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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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The ideas of cost decomposition is summarized to aid in the determination of the relative cost (or 'price') of each component of a linear dynamic system using quadratic performance criteria. In addition to the insights into system behavior that are afforded by such a component cost analysis CCA, these CCA ideas naturally lead to a theory for cost-equivalent realizations.
Filtering, prediction, and smoothing procedures for multi-stage linear dynamic systems using sampled data with sequentially correlated noise
The coordinate-free module-theoretic treatment of transmission zeros for MIMO transfer functions developed by Wyman and Sain (1981) is generalized to include noncontrollable and nonobservable linear dynamical systems. Rational, finitely-generated-modular, and torsion-divisible interpretations of the Rosenbrock system matrix are presented; Gamma-zero and Omega-zero modules are defined and shown to contain the output-decoupling and input-decoupling zero modules, respectively, as submodules; and the cases of left and right invertible transfer functions are considered.
Design of optimal waveforms for optimal estimation or prediction of state of linear dynamical system in presence of Markov and white noise
A procedure is presented for synthesizing time-invariant control logic to cause the outputs of a linear plant to track the outputs of an unforced (or randomly forced) linear dynamic system. The control logic uses feed-forward of the reference system state variables and feedback of the plant state variables. The feed-forward gains are obtained from the solution of a linear algebraic matrix equation of the Liapunov type. The feedback gains are the usual regulator gains, determined to stabilize (or augment the stability of) the plant, possibly including integral control. The method is applied here to the design of control logic for a second-order servomechanism to follow a linearly increasing (ramp) signal, an unstable third-order system with two controls to track two separate ramp signals, and a sixth-order system with two controls to track a constant signal and an exponentially decreasing signal (aircraft landing-flare or glide-slope-capture with constant velocity).
The human decision maker's behavior when predicting future states of discrete linear dynamic systems driven by zero-mean Gaussian processes is modeled. The task is on a slow enough time scale that physiological constraints are insignificant compared with cognitive limitations. The model is basically a linear regression system identifier with a limited memory and noisy observations. Experimental data are presented and compared to the model.
Guiding one state of linear dynamical system to prescribed rms terminal accuracy in presence of injection, measurement and engine-mechanization error
Multistage linear dynamic systems with sequentially correlated noise, evaluating filtering, prediction and smoothing procedures
Global warming is posed to modify the modes of variability that control much of the climate predictability at seasonal to interannual scales. The quantification of changes in climate predictability over any given amount of time, however, remains challenging. Here we build upon recent advances in non-linear dynamical systems theory and introduce the climate community to an information entropy quantifier based on recurrence. The entropy, or complexity of a system is associated with microstates that recur over time in the time-series that define the system, and therefore to its predictability potential. A computationally fast method to evaluate the entropy is applied to the investigation of the information entropy of sea surface temperature in the tropical Pacific and Indian Oceans, focusing on boreal fall. In this season the predictability of the basins is controlled by two regularly varying non-linear oscillations, the El Niño-Southern Oscillation and the Indian Ocean Dipole. We compute and compare the entropy in simulations from the CMIP5 catalog from the historical period and RCP8.5 scenario, and in reanalysis datasets. Discrepancies are found between the models and the reanalysis, and no robust changes in predictability can be identified in future projections. The Indian Ocean and the equatorial Pacific emerge as troublesome areas where the modeled entropy differs the most from that of the reanalysis in many models. A brief investigation of the source of the bias points to a poor representation of the ocean mean state and basins' connectivity at the Indonesian Throughflow.
The paper investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the paper considers the case where the number of measurements available can be smaller than the number of states. In lieu of a batch linear least-squares (LS) approach well-suited for static networks, where a sufficient number of measurements could be collected to obtain a full-rank design matrix the paper proposes an online algorithm to estimate the possibly time-varying state by processing measurements as and when available. The design of the algorithm hinges on a generalized LS cost augmented with a proximal-point-type regularization. With the solution of the regularized LS problem available in closed-form, the online algorithm is written as a linear dynamical system where the state is updated based on the previous estimate and based on the new available measurements. Conditions under which the algorithmic steps are in fact a contractive mapping are shown, and bounds on the estimation error are derived for different noise models. Numerical simulations are provided to corroborate the analytical findings.
A novel technique has been developed for anomaly detection of rocket engine test stand (RETS) data. The objective was to develop a system that postprocesses a csv file containing the sensor readings and activities (time-series) from a rocket engine test, and detects any anomalies that might have occurred during the test. The output consists of the names of the sensors that show anomalous behavior, and the start and end time of each anomaly. In order to reduce the involvement of domain experts significantly, several data-driven approaches have been proposed where models are automatically acquired from the data, thus bypassing the cost and effort of building system models. Many supervised learning methods can efficiently learn operational and fault models, given large amounts of both nominal and fault data. However, for domains such as RETS data, the amount of anomalous data that is actually available is relatively small, making most supervised learning methods rather ineffective, and in general met with limited success in anomaly detection. The fundamental problem with existing approaches is that they assume that the data are iid, i.e., independent and identically distributed, which is violated in typical RETS data. None of these techniques naturally exploit the temporal information inherent in time series data from the sensor networks. There are correlations among the sensor readings, not only at the same time, but also across time. However, these approaches have not explicitly identified and exploited such correlations. Given these limitations of model-free methods, there has been renewed interest in model-based methods, specifically graphical methods that explicitly reason temporally. The Gaussian Mixture Model (GMM) in a Linear Dynamic System approach assumes that the multi-dimensional test data is a mixture of multi-variate Gaussians, and fits a given number of Gaussian clusters with the help of the wellknown Expectation Maximization (EM) algorithm. The parameters thus learned are used for calculating the joint distribution of the observations. However, this GMM assumption is essentially an approximation and signals the potential viability of non-parametric density estimators. This is the key idea underlying the new approach.
Abstract Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . In a widely used algorithm, extended dynamic mode decomposition (EDMD), the dictionary functions are drawn from a fixed class of functions. Deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper, we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Typically, a Koopman dictionary’s nonlinear functions are homogeneous. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm Yeung et al. ( In: 2019 American Control Conference (ACC), 2019). We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves similar accuracy and dimensional scaling to deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.
Actuator hunting is a widespread and often neglected problem in the HVAC field. Hunting is typically characterized by sustained or intermittent oscillations, and can result in decreased efficiency, increased actuator wear, and poor setpoint tracking. Cascaded control loops have been shown to effectively linearize system dynamics and reduce the prevalence of hunting. This paper details the implementation of cascaded control architectures for Air Handling Unit chilled water valves at three university campus buildings. A framework for implementation the control in existing Building Automation software is developed that requires only a single line of additional code. Results gathered for more than a year show that cascaded control not only eliminates hunting in control loops with documented hunting issues, but provides better tracking and more consistent performance during all seasons. A discussion of efficiency losses due to hunting behavior is presented and illustrated with comparative data. Furthermore, an analysis of cost savings from implementing cascaded chilled water valve control is presented. Field tests show 2.2–4.4% energy savings, with additional potential savings from reduced operational costs (i.e., maintenance and controller retuning).
Multistage linear dynamic systems with sequentially correlated noise, evaluating filtering, prediction and smoothing procedures
Optimal control and filtering problem for stochastic linear dynamic system reduced to independent equations
Maximum likelihood smoother using measurements containing correlated noise for application to continuous linear dynamic systems such as inertial navigation
Kalman-Bucy filtering technique for estimation of initial conditions and smoothing in linear dynamic systems, noting rectilinear motion of randomly accelerated spacecraft
Parameter identification algorithm identifying linear dynamic systems by digital computer used to identify human operator characteristics in closed loop control situation