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Summary: This article studies the distributed parameter system that governs adaptive estimation by mobile sensor networks of external fields in a reproducing kernel Hilbert space (RKHS). The article begins with the derivation of conditions that guarantee the well‐posedness of the ideal, infinite dimensional governing equations of evolution for the centralized estimation scheme. Subsequently, convergence of finite dimensional approximations is studied. Rates of convergence in all formulations are established using history‐dependent bases defined from translates of the RKHS kernel that are centered at sample points along the agent trajectories. Sufficient conditions are derived that ensure that the finite dimensional approximations of the ideal estimator equations converge at a rate that is bounded by the fill distance of samples in the agents' assigned subdomains. The article concludes with examples of simulations and experiments that illustrate the qualitative performance of the introduced algorithms. [ABSTRACT FROM AUTHOR]

We develop a family of reduced-order models for the modeling and control of a flow system operating under varying fluid and actuation parameters. The parametric subspaces of the reduced-order models are formed by considering the angle between the reduced-order subspaces that span the velocity fields. This grouping is combined with a discrete switching law to form a switched dynamic system composed of a set of reduced-order models. This methodology is applied to the modeling of a lid-driven cavity under varying translation velocities and phase differentials between the upper and lower walls. It is shown that the subspace angle metric successfully partitions the parametric space and provides insight on the dominant parameters that characterize the flowfields. An open-loop simulation of the resulting switched dynamic system demonstrates its ability to capture the evolution of the flow and input parameters as it occurs in the full-order model.

This paper investigates the modeling of parameter-varying nonlinear aeroelastic systems using Volterra theory. With this approach, the system dynamics are expressed in terms of a set of Volterra kernels. It is well known that the parameters of aeroelastic systems, such as natural frequencies and damping ratios, change with flight condition. Therefore, a system is characterized by a different set of Volterra kernels at each flight condition. These kernels must be extracted from the flight data at each flight condition of interest: a relatively costly procedure. This paper presents a kernel extrapolation method designed to model first- and second-order kernels as functions of a single varying parameter, such as altitude or Mach number. First, using a multiwavelet-based algorithm, a set of Volterra kernels is identified from the input/output data at a number of flight conditions. In this manner, each kernel is represented in terms of a set of multiwavelet basis functions. An extrapolation model is then obtained by using a polynomial curve-fit to express the magnitude of each basis coefficient as a function of the varying parameter. The performance of this kernel extrapolation method is studied in detail for a simulated nonlinear aeroelastic system, demonstrating the validity of the approach. Then, the algorithm is applied to flight data from the F/A-18 Active Aeroelastic Wing. This example illustrates some of the difficulties associated with extrapolating kernels from noisy flight data.

This paper defines a modal scheduling method for obtaining reduced order systems. In contrast to most order reduction schemes for linear structural systems, the methodology in this paper introduces a switched system to achieve order reduction. The switched system model is based on modal participation factors calculated from an input forcing function and the initial conditions at each switching time. Stability of the reduced order model is discussed, and necessary conditions for stability of the proposed switched model are derived. A numerical example that considers a flexible beam provides a testbed for the study of mode switching. The transient response in the testbed example is constructed such that it oscillates between two distinct subspaces. Numerical experiments show that an error indicator based on modal participation factors provides an effective switching strategy. DOI: 10.1061/(ASCE)0893-1321(2004)17:4(146) CE Database subject headings: Hybrid methods; Modal analysis: Scheduling; Stability.

While piezoelectric (PZT) actuators exhibit only mild nonlinear response at low voltage levels, it is well known that the response can be profoundly nonlinear at high field strengths. Moreover, the use of mechanical linkages and structural design to amplify the stroke of PZT-based actuation likewise induces sources of mechanical hysteresis (friction, backlash, etc.) that can couple with this material nonlinearity to yield a structural scale nonlinearity that is nonnegligible. These two sources of hysteresis, due to mechanism response and nonlinear material response, are not easily decoupled. In this paper, we investigate such a nonlinear response in a PZT actuated trailing edge flap attached to a scaled helicopter rotor blade. While the example studied in this paper is quite specific, the methodology derived is generally applicable. We extend the results of previous papers for the derivation of closed loop control for active material actuated devices. The goal is to derive a control methodology that accounts for the overall, total hysteresis due to material nonlinearities and mechanism response. In this technique, a compensator derived from an offline identification of a Krasnoselskii-Pokrovskii hysteresis operator is cascaded with the plant. We show that the methodology is well posed for the class of problems under consideration; we describe relevant closed loop stability and robustness conditions that can be associated with the prediction error in the identified hysteresis operator. We study the performance of our methodology in numerical examples and discuss relevant experimental results. CE Database subject headings: Active control; Hysteresis; Materials; Nonlinear response; Methodology.

While the potential for the use of synthetic jet actuators to achieve flow control has been noted for some time, most of such flow control studies have been empirical or experimental in nature. Several technical issues must be resolved to achieve rigorous, model-based, closed-loop control methodologies for this class of actuators. The goal of this paper is consequently two-fold. First, we seek to derive and evaluate model order reduction methods based on proper orthogonal decomposition that are suitable for synthetic jet actuators. Second, we seek to derive rigorously stable feedback control laws for the derived reduced order models. The realizability of the control strategies is discussed, and a numerical study of the effectiveness of the reduced order models for two-dimensional flow near the jet exit is summarized. [DOI: 10.1115/1.1467598]

New analytical and image processing techniques for digital particle image velocimetry (DPIV) were developed based on wavelet-based representations. The methods, which are used to compute spatially and frequency localized filtered correlations of successive images, were then applied to sample flowfields in water-tunnel experiments. Results showed that the techniques are robust enough to compete with the best Fourier transform-based DPIV methods.

This paper describes the formulation and experimental testing of an estimation of submanifold models of animal motion. It is assumed that the animal motion is supported on a configuration manifold, Q, and that the manifold is homeomorphic to a known smooth, Riemannian manifold, S. Estimation of the configuration submanifold is achieved by finding an unknown mapping, γ , from S to Q. The overall problem is cast as a distribution-free learning problem over the manifold of measurements. This paper defines sufficient conditions that show that the rates of convergence in L μ 2 (S) of approximations of γ correspond to those known for classical distribution-free learning theory over Euclidean space. This paper concludes with a study and discussion of the performance of the proposed method using samples from recent reptile motion studies. [ABSTRACT FROM AUTHOR]

This paper extends a conventional, general framework for online adaptive estimation problems for systems governed by unknown or uncertain nonlinear ordinary differential equations. The central feature of the theory introduced in this paper represents the unknown function as a member of a reproducing kernel Hilbert space (RKHS) and defines a distributed parameter system (DPS) that governs state estimates and estimates of the unknown function. Under the assumption that full state measurements are available, this paper (1) derives sufficient conditions for the existence and stability of the infinite dimensional online estimation problem, (2) derives existence and stability of finite dimensional approximations of the infinite dimensional approximations, and (3) determines sufficient conditions for the convergence of finite dimensional approximations to the infinite dimensional online estimates. A new condition for persistency of excitation in a RKHS in terms of its evaluation functionals is introduced in the paper that enables proof of convergence of the finite dimensional approximations of the unknown function in the RKHS. This paper studies two particular choices of the RKHS, those that are generated by exponential functions and those that are generated by multiscale kernels defined from a multiresolution analysis. [ABSTRACT FROM AUTHOR]

Two models for the dynamic behavior of pressure-sensitive paints are developed. The first of the two models is a purely empirical approach to designing a model and compensator. The second model presented encompasses the physics of the process by which an unsteady pressure field over the paint layer affects the layer and causes an intensity of fluorescence that is fluctuating in time. Within this second model, two different forms for the static calibration are chosen. The effect of the calibration on the system dynamics is demonstrated.

Although reduced-order modeling methods have flourished in the study of structural system dynamics, similar methodologies for the representation of flow are few in comparison. A novel methodology based on biorthogonal wavelet constructions and multiresolution analysis for order reduction of velocity fields obtained via digital particle image velocimetry or computational fluid dynamics is presented. The derivation, algorithmic implementation, and experimental verification of fast projective filtering methods based on divergence-free wavelets are discussed. Experimental evidence presented demonstrates the feasibility of achieving several hundredfold compression for typical velocity fields obtained via experiments using particle image velocimetry. The results also suggest the feasibility and amenability of wavelet methods for diverse problems of interest to the aerospace community including 1) experimental data denoising, 2) local cross-correlation calculations, and 3) feature extraction.

A switched feedback control law is derived for an autonomous pursuing agent that attempts to intercept an evading agent whose dynamics are initially unknown. The model of the pursuer's dynamics is known perfectly, and the evader is modeled as a disturbance. A new method is presented to efficiently update the pursuer's control law as measurements of the parameters that govern the evader's dynamics are received. Using a graph theoretical approach, the control law updates are limited to specific partitions of the state space, which eliminate many unneeded calculations. Results show increases in the time efficiency of the update calculations compared to traditional control law generation methods with a minimal loss in accuracy. An 11.6% overall decrease in calculation time over traditional methods and a 1% error rate compared to the true solution is achieved when solving the homicidal chauffeur game. We show how actual gains in time efficiency depend on the specific application of the controller and the size of the state space grid approximation. Both the theoretical development and implementation of the switched feedback controller are discussed. [ABSTRACT FROM AUTHOR]

The frequency response of an oscillating structure can be tailored by attaching one or more subordinate oscillators. This paper shows how the magnitude and phase of the frequency response can be deliberately shaped by prescribing the distributions of the dynamic properties in an array of such subordinate oscillators. Exact analytic governing equations of motion are derived for the coupled system composed of the primary system and the subordinate array. For a relatively small number (<100) of attached oscillators whose total mass is small (<1%) relative to the primary structure, it is possible to engineer frequency-response functions of the primary oscillator to have, for example, nearly linear phase or constant amplitude over a frequency band of interest. The frequency range over which response shaping is achieved is determined by the band of the attached oscillators. It is shown that the common analytic methodology for designing a dynamic vibration absorber represents the limiting case of a single oscillator in the subordinate set. Moreover, increasing the number of subordinate oscillators (without increasing the total added mass) offers a number of advantages in reshaping the dominant system’s frequency response. [ABSTRACT FROM AUTHOR]

The realization of vision-based, autonomous flight for micro air vehicles presents numerous technical challenges in diverse fields such as image processing, trajectory planning, control theory, and microhardware design. This paper explores one aspect of the overall problem: robust, real-time estimation of aircraft states from a set of tracked feature points. This vision-based approach is realized via an implementation of the implicit extended Kalman filter, a variation of the classical Kalman filter that allows for nonlinear dynamic models and updates from measurements that are implicit functions of the state variables. The epipolar constraint, which is a geometric relationship between the feature point position vectors and the camera translation vector, is employed in this paper as the implicit measurement in the Kalman filter. In order for the vison-based Kalman filter to provide reliable state estimation, it must be robust with respect to modeling errors in the dynamic propagator. This is especially true because the aerodynamic forces and moments acting on a micro air vehicle are frequently not known to a high degree of accuracy. Furthermore, the algorithm must be robust with respect to noise in the measured feature point positions in the image plane. This paper explores both of these robustness issues using results from a micro air vehicle simulation model developed at the NASA Langley Research Center. In particular, a hierarchy of dynamic models, ranging from a random walk model to a high-fidelity nonlinear micro air vehicle model, is employed in the Kalman filter for a simulated micro air vehicle trajectory with varying levels of measurement noise. It is demonstrated that the vision-based measurement updates in the filter are capable of compensating for significant modeling errors and filter initialization errors. As would be expected, superior overall results are achieved using higher-fidelity dynamic models in the Kalman filter. The work presented in this paper represents the first step toward the ultimate objective of incorporating vision-based state estimation into the design of autonomous flight control systems for micro air vehicles operating in urban environments. [ABSTRACT FROM AUTHOR]

The article reports on the use of shaker-based laser vibrometry in locating faults in wall paintings at the U.S. Capitol building in Washington, D.C. The fast, laser-scanned vibration method finds plaster delamination, deconsolidation, and detachment at the paintings. This technology is used as part of the ongoing preservation and restoration program in the building.

The Volterra series provides a convenient framework for the representation of nonlinear dynamical systems. One of the main drawbacks of this approach, however, is the large number of terms that are often needed to represent Volterra kernels. In this paper we present an approach whereby wavelets are used to obtain low-order estimates of first-order and second-order Volterra kernels. Several constructions of tensor-product wavelets have been employed for some Volterra kernel approximations. In this paper, a triangular wavelet basis is constructed for the representation of the triangular form of the second-order kernel. These wavelets are piecewise-constant, orthonormal, and are supported over the triangular domain over which the second-order kernel is defined. The well-known Haar wavelet is used concurrently for the identification of the first-order kernel. This kernel identification algorithm is demonstrated on a prototypical nonlinear oscillator. It is shown that accurate kernel estimates can be obtained in terms of a relatively small number of wavelet coefficients. It is also demonstrated that, for this particular system, the derived Volterra model is valid for input amplitudes below a specified bound. When the input amplitude exceeds this threshold, higher-order kernels are needed to adequately describe the system dynamics. Thus, the approach taken in this paper is applicable to a large class of nonlinear systems provided that the input excitation is sufficiently bounded. [ABSTRACT FROM AUTHOR]

Focuses on study which utilized the structured model reference adaptive control (SMARC) method for the active suppression of limit cycle oscillations for a typical wing section with a structural nonlinearity. Investigation on nonlinear aeroelastic control; Steps in adaptive feedback linearization; Advantages of SMARC over conventional adaptive methods.

Experimental and anecdotal evidences have shown that state-switched control strategies for piezoelectric actuators can be advantageous. However, most discussions of the stability of these systems has relied on heuristic, or physically motivated, arguments. In this paper, we show that recent open-circuit-short-circuit (OC-SC) state-switching control laws can be viewed as hybrid dynamical systems of Witsenhausen type. Within this framework, the closed-loop stability of OC/SC switching is rigorously established using the method of multiple Lyapunov functions. [ABSTRACT FROM AUTHOR]

The paper investigates the accuracy and numerical stability of a class of wavelet Galerkin formulations on irregular domains. The method of numerical boundary measures is based upon a domain embedding strategy in which the irregular domain of interest is embedded in a larger domain having regular geometry. One advantage of the domain embedding method is that the boundary conditions on the larger, regular domain can be enforced in a straightforward manner, and the solution procedure can exploit the highly structured form of the resulting governing equations. The defining characteristic of this method is that the calculation of integrals along the irregular boundary are carried out using recently derived numerical boundary measures. In addition, the coercive bilinear forms characterizing the boundary value problem of interest must be calculated when restricted to the actual domain. In the case of wavelet Galerkin formulations, this calculation is accomplished with the three term connection coefficients that characterize the numerical boundary measure. The numerical stability and accuracy of the domain embedding procedure is compared to a newly developed wavelet-based finite element formulation. [ABSTRACT FROM AUTHOR]

Active material actuators, sometimes referred to as "smart" actuators, are gaining widespread use for control actuation. Many of these actuators exhibit hysteresis to some degree between their input and output response. There exists an extensive body of research concerning the modeling of hysteresis for the linearization, or compensation, of these hysteresis nonlinearities. However, the models have typically been identified off-line and mainly used in open-loop compensation. When the identified models do not exactly match the actuator nonlinearities, the compensation can create an error between the desired and actual control output. The hysteresis for several of these actuators has been shown to evolve over time, and can render a fixed hysteresis model inadequate to linearize the hysteretic nonlinearities. This paper presents an adaptive hysteresis model for on-line identification and closed-loop compensation. Laboratory experiments with a shape memory alloy wire actuator provide evidence of the success of the adaptive identification and compensation. In addition, the means of determining the saturation of the SMA using updated information from the adaptive hysteresis model is provided. [ABSTRACT FROM PUBLISHER]