Measurements Of State Vector Research Articles

Model-free forecasting of partially observable spatiotemporally chaotic systems

Reservoir computing is a powerful tool for forecasting turbulence because its simple architecture has the computational efficiency to handle high-dimensional systems. Its implementation, however, often requires full state-vector measurements and knowledge of the system nonlinearities. We use nonlinear projector functions to expand the system measurements to a high dimensional space and then feed them to a reservoir to obtain forecasts. We demonstrate the application of such reservoir computing networks on spatiotemporally chaotic systems, which model several features of turbulence. We show that using radial basis functions as nonlinear projectors enables complex system nonlinearities to be captured robustly even with only partial observations and without knowing the governing equations. Finally, we show that when measurements are sparse or incomplete and noisy, such that even the governing equations become inaccurate, our networks can still produce reasonably accurate forecasts, thus paving the way towards model-free forecasting of practical turbulent systems.

A wavelet-based dynamic mode decomposition for modeling mechanical systems from partial observations

Dynamic mode decomposition (DMD) has emerged as a popular data-driven modeling approach to identifying spatio-temporal coherent structures in dynamical systems, owing to its strong relation with the Koopman operator. For dynamical systems with external forcing, the identified model should not only be suitable for a specific forcing function but should generally approximate the input–output behavior of the underlying dynamics. A novel methodology for modeling those classes of dynamical systems is proposed in the present work, using wavelets in conjunction with the input–output dynamic mode decomposition (ioDMD). The wavelet-based dynamic mode decomposition (WDMD) builds on the ioDMD framework without the restrictive assumption of full state measurements. Our non-intrusive approach constructs numerical models directly from trajectories of the full model’s inputs and outputs, without requiring the full-model operators. These trajectories are generated by running a simulation of the full model or observing the original dynamical systems’ response to inputs in an experimental framework. Hence, the present methodology is applicable for dynamical systems whose internal state vector measurements are not available. Instead, data from only a few output locations are only accessible, as often the case in practice. The present methodology’s applicability is explained by modeling the input–output response of an Euler–Bernoulli finite element beam model. The WDMD provides a linear state-space representation of the dynamical system using the response measurements and the corresponding input forcing functions. The developed state-space model can then be used to simulate the beam’s response towards different types of forcing functions. The method is further validated on a real (experimental) data set using modal analysis on a simple free–free beam, demonstrating the efficacy of the proposed methodology as an appropriate candidate for modeling practical dynamical systems despite having no access to internal state measurements and treating the full model as a black-box.

State estimation with multi-level vector quantisation and communication uncertainty

In this paper, we design a state estimation algorithm for vector state-vector measurement systems over wireless sensor networks subject to bandwidth limitation and communication uncertainty. With the aid of Mahalanobis transformation, vector measurement innovations are decorrelated into the normalised ones to facilitate parallel quantisation. Then, taking account of Gaussian channel noises, a generalised multi-level quantisation mechanism and the minimum mean square error (MMSE) estimator are jointly designed, where optimal quantisation parameters can be solved by minimising the estimation error covariance with given quantisation level. The proposed MMSE estimator not only has a similar recursive structure as the classical Kalman filter, but also dramatically reduces the sensor-to-estimator communication requirement with only a slight deterioration of estimation performance. The combined effect of quantisation mechanism and communication uncertainty on estimation performance is also discussed. Finally, Monte Carlo simulation results illustrate the effectiveness and efficiency of the proposed quantised estimator.

Attitude determination & control system design for gravity recovery missions like GRACE

This paper is dedicated to the attitude control law synthesis for GRACE-like missions. Namely, two satellites move along the same orbit at a distance of several hundred kilometers and “look” at each other. This angular motion resembles the stabilization at unstable equilibrium position in the Orbital Frame. The reaction wheels cannot be used because they greatly affect the accelerometers measurements. Hence, only magnetorquers and thrusters may be utilized for the attitude control. Two different approaches are considered: linear quadratic regulator and Lyapunov-based controller. Control coefficients of the latter are obtained using the Floquet theory. Numerical simulation including atmospheric drag, solar radiation pressure and state vector measurements errors is carried out to validate suggested control techniques. The developed attitude determination and control system algorithms are tested for GRACE and GRACE-FO mission scenarios with relevant requirements and parameters.

Adaptive concept of state estimation with incomplete state vector measurement

The paper presents the design and simulation experiments of the adaptive approach in the estimation of the object state realized by filter whose gain is calculated on-line. The adopted concept of determining the gain uses a defined for this purpose signal called an error and on the basis of its waveform features introduces an incremental correction of the amplification factor of the estimation filter. The obtained results of state estimation are characterized by stability and strong correctness even for cases of non-stationary disturbances

Оptimization of unmanned aerial vehicle robust flight control system with incomplete state vector measurements

Оptimization of unmanned aerial vehicle robust flight control system with incomplete state vector measurements

Synthesis of robust discrete guidance system for solid body with incomplete state vector measurements

The paper is deals system synthesis method of the robust control. The method is based on estimation of perfo-?mance and robustness represented by Н2 - and Н - norms accordingly. Particularities of the control object (solid body) establish the following sequence of steps in order to solve a problem: 1) restoring the full state-space vector applying the Luenberger observer; 2) optimal linear-quadratic regulator synthesis; 3) utilization the procedure of Н2/Н robust optimization. This technique has been applied taking into account the constraints on oscillations of the closed-loop system. The same procedure has been applied without the above-mentioned constraints. Simulation results have confirmed the effectiveness and efficiency of the proposed approach.

Process regulation via genealogical decision trees

AbstractThis paper deals with regulation control on the basis of genealogical decision trees (GDTs). GDTs are a population‐based random search technique for solving sequential multimodal and multivariable trajectory tracking problems, when gradient information is not available or does not exist. A direct application of GDT results in an open‐loop control. In this paper, feedback regulation based on GDT is considered. In the proposed scheme, GDTs are used for solving off‐line a number of predictive control problems; a finite set of initial states is then constructed from these simulations, for each of which an optimal control sequence has been computed. Natural handling of missing state vector measurements is provided. Numerical examples dealing with the van der Vusse CSTR illustrate the feasibility and the efficiency of this feedback control algorithm. A discussion on alternative approaches and a numerical comparison with the Markov‐decision‐process‐based optimal policy are provided. Copyright © 2008 John Wiley & Sons, Ltd.

On identifiability of mathematical models of evolutionary processes from data of discrete measurements of state vector

On identifiability of mathematical models of evolutionary processes from data of discrete measurements of state vector

Methods and uses of precise time in power systems

As evidenced by recent work on disturbance recorder synchronization, protective and adaptive relaying, and state vector measurement, utility interest in using accurate and standardized time over wide geographical areas has increased. Microsecond timekeeping is now available to the utility user. Power system applications include maintaining the general public's timekeeping, event recorder synchronization, relay testing, synchronous digital sampling, voltage phase angle (and hence system state vector) measurement, and fault location. The authors describe worldwide standard times, practical methods of transferring time from government standards agencies to the utility user, applications, and utility experience. New material is presented on the performance of standard timekeeping services and utility experience with equipment in substations and control centers.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Identification of a class of linear discrete-time systems

The system identification procedure is developed for a class of linear discrete-time systems. It is assumed that the state vector measurements are available. Applications of this procedure to parameter identification of different system structures are proposed.

Partial reconstruction of state vectors in decentralized dynamic systems

The extent to which the state vector information can be recovered in a decentralized control system from a partial observation record of the state vector measurement and also of the control vectors is discussed. That subspaces associated with partial reconstruction of the state space can be obtained recursively and that they have certain invariance properties is shown.