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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.
The problem of estimating the prior probabilities q sub k of a mixture of known density functions f sub k(X), based on a sequence of N statistically independent observations is considered. It is shown that for very mild restrictions on f sub k(X), the maximum likelihood estimate of Q is asymptotically efficient. A recursive algorithm for estimating Q is proposed, analyzed, and optimized. For the M = 2 case, it is possible for the recursive algorithm to achieve the same performance with the maximum likelihood one. For M 2, slightly inferior performance is the price for having a recursive algorithm. However, the loss is computable and tolerable.
The muscle spindle, the feedback element in the myotatic (stretch) reflex, is a major contributor to muscular control. Therefore, an accurate description of behavior of the muscle spindle during active contraction of the muscle, as well as during passive stretch, is essential to the understanding of muscle control. Animal experiments were performed in order to obtain the data necessary to model the muscle spindle. Spectral density functions were used to identify a linear approximation of the two types of nerve endings from the spindle. A model reference adaptive control system was used on a hybrid computer to optimize the anatomically defined lumped parameter estimate of the spindle. The derived nonlinear model accurately predicts the behavior of the muscle spindle both during active discharge and during its silent period. This model is used to determine the mechanism employed to control muscle movement.
It is demonstrated that use of the square root information filter (SRIF) can reduce the storage and computation required for estimation of certain classes of large-scale interconnected systems. The SRIF uses an information array that is related to the Kalman filter covariance and estimate. The SRIF algorithm, which is optimal, is a direct application of matrix partitioning to some optimal filtering algorithms described in the literature. The SRIF algorithm is able to reduce the storage requirements of a 40-subsystem 10-state problem by a full order of magnitude.
This paper presents a partial evaluation on the use of singular perturbation methods for developing computer algorithms for on-line optimal control of aircraft. The evaluation is based on a study of the minimum time intercept problem using F-4 aerodynamic and propulsion data as a base line. The extensions over previous work on this subject are that aircraft turning dynamics (in addition to position and energy dynamics) are included in the analysis, the algorithm is developed for a moving end point and is adaptive to unpredictable target maneuvers, and short range maneuvers that do not have a cruise leg are included. Particular attention is given to identifying those quantities that can be precomputed and stored (as a function of aircraft total energy), thus greatly reducing the onboard computational load. Numerical results are given that illustrate the nature of the optimal intercept flight paths, and an estimate is given for the execution time and storage requirements of the control algorithm.
An overview is given of the Cargo/Logistics Airlift Systems Study (CLASS) project which was a 10 man-year effort carried out by two contractor teams, aimed at defining factors impacting future system growth and obtaining market requirements and design guidelines for future air freighters. Growth projection was estimated by two approaches: one, an optimal systems approach with a more efficient and cost effective system considered as being available in 1990; and the other, an evolutionary approach with an econometric behavior model used to predict long term evolution from the present system. Both approaches predict significant growth in demand for international air freighter services and less growth for U.S. domestic services. Economic analysis of air freighter fleet options indicate very strong market appeal of derivative widebody transports in 1990 with little incentive to develop all new dedicated air freighters utilizing the 1990's technology until sometime beyond the year 2000. Advanced air freighters would be economically attractive for a wide range of payload sizes (to 500 metric tons), however, if a government would share in the RD and T costs by virtue of its needs for a slightly modified version of a civil air freighter design (a.g. military airlifter).
The requirements of symmetry and convexity in the application of algorithms for the minimization or maximization of a function are discussed. It is argued that if a function of a single variable is convex and symmetric in a neighborhood of an extremum, the extremum may be approximated to the precision that increases by at least a power of two per functional evaluation. The procedure may be used to drive a complex optimization procedure in the multivariate area estimation problem encountered in remote sensing.
A pilot data center to compute ocean atmosphere heat exchange over the tropical ocean is prposed at the Jet Propulsion Laboratory (JPL) in response to the scientific needs of the Tropical Ocean and Global Atmosphere (TOGA) Program. Optimal methods will be used to estimate sea surface temperature (SET), surface wind speed, and humidity from spaceborne observations. A monthly summary of these parameters will be used to compute ocean atmosphere latent heat exchanges. Monthly fields of surface heat flux over tropical oceans will be constructed using estimations of latent heat exchanges and short wave radiation from satellite data. Verification of all satellite data sets with in situ measurements at a few locations will be provided. The data center will be an experimental active archive where the quality and quantity of data required for TOGA flux computation are managed. The center is essential to facilitate the construction of composite data sets from global measurements taken from different sensors on various satellites. It will provide efficient utilization and easy access to the large volume of satellite data available for studies of ocean atmosphere energy exchanges.
Employing a synthetic aperture radar (SAR) imaging model based on fundamental models of nonlinear hydrodynamics, electromagnetic scattering from a two-scale surface, and SAR imaging of a time-variant scene, the optimal (minimum mean-square error) estimates of the parameters of a sinusoidal, long gravity wave, and the short gravity wave ensemble are found in an efficient recursive form and their performance evaluated, generally by numerical simulation, in a one-dimensional stationary version. An application is made to Seasat-SAR complex imagery.
The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.
Attitude determination is a major element of the operation and maintenance of a spacecraft. There are several existing methods of determining the attitude of a spacecraft. One of the most commonly used methods utilizes the Kalman filter to estimate the attitude of the spacecraft. Given an accurate model of a system and adequate observations, a Kalman filter can produce accurate estimates of the attitude. If the system model, filter parameters, or observations are inaccurate, the attitude estimates may be degraded. Therefore, it is advantageous to develop a method of automatically tuning the Kalman filter to produce the accurate estimates. In this paper, a three-axis attitude determination Kalman filter, which uses only magnetometer measurements, is developed and tested using real data. The appropriate filter parameters are found via the Process Noise Covariance Estimator (PNCE). The PNCE provides an optimal criterion for determining the best filter parameters.
Measurements of boundary layer winds are presented using a 2-micrometer coherent Doppler lidar and the optimal performance of the maximum likelihood estimator. The systematic error for single-shot estimates was estimated as 3.6 cm/s using measurements from a stationary hard target. The estimation error for measurements of the radial component of the wind field was determined, as well as the fraction of the estimates that are randomly distributed over the velocity search space, when the signal power is low and speckle fading is important. The results from actual data are compared with the results from ideal simulations. The first direct estimation of the spatial structure function of the radial wind field and of the energy dissipation rate is presented for both horizontal and vertical directions of propagation. The rms estimation error of the velocity estimates is found to be within 30% of ideal performance based on simulation.
Department of Mathematical Sciences, University of Alberta, Edmonton, Canada This paper describes the fundamental theory of the ensemble canonical correlation (ECC) algorithm for the seasonal climate forecasting. The algorithm is a statistical regression sch eme based on maximal correlation between the predictor and predictand. The prediction error is estimated by a spectral method using the basis of empirical orthogonal functions. The ECC algorithm treats the predictors and predictands as continuous fields and is an improvement from the traditional canonical correlation prediction. The improvements include the use of area-factor, estimation of prediction error, and the optimal ensemble of multiple forecasts. The ECC is applied to the seasonal forecasting over various parts of the world. The example presented here is for the North America precipitation. The predictor is the sea surface temperature (SST) from different ocean basins. The Climate Prediction Center's reconstructed SST (1951-1999) is used as the predictor's historical data. The optimally interpolated global monthly precipitation is used as the predictand?s historical data. Our forecast experiments show that the ECC algorithm renders very high skill and the optimal ensemble is very important to the high value.
The Metropolis-Hastings (MH) algorithm is a way to sample a provided target distribution pi(z). It works by repeatedly sampling a separate proposal distribution T(x,x') to generate a random walk {x(t)}. We consider a modification of the MH algorithm in which T is dynamically updated during the walk. The update at time t uses the {x(t' less than t)} to estimate the product distribution that has the least Kullback-Leibler distance to pi. That estimate is the information-theoretically optimal mean-field approximation to pi. We demonstrate through computer experiments that our algorithm produces samples that are superior to those of the conventional MH algorithm.
We have measured the thermal conductance of a mechanical heat switch actuated by a piezoelectric positioner, the PZHS (PieZo electric Heat Switch), at cryogenic temperatures. The thermal conductance of the PZHS was measured between 4 K and 10 K, and on/off conductance ratios greater than 100 were achieved when the positioner applied its maximum force of 8 N. We discuss the advantages of using this system in cryogenic applications, and estimate the ultimate performance of an optimized PZHS.
This paper discusses the design and application of model-based engine control (MBEC) for use during emergency operation of the aircraft. The MBEC methodology is applied to the Commercial Modular Aero-Propulsion System Simulation 40,000 (CMAPSS40,000) and features an optimal tuner Kalman Filter (OTKF) to estimate unmeasured engine parameters, which can then be used for control. During an emergency scenario, normally-conservative engine operating limits may be relaxed to increase the performance of the engine and overall survivability of the aircraft; this comes at the cost of additional risk of an engine failure. The MBEC architecture offers the advantage of estimating key engine parameters that are not directly measureable. Estimating the unknown parameters allows for tighter control over these parameters, and on the level of risk the engine will operate at. This will allow the engine to achieve better performance than possible when operating to more conservative limits on a related, measurable parameter.
This paper discusses the design and application of model-based engine control (MBEC) for use during emergency operation of the aircraft. The MBEC methodology is applied to the Commercial Modular Aero-Propulsion System Simulation 40k (CMAPSS40k) and features an optimal tuner Kalman Filter (OTKF) to estimate unmeasured engine parameters, which can then be used for control. During an emergency scenario, normally-conservative engine operating limits may be relaxed to increase the performance of the engine and overall survivability of the aircraft; this comes at the cost of additional risk of an engine failure. The MBEC architecture offers the advantage of estimating key engine parameters that are not directly measureable. Estimating the unknown parameters allows for tighter control over these parameters, and on the level of risk the engine will operate at. This will allow the engine to achieve better performance than possible when operating to more conservative limits on a related, measurable parameter.
A global, satellite-based, terrestrial snow mission planning tool is proposed to help inform experimental mission design with relevance to snow depth and snow water equivalent (SWE). The idea leverages the capabilities of NASAs Land Information System (LIS) and the Tradespace Analysis Tool for Constellations (TAT C) to harness the information content of Earth science mission data across a suite of hypothetical sensor designs, orbital configurations, data assimilation algorithms, and optimization and uncertainty techniques, including cost estimates and risk assessments of each hypothetical orbital configuration.One objective the proposed observing system simulation experiment (OSSE) is to assess the complementary or perhaps contradictory information content derived from the simultaneous collection of passive microwave (radiometer), active microwave (radar), and LIDAR observations from space-based platforms. The integrated system will enable a true end-to-end OSSE that can help quantify the value of observations based on their utility towards both scientific research and applications as well as to better guide future mission design. Science and mission planning questions addressed as part of this concept include:1. What observational records are needed (in space and time) to maximize terrestrial snow experimental utility?2. How might observations be coordinated (in space and time) to maximize utility? 3. What is the additional utility associated with an additional observation?4. How can future mission costs being minimized while ensuring Science requirements are fulfilled?