Components Of State Vector Research Articles

Analytical Algorithm for Constructing the Orbital Orientation of a Spacecraft with an Incomplete Measurement of the State Vector Components

The problem of joint synthesis of a modal controller and observer is solved analytically for a sixth-order system that describes the rotational motion of a spacecraft with the available measurements of five components of the state vector. The modeling results that describe the application of the synthesized control and observation laws for the construction of the orbital orientation of a spacecraft are presented in the paper.

Adaptive disturbance attenuation for a class of uncertain nonlinear systems: A double-gain nonlinear observer method

This paper is concerned with the problem of adaptive disturbance attenuation for a class of nonlinear systems. The traditional adaptive methods are almost impossible to compensate the time-varying unknown disturbance by designing parameter adaptive laws without a priori knowledge about the bounds of external disturbances. To solve the problem, a new strategy is proposed by constructing an augmented system where the external disturbance is considered as another component of the augmented state vector. Based on this, a double-gain nonlinear observer is employed to estimate the state of the augmented nonlinear system. Further, an output feedback control strategy is designed, and it is proved that the proposed strategy ensures that all the signals are bounded and the tracking error exponentially converges to an adjustable compact set. Finally, an example is performed to demonstrate the validity of the proposed scheme.

Receding Horizon Unbiased FIR Filters and Their Application to Sea Target Tracking

Finite impulse response (FIR) state estimation algorithms have been much discussed in literature lately. It is well known that they allow overcoming the Kalman filter divergence caused by modeling uncertainties. In this paper, new receding horizon unbiased FIR filters ignoring noise statistics for time-varying discrete state-space models are proposed. They have the following advantages. First, the proposed filters use only known means of state vector components at starting points of sliding windows. This allows us to take into account priory statistical information (on average) about specified movements of the system. Second, the iterative version of the filter has a Kalman-like form. Besides, its initialization does not include a training cycle in a batch form. Such filters may have a wide range of applications. In this paper, position and speed estimation of sea targets using angle measurements in azimuth and elevation is considered as an example.

New results on dissipativity analysis of singular systems with time-varying delay

This paper focuses on the dissipativity analysis of singular systems with time-varying delay. The objective is to obtain a less conservative criterion with less computational demand. Based on the state decomposition method, singular systems are rewritten as differential subsystems and algebraic ones. First of all, the components of state vectors are applied to design a novel Lyapunov–Krasovskii functional (LKF) for the differential subsystems. Then, in the derivative of the LKF, the algebraic ones are introduced and the Wirtinger-based integral inequality together with the extended reciprocally convex matrix inequality is adopted to estimate the single integral term. Therefore, a new dissipativity criterion is obtained, which realizes both less conservativeness and less computational demand. Finally, two numerical examples are given to verify the superiority of the proposed method.

Constructive stability and stabilizability of positive linear discrete-time switching systems

We describe a new class of positive linear discrete-time switching systems for which the problems of stability or stabilizability can be resolved constructively. This class generalizes the class of systems with independently switching state vector components. The distinctive feature of this class is that, for any system from this class, its components or blocks can be arbitrarily connected in parallel or in series without loss of the `constructive resolvability' property. It is shown also that, for such systems, it is possible to build constructively the individual positive trajectories with the greatest or the lowest rate of convergence to the zero.

A Bayesian multivariate joint frailty model for disease recurrences and survival.

Motivated by a study for soft tissue sarcoma, this article considers the analysis of diseases recurrence and survival. A multivariate frailty hazard model is established for joint modeling of three correlated time-to-event outcomes: local disease recurrence, distant disease recurrence (metastasis), and death. The goals are to find out (i) the effects of treatments on local and distant disease recurrences, and death, (ii) the effects of local and distant disease recurrences on death, and (iii) the correlation between local and distant recurrences. By our approach, all these three important questions, which are commonly asked in similar medical research studies, can be answered by a single model. We put the proposed joint frailty model in a Bayesian framework and use a hybrid Monte Carlo algorithm for the computation of posterior distributions. This hybrid algorithm relies on the evaluation of the gradient of target log density and a guided walk progress, and it combines these two strategies to suppress random walk behavior. A further distinction is that the hybrid algorithm can update all the components of a multivariate state vector simultaneously. Simulation studies are conducted to assess the proposed joint frailty model and the computation algorithm. The motivating soft tissue sarcoma data set is analyzed for illustration purpose. Copyright © 2016 John Wiley & Sons, Ltd.

Application of Gravity Gradients in the Process of GOCE Orbit Determination

The possibility of improving the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) mission satellite orbit using gravity gradient observations was investigated. The orbit improvement is performed by a dedicated software package, called the Orbital Computation System (OCS), which is based on the classical least squares method. The corrections to the initial satellite state vector components are estimated in an iterative process, using dynamic models describing gravitational perturbations. An important component implemented in the OCS package is the 8th order Cowell numerical integration procedure, which directly generates the satellite orbit. Taking into account the real and simulated GOCE gravity gradients, different variants of the solution of the orbit improvement process were obtained. The improved orbits were compared to the GOCE reference orbits (Precise Science Orbits for the GOCE satellite provided by the European Space Agency) using the root mean squares (RMS) of the differences between the satellite positions in these orbits. The comparison between the improved orbits and the reference orbits was performed with respect to the inertial reference frame (IRF) at J2000.0 epoch. The RMS values for the solutions based on the real gravity gradient measurements are at a level of hundreds of kilometers and more. This means that orbit improvement using the real gravity gradients is ineffective. However, all solutions using simulated gravity gradients have RMS values below the threshold determined by the RMS values for the computed orbits (without the improvement). The most promising results were achieved when short orbital arcs with lengths up to tens of minutes were improved. For these short arcs, the RMS values reach the level of centimeters, which is close to the accuracy of the Precise Science Orbit for the GOCE satellite. Additional research has provided requirements for efficient orbit improvement in terms of the accuracy and spectral content of the measured gravity gradients.

The Influence of Application a Simplified Transformation Model Between Reference Frames ECEF and ECI onto Prediction Accuracy of Position and Velocity of GLONASS Satellites

Abstract In computational tasks of satellite geodesy there is a need for transformation of coordinates between reference frames ECEF – Earth Centered, Earth Fixed and ECI – Earth Centered, Inertial. Strict and simplified transformation models, which can be used in case of the position and velocity short-term predictions of GLONASS satellites, have been presented in this study. Comparison of the results of state vector components predictions of the GLONASS satellites, in dependence of the used transformation model, have also been presented. Accuracy of the prediction has been determined on the basis of the analyse of deviations of the predicted positions and velocities of GLONASS satellites from their values given in broadcast ephemeris.

Fast local reduced basis updates for the efficient reduction of nonlinear systems with hyper-reduction

Projection-based model reduction techniques rely on the definition of a small dimensional subspace in which the solution is approximated. Using local subspaces reduces the dimensionality of each subspace and enables larger speedups. Transitions between local subspaces require special care and updating the reduced bases associated with each subspace increases the accuracy of the reduced-order model. In the present work, local reduced basis updates are considered in the case of hyper-reduction, for which only the components of state vectors and reduced bases defined at specific grid points are available. To enable local reduced basis updates, two comprehensive approaches are proposed. The first one is based on an offline/online decomposition. The second approach relies on an approximated metric acting only on those components where the state vector is defined. This metric is computed offline and used online to update the local bases. An analysis of the error associated with this approximated metric is then conducted and it is shown that the metric has a kernel interpretation. Finally, the application of the proposed approaches to the model reduction of two nonlinear physical systems illustrates their potential for achieving large speedups and good accuracy.

Reformulation of Relativistic Quantum Field Theory Using Region-Like Idealization of the Elementary Particle

The existence of any elementary particle in universe requires the existence of some region of universe occupied by it. By taking the volume of this occupied region, the author will reformulate the relativistic quantum field theory using new 3-dimensional region-like idealization of elementary particles and hereinafter will call the total volume of all regions occupied by the elementary constituent particles of the quantum system the occupied volume. Also the author will call the set of all regions of universe filled by elementary constituent particles of the quantum system the occupied path. Always any quantum system is existed at a head of its occupied path. This path is growing by mutual filling and leaving regions of universe by its elementary constituent particles. The conservation of this elementary constituent particle requires the conservation of its occupied volume during this process. This requirement could be summarized by the following conditions: 1) the total volume of all regions of universe filled by the elementary constituent particles of the quantum system minus the total volume of all regions of universe left by these elementary constituent particles must be equal to the occupied volume of the quantum system; 2) the total increase in the occupied volume of the quantum system due to the absorption of another elementary particles from outside its occupied regions minus the total decreasing in its occupied volume due to the emission of another elementary particles outside its occupied regions must be equal to the occupied volume of it. The wave-particle duality of the elementary constituent particles implied accumulation of them as the finite set of interfered waves. This accumulation of elementary constituent particles causes the absolute probabilistic nature of event of finding the elementary consistent particle in specified interfered wave, and hence the mathematical representation of this interfered wave should take into account the value of probability amplitude of finding an elementary particle inside the region occupied specified interfered wave. In quantum theory this probability amplitude corresponds to complex amplitude of the wave function of interfered wave. Also in Hilbert’s representation of the quantum theory these wave functions are representing the components of the quantum state vector. In this paper the author will develop the transformation theory of the region-like quantum state of the quantum system.

Particle Swarm Optimization of the Multioscillatory LQR for a Three-Phase Four-Wire Voltage-Source Inverter With an <inline-formula> <tex-math notation="TeX">$LC$</tex-math></inline-formula> Output Filter

This paper presents evolutionary optimization of the linear quadratic regulator (LQR) for a voltage-source inverter with an LC output filter. The procedure involves particle-swarm-based search for the best weighting factors in the quadratic cost function. It is common practice that the weights in the cost function are set using the guess-and-check method. However, it becomes quite challenging, and usually very time-consuming, if there are many auxiliary states added to the system. In order to immunize the system against unbalanced and nonlinear loads, oscillatory terms are incorporated into the control scheme, and this significantly increases the number of weights to be guessed. All controller gains are determined altogether in one LQR procedure call, and the originality reported here refers to evolutionary tuning of the weighting matrix. There is only one penalty factor to be set by the designer during the controller synthesis procedure. This coefficient enables shaping the dynamics of the closed-loop system by penalizing the dynamics of control signals instead of selecting individual weighting factors for augmented state vector components. Simulational tuning and experimental verification (the physical converter at the level of 21 kVA) are included.

Static characteristics of electromechanical systems with second order sliding mode

The article is devoted to analytical investigation of the steady state points of generalized closed electromechanical systems that are experiencing the oscillatory processes. The main purpose of this paper is to develop the method for steady-state values determining of the state vector components of a closed system, depending on its control algorithms and equations of motion. Methods of differential geometry and modern control theory allow converting these equations, representing them to the different phase spaces. Transition to the space, the coordinates of which are interconnected by differential dependencies, is done in the work by the feedback conversions and a system of equations of a generalized electromechanical object motion in controlled Brunovsky form is obtained. Based on the analysis of the system it is found the equation of static equilibrium of the object, and it is shown that this equation equating to controller algorithm simplifies the determination of steady-state values of the state variables of the object. Using the proposed method is illustrated by the definition of control error and finding the static characteristics of control loop of DC electric drive position. This material can be useful for specialists in the field of electromechanical systems of automation and control systems of dynamic objects.

Towards denoising XMCD movies of fast magnetization dynamics using extended Kalman filter.

The Kalman filter is a well-established approach to get information on the time-dependent state of a system from noisy observations. It was developed in the context of the Apollo project to see the deviation of the true trajectory of a rocket from the desired trajectory. Afterwards it was applied to many different systems with small numbers of components of the respective state vector (typically about 10). In all cases the equation of motion for the state vector was known exactly. The fast dissipative magnetization dynamics is often investigated by x-ray magnetic circular dichroism movies (XMCD movies), which are often very noisy. In this situation the number of components of the state vector is extremely large (about 10(5)), and the equation of motion for the dissipative magnetization dynamics (especially the values of the material parameters of this equation) is not well known. In the present paper it is shown by theoretical considerations that - nevertheless - there is no principle problem for the use of the Kalman filter to denoise XMCD movies of fast dissipative magnetization dynamics.

Насколько близко И.Р. Пригожин, Н. Наken и С.П. Курдюмов подошли к пониманию неизбежности ТХС?

Advances in molecular biology and biophysics (at molecular-cellular level) do not contribute to understanding of life phenomena. Achievements of synergetics (H. Haken) and complexity theory (I. Prigogine) have intensified differences between physical-chemical understandings of life and systemic understandings. In addition to that, the systems approach provides the understanding of effects of living objects and especially its more organized and evolving part – human and humanity. Human-scaled systems possess the unique property – continuous and chaotic movement of many components of a system state vector x= x(t). Taking this property into consideration causes the denial of any known types of stationary nodes (for example, dx/dt=0) and requires reconsideration of concept of chaos. A novel approach for understanding of living systems (as the third paradigm of natural science) and novel methods of studying of living systems (as theory of chaos and self-organization) are proposed by the third paradigm and theory of chaos and self-organization.

Joint range ambiguity resolving and multiple maneuvering targets tracking in clutter via MMPHDF-DA

It is difficult to track multiple maneuvering targets of which the number is unknown and time-varying, especially when there is range ambiguity. The random finite sets (RFS) based probability hypothesis density filter (PHDF) is an effective solution to the problem of multiple targets tracking. However, when tracking multiple targets via the range ambiguous radar, the problem of range ambiguity has to be solved. In this paper, a multiple model PHDF and data association (MMPHDF-DA) based method is proposed to address multiple maneuvering targets tracking with range ambiguous radar in clutter. Firstly, by introducing the turn rate of target and the discrete pulse interval number (PIN) as components of target state vector, and modeling the incremental variable of the PIN as a three-state Markov chain, the problem of multiple maneuvering targets tracking with range ambiguity is converted into a hybrid state filtering problem. Then, by implementing a novel “track-estimate” oriented association with the filtering results of the hybrid filter, target tracks are provided at each time step. Simulation results demonstrate that the MMPHDF-DA can estimate target state as well as the PIN simultaneously, and succeeds in multiple maneuvering target tracking with range ambiguity in clutter. Simulation results also demonstrate that the MMPHDF-DA can overcome the limitation of the Chinese Remainder Theorem for range ambiguity resolving.

An algorithm for synthesis of the suboptimal control law for quasi-linear stochastic dynamical systems

We consider the information constrained optimization problem for stochastic dynamical systems governed by quasi-linear Ito equations. Let us describe the information constraints. We suppose that each control vector component depends on a prespecified set of precisely measured state vector components. In this article we present an algorithm for synthesis of the suboptimal control law. This control law is the linear feedback regulator. The linear parameter and the constant term of the regulator are polynomial functions of time. The algorithm is successfully applied to the problem of two-link robotic arm optimal control. These manipulators may be effectively used at space stations, e.g. for moving cargo in outer space.

Extreme deviations of landing parameters for heavy aircraft

We estimate the statistic characteristics and extreme deviations of the state vector components for the Ilyushin Il 96–300 systems at automatic landing.

Optimal structure of continuous nonlinear reduced-order Pugachev filter

A non-parametric synthesis problem is considered for a fast nonlinear low-memory filter consisting of the same number of equations as the number of only information components of the diffusion Markovian state vector of the observation plant. The algorithm for finding mean-square locally optimal structural functions of the filter and the reduced Fokker-Planck-Kolmogorov equation to be used to find the respective instantaneously conditional probability distribution are obtained. The proposed filter in its full order is proved to coincide with the linear Kalman-Bucy filter in various linear Gaussian cases. Ways to construct Gaussian and linearized suboptimal filters are proposed. The example is given where the latter are compared with their analogues.

Bounds and invariant sets for a class of discrete-time switching systems with perturbations

We present a novel method to compute componentwise ultimate bounds and invariant regions for a class of switching discrete-time linear systems with perturbation bounds that may depend nonlinearly on a delayed state. The method has the important advantage that it allows each component of the perturbation vector to have an independent bound and that the bounds and sets obtained are also given componentwise. This componentwise method does not employ a standard norm for bounding either the perturbation or state vectors, and thus may avoid conservativeness due to different perturbation or state vector components having substantially different bounds. We also establish the relationship between the class of switching linear systems to which the proposed method can be applied and those that admit a common quadratic Lyapunov function. We illustrate the application of our method via numerical examples, including the fault tolerance analysis of the feedback control of a winding machine.

Multiple model particle filter track-before-detect for range ambiguous radar

The middle pulse repetition frequency (MPRF) and high pulse repetition frequency (HPRF) modes are widely adopted in airborne pulse Doppler (PD) radar systems, which results in the problem that the range measurement of targets is ambiguous. The existing data processing based range ambiguity resolving methods work well on the condition that the signal-to-noise ratio (SNR) is high enough. In this paper, a multiple model particle filter (MMPF) based track-before-detect (TBD) method is proposed to address the problem of target detection and tracking with range ambiguous radar in low-SNR environment. By introducing a discrete variable that denotes whether a target is present or not and the discrete pulse interval number (PIN) as components of the target state vector, and modeling the incremental variable of the PIN as a three-state Markov chain, the proposed algorithm converts the problem of range ambiguity resolving into a hybrid state filtering problem. At last, the hybrid filtering problem is implemented by a MMPF-based TBD method in the Bayesian framework. Simulation results demonstrate that the proposed Bayesian approach can estimate target state as well as the PIN simultaneously, and succeeds in detecting and tracking weak targets with the range ambiguous radar. Simulation results also show that the performance of the proposed method is superior to that of the multiple hypothesis (MH) method in low-SNR environment.