal control. The maximum likelihood estimation technique that accounted for the effects of turbulence provided good estimates of the unknown coefficients and of the turbulence. The assessment of the stochastic optimal control based on the maximum likelihood estimates showed that the desired effects were attained for the regulator problem of minimizing pitch angle and the tracking problem of requiring normal acceleration to follow the pilot input.

Iliff, K. W.↗
NASA NTRS1976

Frequency domain approach for evaluation of stochastic control of elastic spacecraft

An attempt is made to develop a reduced-order filter for an elastic spacecraft. The frequency-domain approach is resorted to both for arriving at an appropriate ROF and for evaluating the resulting stochastic flight controller. The frequency-domain approach employed is contrasted to the time-domain approach previously utilized by the authors. A linearized deterministic dynamical model of a solar electric propulsion spacecraft is analyzed. Flexibility modes were incorporated profitably into the ROF model, and the stochastic controllers exhibit notching of structural resonances reminiscent of classical notch filters. Accurate estimates of modal parameters (damping, natural frequency) are deemed crucial, and use of worst-case values in the ROF design is recommended.

Larson, V.↗
NASA NTRS1977

Models for interrupted monitoring of a stochastic process

As computers are added to the cockpit, the pilot's job is changing from of manually flying the aircraft, to one of supervising computers which are doing navigation, guidance and energy management calculations as well as automatically flying the aircraft. In this supervisorial role the pilot must divide his attention between monitoring the aircraft's performance and giving commands to the computer. Normative strategies are developed for tasks where the pilot must interrupt his monitoring of a stochastic process in order to attend to other duties. Results are given as to how characteristics of the stochastic process and the other tasks affect the optimal strategies.

Palmer, E.↗