State Vector Of System Research Articles

An integrity monitoring algorithm for WiFi/PDR/smartphone-integrated indoor positioning system based on unscented Kalman filter

Indoor positioning navigation technologies have developed rapidly, but little effort has been expended on integrity monitoring in Pedestrian Dead Reckoning (PDR) and WiFi indoor positioning navigation systems. PDR accuracy will drift over time. Meanwhile, WiFi positioning accuracy decreases in complex indoor environments due to severe multipath propagation and interference with signals when people move about. In our research, we aimed to improve positioning quality with an integrity monitoring algorithm for a WiFi/PDR-integrated indoor positioning system based on the unscented Kalman filter (UKF). The integrity monitoring is divided into three phases. A test statistic based on the innovation of UKF determines whether the positioning system is abnormal. Once a positioning system abnormality is detected, a robust UKF (RUKF) is triggered to achieve higher positioning accuracy. Again, the innovation of RUKF is used to judge the outliers in observations and identify positioning system faults. In the last integrity monitoring phase, users will be alerted in time to reduce the risk from positioning fault. We conducted a simulation to analyze the computational complexity of integrity monitoring. The results showed that it did not substantially increase the overall computational complexity when the number of dimensions in the state vector and observation vector in the system is small (< 20). In practice, the number of dimensions of state vector and observation vector in an indoor positioning system rarely exceeds 20. The proposed integrity monitoring algorithm was tested in two field experiments, showing that the proposed algorithm is quite robust, yielding higher positioning accuracy than the traditional method, using only UKF.

H∞ Stabilization of Discrete-Time Nonlinear Semi-Markov Jump Singularly Perturbed Systems With Partially Known Semi-Markov Kernel Information

In this paper, the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> stabilization problem is studied for discrete-time semi-Markov jump singularly perturbed systems (SMJSPSs) with repeated scalar nonlinearities. As the exact statistical information of the sojourn time or the mode transition is difficult to obtain, the case with only partial semi-Markov kernel information available is considered. Furthermore, introducing an external disturbance or nonlinearity into the analysis of discrete-time semi-Markov jump systems (DTSMJSs) meets critical obstacles, since the relation between the system state vectors at two nonadjacent instants is difficult to determine. To address this issue, the variation trend of the Lyapunov function for a semi-Markov jump sequence is analyzed in detail. Subsequently, criteria of mean-square exponential stability (MSES) for DTSMJSs are established for the first time based on the Lyapunov stability theory. By virtue of the criteria obtained and the cone complementary linearization algorithm, a controller ensuring MSES and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for discrete-time nonlinear SMJSPSs is constructed. Finally, the effectiveness and applicability of the proposed method are validated by simulation examples including an inverted pendulum model.

Consensus-Based Distributed Reduced-Order Observer Design for LTI Systems.

In this article, we refocus on the distributed observer construction of a continuous-time linear time-invariant (LTI) system, which is called the target system, by using a network of observers to measure the output of the target system. Each observer can access only a part of the component information of the output of the target system, but the consensus-based communication among them can make it possible for each observer to estimate the full state vector of the target system asymptotically. The main objective of this article is to simplify the distributed reduced-order observer design for the LTI system on the basis of the consensus communication pattern. For observers interacting on a directed graph, we first address the problem of the distributed reduced-order observer design for the detectable target system and provide sufficient conditions involving the topology information to guarantee the existence of the distributed reduced-order observer. Then, the dependence on the topology information in the sufficient conditions will be eliminated by using the adaptive strategy and so that a completely distributed reduced-order observer can be designed for the target system. Finally, some numerical simulations are proposed to verify the theoretical results.

An Optimal Recurrent Logical-Dynamical Filter of a High Order and Its Covariance Approximations

The problem of logical recognition of the operating mode and dynamic estimation of the intra-mode state vector of a discrete-time stochastic Markov system with a random structure is considered. To develop an estimation algorithm implemented at the pace of system time on a computer of limited power, a method for designing a new finite-dimensional optimal structure filter is proposed. Its state vector consists of several latest estimates, and the current estimate is found in the form of an optimal-accuracy dependence on the last measurement and the vector of the previous filter state. The structural functions of the filter are designed in advance, which can be performed by the Monte Carlo method by obtaining their multivariate histograms. Due to the computational complexity of this procedure, algorithms are also proposed for constructing two numerical-analytical approximations of the filter, which take into account only the first two moments of random variables.

Robust fault estimation and fault-tolerant control for nonlinear Markov jump systems with time-delays

The problem of the robust fault estimation and robust fault-tolerant control, for a class of nonlinear time-delayed Markov jump systems (MJSs) with both actuator and sensor faults, was studied. Firstly, by extending the system state, the actuator fault state vector, the sensor fault state vector and the original system state vector were extended to auxiliary state variables, and the original system was extended to a generalized system. Then, for the singular system, a generalized observer was designed to achieve the simultaneous estimation of its actuator faults, sensor faults and original system state. In addition, based on the observer estimation, a state feedback fault-tolerant controller was designed to make the closed-loop system stable and meet certain performance indicators. By solving linear matrix inequality, sufficient conditions for the existence of generalized observer and fault-tolerant controller were given. Finally, a numerical example and a practical example were given to demonstrate the effectiveness of the proposed approach.

Fault estimation for nonlinear systems with sensor gain degradation and stochastic protocol based on strong tracking filtering

This paper focuses on the fault estimation problem for a class of nonlinear systems with sensor gain degradation and stochastic protocol (SP) based on strong tracking filtering. The phenomenon of the sensor gain degradation is described by sequences of stochastic variables in a known interval. The stochastic protocol (SP) is used to deal with possible data conflicts in multi-signal transmission. The augmented system is constructed by combining the original system state vectors and the related faults into an augmented state vectors. The strong tracking filter (STF) is designed by introducing a fading factor into the filter structure to solve the problem of burst faults. Finally, a simulation example is given to verify the effectiveness and applicability of the proposed filter.

A Distributed Luenberger Observer for Linear State Feedback Systems With Quantized and Rate-Limited Communications

This article addresses the problem of simultaneous distributed state estimation, and control of linear systems with linear state feedback, subjected to process, and measurement noise, under the constraints of quantized, and rate-limited network data transmission. In the set-up adopted, sensors and actuators communicate through a network with a strongly connected topology. Unlike the case of centralized linear systems, for which the separation principle holds, the above practical assumption prevents the separate design of observers, and controller because each of the nodes does not necessarily have access to the control inputs generated at all the other nodes. We derive a linear distributed Luenberger observer, and a set of sufficient conditions that guarantee ultimate boundedness of the estimation error, and system state vectors, with bounds that depend on the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> norm of the noise signals, and the number of bits used in the transmissions. A numerical example illustrates the performance and effectiveness of the proposed algorithm in controlling a network of open-loop unstable systems.

A Parameter Eigenstructure Assignment Design with Any Desired State Vector in Linear Time-Invariant System

The parametric design problem for eigenstructure assignment with arbitrary expected state vector is studied via state feedback in linear time invariant systems. The main idea of the considered problem is to design a parametric form of the state feedback, so that the designed closed-loop system has the desired eigenvalues, the desired eigenvectors and arbitrary expected state vector. Based on the parametric solution for a class of Sylvester matrix equation, the parametric expression of all the state feedback gain matrices is given in this paper. The free parameters including in the state feedback gain matrix can be further used to meet other performance requirements for the control system design. Finally, a simulation experiment is given to illustrate the effectiveness and simplicity of the proposed parametric method for the state feedback eigenstructure assignment problem with arbitrary expected state vector in the linear time invariant systems.

Unknown Input Reconstruction via Interval Observer and State and Unknown Input Compensation Feedback Controller Designs

In this paper, we investigate the state estimation, unknown input and measurement noise reconstruction problems and the feedback controller design issues for a linear discrete-time system with both unknown inputs and measurement noises. First, an augmented system is constructed and the state vector of the augmented system consists of the original system state and the measurement noise, and the preconditions between the original system and the augmented system is discussed in detail. Second, for the augmented system, a reduced-order observer is designed so that the original system state estimates and the measurement noise reconstruction can be obtained. Third, in order to get the asymptotical unknown input reconstruction, an interval observer for part of the measurable output is proposed and an unknown input reconstruction method based on the interval observer is developed. Finally, an observer-based state feedback and unknown input controller is designed and the closed-loop system stability is analyzed. We point out that the closed-loop system satisfies the so-called separation property. At last, two simulation examples are given to verify the effectiveness of the proposed methods.

A weighted distributed predictor-feedback control synthesis for interconnected time delay systems

The paper investigates the control design of interconnected time delay systems by means of distributed predictor-feedback delay compensation approaches and event-triggered mechanism. The idea behind delay compensation is to counteract the negative effects of delays in the control-loop by feeding back future predictions of the system state. Nevertheless, an exact prediction of the overall system state vector cannot be obtained providing that each system has only knowledge of their local data regarding the system model and state variables. Consequently, predictor-feedback delay compensation may lose effectiveness if the coupling between subsystems is sufficiently strong. To circumvent this drawback, the proposed distributed predictor-feedback control incorporates extra degree of freedom for control synthesis by introducing new weighting factors for each local prediction term. The design of the weighting factors is addressed, together with the event-triggered parameters, by an algorithm based on Linear Matrix Inequalities (LMI) and the Cone Complementarity Linearization (CCL). Simulation results are provided to show the achieved improvements and validate the effectiveness of the proposed method, even in the case that other control strategies fail to stabilize the closed-loop system.

State Observer for the Pacemaker Model Based on the Van der Pol Equation

A Dutch physiologist and a founder of electrocardiography V. Einthoven [10] proposed the first known model of the cardiac electrical activity. Later, van der Pol and van der Mark [11] developed a model of the heart, where the heartbeat is considered as a relaxation oscillation. From this point of view, to model the operation of pacemakers, the van der Pol equation [14,15,19] can be useful. The paper offers modeling of only one heart node that is the S-A (sinoatrial) node, which is the main heart pacemaker [20].Many control algorithms for dynamic systems are based on feedback, which involves the full state vector of a dynamic system. However, in practice, the full state vector is not always known. So, in the case of cardiac electrical activity, the potentials of the nodes rather than their changing rates are measured. To restore the full state vector from existing measurements, state observers are often used.In this paper, we solve the task of constructing an observer with linear error dynamics [22.25]. A necessary condition for the existence of such an observer is the system observability. The sufficient conditions can be formulated in the framework of the differential-geometric approach [25] using the ideas of duplicity [25,26]. Within this approach, an algorithm for observer construction can be developed. In the paper, a general problem to construct an observer for two-dimensional systems is solved and the results obtained are applied to the pacemaker model based on the Van der Pol oscillator. The numerical simulation enables us to illustrate operation of the observer developed.

Interval observers for linear functions of states and unknown inputs of nonlinear fractional-order systems with time delays

The main objective of this paper is to design interval observers using the output signals and the delayed output signals to estimate the state vector and unknown input vector of nonlinear fractional-order systems with time delay. We first propose and design two new functional observers, such that they bound the set of all admissible values of a linear function of the state vector and the unknown input vector at each instant of time. We then derive conditions for the existence of interval functional observers and provide an effective design algorithm for computing unknown observer matrices. Finally, an example is given to show the effectiveness of the proposed design approach.

Decoherence attenuation in the Tavis-Cummings model via transition frequency modulation with dipole–dipole interaction and multi-photon transitions

Producing and protecting the coherence and entanglement is of practical importance in quantum information processing and technologies. In this paper, using the Tavis-Cummings model we investigate the interaction between two two-level atoms with a reservoir via applying qubit transition frequency modulation and considering dipole–dipole interaction and multi-photon transitions in the Markovian and non-Markovian regimes. After introducing the model as well as its proper Hamiltonian, via the time-dependent Schrödinger equation we obtain the probability amplitudes of the system state vector, by which we analyze the coherence properties by considering different involved parameters. Generally, it will be observed that transition frequency modulation prevents the attenuation of coherence of two-qubit system. In particular, we find that, in the non-Markovian regime, by applying the frequency modulation in a certain range of dipole–dipole interaction strength, the amount of coherence is reduced; however, by increasing the dipole–dipole coupling, the degree of coherence is increased. Also, for single- and two-photon transitions, comparing with four-photon case, decoherence occurs in longer times.

Variational Adaptive Kalman Filter With Gaussian-Inverse-Wishart Mixture Distribution

In this article, a new variational adaptive Kalman filter with Gaussian-inverse-Wishart mixture distribution is proposed for a class of linear systems with both partially unknown state and measurement noise covariance matrices. The state transition and measurement likelihood probability density functions are described by a Gaussian-inverse-Wishart mixture distribution and a Gaussian-inverse-Wishart distribution, respectively. The system state vector together with the state noise covariance matrix and the measurement noise covariance matrix are jointly estimated based on the derived hierarchical Gaussian model. Examples are provided to demonstrate the effectiveness and potential of the developed new filtering design techniques.

Quantum Fisher Information of Two Moving Four-Level Atoms

We investigate dynamics of quantum entanglement (QE) and quantum Fisher information (QFI) of a system of two four-level atoms moving in the thermal environment. The time evolution of the state vector of the whole quantum system interacting with the thermal field is investigated numerically in the presence of intrinsic decoherence (ID). We see that ID and the thermal environment play a prominent role in the time evolution of the quantum system. QFI and von Neumann entropy (VNE) show the opposite response during their time evolution in the presence of the thermal environment. QFI is seen as more prone to intrinsic decoherence when compared with the VNE in the presence of the thermal environment. VNE changes remarkably with increase in the intrinsic decoherence parameter without the atomic motion. However, the periodic response of VNE is seen because of the atomic motion which gets modest under environmental effects. The decay of VNE is further damped at larger time scales that confirm that ID affects the system dynamics in a thermal environment. Moreover, VNE and QFI saturate to a lower level for larger time-scales under these environments. The damping response of VNE is observed under intrinsic decoherence for larger time scales. The VNE and QFI saturate to a lower level for larger time scales under the environmental effects. Moreover, one sees that the thermal environment induces a quicker decay of VNE when compared with the decay induced by ID. In this manner, the ID and thermal environment are found to suppress the nonclassical effects of the quantum system.

The model of optimal enterprise maturity management in the conditions of noisy source data

The purpose of this work is to propose a mathematical model of the optimal process for managing the organization›s maturity levels in the presence of interference in the source data. Changes in the organizational maturity of a company are described in terms of linear dynamic management systems. The proposed methodology for optimal management of the organization’s maturity level is demonstrated by the example of evaluating and forecasting the maturity level of one of the departments of a technical university. Baseline data is collected by assessing organizational maturity over several years. The paper uses the Kalman-Letov method of analytical design of optimal controllers, as well as a Kalman recursive filter that estimates the state vector of a dynamic system based on a number of incomplete and noisy data. The constructed model demonstrates plausible behavior in predicting the process of managing organizational maturity. The effect of accelerated growth of controlled indicators, identified as priority ones in the model, is reproduced. Using the Kalman filter allows you to create a control effect on the dynamics of organizational maturity indicators in such a way that the target values of maturity levels are achieved even in conditions significantly distorted when measuring the source data.

Observer‐based tracking controller design for a class of polynomial fuzzy systems with disturbance

AbstractIn this paper, the tracking control law design problem for a class of polynomial fuzzy systems subjected to external bounded disturbance is studied. The tracking control design problem is solved using the observer‐based tracking controller design method in which the observer estimates the controlled system state vector and also the system states will follow the state vector of a stable reference model subject to an H∞ performance. The process of calculating controller parameters is formulated as an SOS feasibility program. Simulation results are presented to show the merits of the proposed control design approach.

Information-analytical system of cardiographic information functional diagnostics

The article considers the Information-analytical system of cardiographic information functional diagnostics, which allows expanding the functionality of using miniature medical devices for non-invasive diagnostics of parameters of complex dynamic biomedical systems, using the example of cardio-intervals of the cardiovascular system. The system is based on not only the methods of the deterministic-stochastic approach but also the methods of the theory of chaos-self-organization, as a new scientific approach in the natural sciences. The method is based on calculating the parameters of quasi attractors and analyzing matrices of pairwise comparisons of time series of complex biomedical systems, which allows quantitatively and qualitatively describing the chaotic dynamics of the system state vector behaviour, obtaining objective information about changes in the functional state of the system, and also warning about these changes in time (if pathologies), which creates conditions for the status of the functional systems of the human body physiological monitoring.

Sensor-Fault-Estimation-Based Tolerant Control for Single-Phase Two-Level PWM Rectifier in Electric Traction System

This article presents a fault-estimation-based tolerant control strategy for single-phase two-level pulsewidth modulation rectifier subjected to catenary current sensor fault and dc-link voltage sensor fault. First, an augmented descriptor system is developed for the rectifier, whose augmented state vector consists of the state vector of original system as well as the sensor fault together with the measurement disturbance. Then, a linear reduced-order observer is designed for the descriptor plant. Accurate asymptotic estimation of the original state vector and the disturbed sensor fault are thus achieved simultaneously. Finally, the fault tolerant design method is addressed through sensor fault compensation, which allows the pre-design controller to continue to function normally even when both catenary current sensor and dc-link voltage sensor are faulty. Simulation and hardware-in-the-loop test results confirm the effectiveness of the proposed method.

Solution of Fault Accommodation Problem in Nonlinear Systems by Methods of Linear Algebra

Solution of the problem of fault accommodation in nonlinear dynamic systems is related to constructing the control law which provides full decoupling with respect to fault effects. The possibility of this solution is strictly limited by the demand on the system state vector availability (this vector is immediately included into control law description). As a rule, not all components of the state vector are immediately measurable at practice. Also, it is impossible to estimate full state vector for the system with unknown (affected by the faults) dynamics. The purpose of this article is to solve the problem of full decoupling by constructing a compensator that is independent of the fault effects a nd is based on a new control law. A solution is based on so-called logic-dynamic approach using only linear methods to solve the problem for nonlinear systems. The implementation of this method does not require a preliminary estimation of the parameters. It is assumed that fault detection and isolation procedure is performed by known methods. Assume the fault occurred and detected, then a solution of the control problem is performed on the basis of additional system that corresponding in a definite sense to the initial model. To solve the problem of accommodation, an efficient algorithm based on a logical-dynamic approach is presented, as a result of which a compensator is constructed. Additional system does not contain unknown vector that describes defects. As a result, fault accommodation effect is achieved. Theoretical results are demonstrated by illustrative and illustrative example.