Showing papers on "State vector published in 2015"

Fault-Tolerant Sliding-Mode-Observer Synthesis of Markovian Jump Systems Using Quantized Measurements

Abstract: This paper investigates the design problem of sliding mode observer (SMO) using quantized measurements for a class of Markovian jump systems against actuator faults. Such a problem arises in modern networked-based digital systems, where data have to be transmitted and exchanged over a digital communication channel. In this paper, a new descriptor SMO approach using quantized signals is presented, in which a discontinuous input is synthesized to reject actuator faults by an offline static compensation of quantization effects. It is revealed that the lower bound on the density of a logarithmic quantizer is 1/3, under which the quantization effects could be compensated completely by using the SMO approach. Based on the proposed observer method, the asymptotical estimations of state vector and quantization errors can be obtained simultaneously. Finally, an example of a linearized model of an F-404 aircraft engine system is included to show the effectiveness of the presented observer design method.

Reach-avoid problems with time-varying dynamics, targets and constraints

Abstract: We consider a reach-avoid differential game, in which one of the players aims to steer the system into a target set without violating a set of state constraints, while the other player tries to prevent the first from succeeding; the system dynamics, target set, and state constraints may all be time-varying. The analysis of this problem plays an important role in collision avoidance, motion planning and aircraft control, among other applications. Previous methods for computing the guaranteed winning initial conditions and strategies for each player have either required augmenting the state vector to include time, or have been limited to problems with either no state constraints or entirely static targets, constraints and dynamics. To incorporate time-varying dynamics, targets and constraints without the need for state augmentation, we propose a modified Hamilton-Jacobi-Isaacs equation in the form of a double-obstacle variational inequality, and prove that the zero sublevel set of its viscosity solution characterizes the capture basin for the target under the state constraints. Through this formulation, our method can compute the capture basin and winning strategies for time-varying games at virtually no additional computational cost relative to the time-invariant case. We provide an implementation of this method based on well-known numerical schemes and show its convergence through a simple example; we include a second example in which our method substantially outperforms the state augmentation approach.

A derivative UKF for tightly coupled INS/GPS integrated navigation.

Abstract: The tightly coupled INS/GPS integration introduces nonlinearity to the measurement equation of the Kalman filter due to the use of raw GPS pseudorange measurements. The extended Kalman filter (EKF) is a typical method to address the nonlinearity by linearizing the pseudorange measurements. However, the linearization may cause large modeling error or even degraded navigation solution. To solve this problem, this paper constructs a nonlinear measurement equation by including the second-order term in the Taylor series of the pseudorange measurements. Nevertheless, when using the unscented Kalman filter (UKF) to the INS/GPS integration for navigation estimation, it causes a great amount of redundant computation in the prediction process due to the linear feature of system state equation, especially for the case with system state vector in much higher dimension than measurement vector. To overcome this drawback in computational burden, this paper further develops a derivative UKF based on the constructed nonlinear measurement equation. The derivative UKF adopts the concise form of the original Kalman filter (KF) to the prediction process and employs the unscented transformation technique to the update process. Theoretical analysis and simulation results demonstrate that the derivative UKF can achieve higher accuracy with a much smaller computational cost in comparison with the traditional UKF.

Actuator fault estimation observer design for discrete-time linear parameter-varying descriptor systems

Abstract: SUMMARY This paper deals with actuator fault estimation for a class of discrete-time Linear Parameter-Varying (LPV) descriptor systems. By considering the fault as an auxiliary state vector, an augmented system is established. Then, a fault estimation observer is designed based on the augmented system. In this paper, the fault estimation observer design is formulated as a Linear Matrix Inequality (LMI) feasibility problem. Therefore, all parameters of the observer can be simultaneously designed by solving a set of strict LMIs. In order to attenuate the effect of the unknown disturbance, fault variation, and measurement noise, we further propose a robust fault estimation observer design method, which is the main contribution of this paper. Finally, performance of the proposed robust fault estimation observer is shown through the application to a trucktrailer model. Copyright c ⃝ 2013 John Wiley & Sons, Ltd.

Particle Swarm Optimization of the Multioscillatory LQR for a Three-Phase Four-Wire Voltage-Source Inverter With an $LC$ Output Filter

Abstract: 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.

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

Abstract: 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.

Optimal transport over a linear dynamical system

Abstract: We consider the problem of steering an initial probability density for the state vector of a linear system to a final one, in finite time, using minimum energy control. In the case where the dynamics correspond to an integrator ($\dot x(t) = u(t)$) this amounts to a Monge-Kantorovich Optimal Mass Transport (OMT) problem. In general, we show that the problem can again be reduced to solving an OMT problem and that it has a unique solution. In parallel, we study the optimal steering of the state-density of a linear stochastic system with white noise disturbance; this is known to correspond to a Schrodinger bridge. As the white noise intensity tends to zero, the flow of densities converges to that of the deterministic dynamics and can serve as a way to compute the solution of its deterministic counterpart. The solution can be expressed in closed-form for Gaussian initial and final state densities in both cases.

Robust sliding-mode observer-based sensor fault estimation, actuator fault detection and isolation for uncertain nonlinear systems

Abstract: This paper deals with the issues of sensor fault estimation, actuator fault detection and isolation for a class of uncertain nonlinear systems. By taking the sensor fault vector as a part of an extended state vector, the original system with sensor faults, actuator faults and unknown inputs is transformed into an augmented singular system which is just with actuator faults and unknown inputs. For the constructed singular system, a robust sliding-mode observer is developed to simultaneously estimate the states and sensor faults of original system, and the observer gain matrices are computed in terms of linear matrix inequalities by solving an optimization problem. Then an actuator fault detector is designed to detect actuator faults when ones occur, and multiple observers used as actuator fault isolators are proposed to identify which actuator is with fault. Finally, a simulation example is given to illustrate the effectiveness of the proposed methods.

Balancing aggregation and smoothing errors in inverse models

Abstract: . Inverse models use observations of a system (observation vector) to quantify the variables driving that system (state vector) by statistical optimization. When the observation vector is large, such as with satellite data, selecting a suitable dimension for the state vector is a challenge. A state vector that is too large cannot be effectively constrained by the observations, leading to smoothing error. However, reducing the dimension of the state vector leads to aggregation error as prior relationships between state vector elements are imposed rather than optimized. Here we present a method for quantifying aggregation and smoothing errors as a function of state vector dimension, so that a suitable dimension can be selected by minimizing the combined error. Reducing the state vector within the aggregation error constraints can have the added advantage of enabling analytical solution to the inverse problem with full error characterization. We compare three methods for reducing the dimension of the state vector from its native resolution: (1) merging adjacent elements (grid coarsening), (2) clustering with principal component analysis (PCA), and (3) applying a Gaussian mixture model (GMM) with Gaussian pdfs as state vector elements on which the native-resolution state vector elements are projected using radial basis functions (RBFs). The GMM method leads to somewhat lower aggregation error than the other methods, but more importantly it retains resolution of major local features in the state vector while smoothing weak and broad features.

Robust Sensor Fault Estimation for Descriptor-LPV Systems with Unmeasurable Gain Scheduling Functions

Abstract: This paper addresses the design of a state estimation and sensor fault detection, isolation and fault estimation observer for descriptor-linear parameter varying D-LPV systems. In contrast to where the scheduling functions depend on some measurable time varying state, the proposed method considers the scheduling function depending on an unmeasurable state vector. In order to isolate, detect and estimate sensor faults, an augmented system is constructed by considering faults to be auxiliary state vectors. An unknown input LPV observer is designed to estimate simultaneously system states and faults. Sufficient conditions to guarantee stability and robustness against the uncertainty provided by the unmeasurable scheduling functions and the influence of disturbances are synthesized via a linear matrix inequality LMI formulation by considering H∞ and Lyapunov approaches. The performances of the proposed method are illustrated through the application to an anaerobic bioreactor model.

Numerically Accelerated Importance Sampling for Nonlinear Non-Gaussian State-Space Models

Abstract: We propose a general likelihood evaluation method for nonlinear non-Gaussian state-space models using the simulation-based method of efficient importance sampling. We minimize the simulation effort by replacing some key steps of the likelihood estimation procedure by numerical integration. We refer to this method as numerically accelerated importance sampling. We show that the likelihood function for models with a high-dimensional state vector and a low-dimensional signal can be evaluated more efficiently using the new method. We report many efficiency gains in an extensive Monte Carlo study as well as in an empirical application using a stochastic volatility model for U.S. stock returns with multiple volatility factors. Supplementary materials for this article are available online.

Conjugate Unscented Transformation-Based Approach for Accurate Conjunction Analysis

Abstract: This paper presents a methodology to estimate the probability of conjunction between two space objects when probability density functions for orbital state vector are significantly non-Gaussian in ...

An algorithm based on two-step Kalman filter for intelligent structural damage detection

Abstract: Summary In the traditional extended Kalman filter approach, unknown structural parameters are included in the extended state vector. Then, the sizes of the extended state vector and the corresponding state equation are quite large, and the state equation is highly nonlinear with respect to the extended state vector. This may cause identification divergent for a large number of unknown parameters. Also, such strategy requires large computational effort and storage capacities, which is not appropriate for intelligent structural damage detection implemented by smart sensors with microprocessors. In this paper, an algorithm based on a two-step Kalman filter approach is proposed to remove the aforementioned drawbacks of the traditional extended Kalman filter. In the first step, recursive estimation of structural state vector is derived by Kalman filter with assumed structural parameters. In the second step, structural parameters and the updated structural state vector are estimated by the Kalman filter and the recursive estimation in the first step. Thus, the number of estimated variables in each step is reduced, which reduces the computational effort and storage requirements. This superiority is important for intelligent structural damage detection implemented by smart sensor in wireless sensor network. The proposed algorithm is first validated by numerical simulations results of structural damage detection of the phase-I 3-D ASCE benchmark building for structural health monitoring, a 30-story shear building with minor damage, and an experimental test of damage detection of a lab multistory frame model. Then, it is applied to structural damage detection of a lab multistory model-employed smart sensors embedded with the proposed algorithm. Copyright © 2014 John Wiley & Sons, Ltd.

Conditional Gauss–Hermite Filtering With Application to Volatility Estimation

Abstract: The conditional Gauss–Hermite filter (CGHF) utilizes a decomposition of the filter density by conditioning on an appropriate part of the state vector. In contrast to the usual Gauss—Hermite filter (GHF) it is only assumed that the terms in the decomposition can be approximated by Gaussians. Due to the nonlinear dependence on the condition, quite complicated densities can be modeled, but the advantages of the normal distribution are preserved. For example, in models with multiplicative noise occuring in Bayesian estimation, the joint density of state and variance parameter strongly deviates from a bivariate Gaussian, whereas the conditional density can be well approximated by a normal distribution. As in the GHF, integrals in the time and measurement updates are computed by Gauss—Hermite quadrature. Alternatively, the unscented transform can be used, leading to a conditional unscented Kalman filter (CUKF).

Robust Sliding Mode Observer based Fault Estimation for Certain Class of Uncertain Nonlinear Systems

Abstract: This paper proposes a new scheme for estimating the actuator and sensor fault for Lipschitz nonlinear systems with unstructured uncertainties using the sliding mode observer (SMO) technique. Initially, a coordinate transformation is introduced to transform the original state vector into two parts such that the actuator faults only appear in the dynamics of the second state vector. The concept of equivalent output error injection is then employed to estimate the actuator fault. The effects of system uncertainties on the estimation errors of states and faults are minimized by integrating an uncertainty attenuation level into the observer. The sufficient conditions for the state estimation error to be bounded and satisfy a prescribed performance are derived and expressed as a linear matrix inequality (LMI) optimization problem. Furthermore, the proposed actuator fault estimation method is extended to sensor fault estimation. Finally, the effectiveness of the proposed scheme in estimating actuator and sensor faults has been illustrated considering an example of a single-link flexible joint robot system.

Inverse sliding-window filters for vision-aided inertial navigation systems

Abstract: This disclosure describes inverse filtering and square root inverse filtering techniques for optimizing the performance of a vision-aided inertial navigation system (VINS). In one example, instead of keeping all features in the system's state vector as SLAM features, which can be inefficient when the number of features per frame is large or their track length is short, an estimator of the VINS may classify the features into either SLAM or MSCKF features. The SLAM features are used for SLAM-based state estimation, while the MSCKF features are used to further constrain the poses in the sliding window. In one example, a square root inverse sliding window filter (SQRT-ISWF) is used for state estimation.

Robust observer-based sensor fault reconstruction for discrete-time systems via a descriptor system approach

Abstract: This paper addresses the problem of observer-based sensor fault reconstruction for discretetime systems subject to external disturbances via a descriptor system approach. First, an augmented descriptor system is formulated by letting the sensor fault term be an auxiliary state vector; then a discrete-time descriptor state observer is constructed to achieve concurrent reconstructions of original system states and sensor faults. Sufficient and necessary conditions for the asymptotic stability of the proposed observer are explicitly provided. To broaden its application scope, less restrictive existence conditions are further discussed. Further, sufficient conditions for the robust stability of the proposed observer are formulated in terms of linear matrix inequalities (LMIs) that can be conveniently solved using LMI optimization techniques. After that, an extension of the proposed linear approach to discretetime nonlinear systems with Lipschitz constraint is investigated. At last, two illustrative examples are given to verify the effectiveness of the proposed techniques.

Indirect determination of the displacement components in an electric motor drive

Abstract: High technological process quality requires the use of deviation closed-loop systems and the formation of appropriate informational support for a control process. The article discusses two approaches to obtaining information on displacement components: direct measurement of speed and/or position with the help of a sensor on the motor shaft and indirect determination of the object state vector using the available variables for the direct measurement without the shaft sensor (current and voltage). The main disadvantages of optical encoders are identified. An overview, a classification, a comparative analysis, and the ranges of application of indirect methods of determining displacement components are given (calculation for a model of an electric machine with the measurement of current and voltage of the stator and calculation of the static functional dependence).

Joint spatial- and Doppler-based ego-motion estimation for automotive radars

Abstract: An ego-motion estimation method based on the spatial and Doppler information obtained by an automotive radar is proposed. The estimation of the motion state vector is performed in a density-based framework. Compared to standard vehicle odometry the approach is capable to estimate the full two dimensional motion state with three degrees of freedom. The measurement of a Doppler radar sensor is represented as a mixture of Gaussians. This mixture is matched with the mixture of a previous measurement by applying the appropriate egomotion transformation. The parameters of the transformation are found by the optimization of a suitable join metric. Due to the Doppler information the method is very robust against disturbances by moving objects and clutter. It provides excellent results for highly nonlinear movements. Real world results of the proposed method are presented. The measurements are obtained by a 77GHz radar sensor mounted on a test vehicle. A comparison using a high-precision inertial measurement unit with differential GPS support is made. The results show a high accuracy in velocity and yaw-rate estimation.

Asynchronous sensor space alignment algorithm

Abstract: The invention discloses an asynchronous sensor space alignment algorithm. Data of two sensors are synchronized by the aid of an interpolation and extrapolation time alignment algorithm, a pseudo measurement equation is built according to time alignment results, and the asynchronous sensor space alignment algorithm based on the interpolation and extrapolation time alignment algorithm and a geocentric earth fixed coordinate system is provided to solve the problem of space alignment under target maneuvering conditions. The building process of the pseudo measurement equation is unrelated to a target state vector, and pseudo measurement built by the time alignment results can be proved to be unrelated to the target state vector, so that the algorithm can effectively solve the problem of asynchronous sensor space alignment under the target maneuvering conditions. Simulation experiments confirm that the algorithm can still accurately estimate system errors of the sensors under the condition of snakelike maneuvering of a target, and the influence of the sampling period ratio of the sensors and random errors on system error estimation precision is analyzed by simulation.

One-state vector formalism for the evolution of a quantum state through nested Mach-Zehnder interferometers

Abstract: Linear-optical interferometers play a key role in designing circuits for quantum information processing and quantum communications. Even though nested Mach-Zehnder interferometers appear easy to describe, there are occasions when they provide unintuitive results. This paper explains the results of a highly discussed experiment performed by Danan et al. [Phys. Rev. Lett. 111, 240402 (2013).] using a standard approach. We provide a simple and intuitive one-state vector formalism capable of interpreting their experiment. Additionally, we cross-checked our model with a classical-physics-based approach and found that both models are in complete agreement. We argue that the quantity used in the mentioned experiment is not a suitable which-path witness, producing seemingly contraintuitive results. To circumvent this issue, we establish a more reliable which-path witness and show that it yields well-expected outcomes of the experiment.

Entanglement Criteria of Two Two-Level Atoms Interacting with Two Coupled Modes

Abstract: In this paper, we study the interaction between two two-level atoms and two coupled modes of a quantized radiation field in the form of parametric frequency converter injecting within an optical cavity enclosed by a medium with Kerr nonlinearity. It is demonstrated that, by applying the Bogoliubov-Valatin canonical transformation, the introduced model is reduced to a well-known form of the generalized Jaynes-Cummings model. Then, under particular initial conditions for the atoms (in a coherent superposition of its ground and upper states) and the fields (in a standard coherent state) which may be prepared, the time evolution of state vector of the entire system is analytically evaluated. In order to understand the degree of entanglement between subsystems (atom-field and atom-atom), the dynamics of entanglement through different measures, namely, von Neumann reduced entropy, concurrence and negativity is evaluated. In each case, the effects of Kerr nonlinearity and detuning parameter on the above measures are numerically analyzed, in detail. It is illustrated that the amount of entanglement can be tuned by choosing the evolved parameters, appropriately.

Fast covariance recovery in incremental nonlinear least square solvers

Abstract: Many estimation problems in robotics rely on efficiently solving nonlinear least squares (NLS). For example, it is well known that the simultaneous localisation and mapping (SLAM) problem can be formulated as a maximum likelihood estimation (MLE) and solved using NLS, yielding a mean state vector. However, for many applications recovering only the mean vector is not enough. Data association, active decisions, next best view, are only few of the applications that require fast state covariance recovery. The problem is not simple since, in general, the covariance is obtained by inverting the system matrix and the result is dense. The main contribution of this paper is a novel algorithm for fast incremental covariance update, complemented by a highly efficient implementation of the covariance recovery. This combination yields to two orders of magnitude reduction in computation time, compared to the other state of the art solutions. The proposed algorithm is applicable to any NLS solver implementation, and does not depend on incremental strategies described in our previous papers, which are not a subject of this paper.

Convergence within a polyhedron: controller design for time-delay systems with bounded disturbances

Abstract: This study considers linear systems with state/input time-varying delays and bounded disturbances. The authors study a new problem of designing a static output feedback controller which guarantees that the state vector of the closed-loop system converges within a pre-specified polyhedron. Based on the Lyapunov–Krasovskii method combining with the free-weighting matrix technique, a new sufficient condition for the existence of a static output feedback controller is derived. The author's condition is expressed in terms of linear matrix inequalities with two parameters need to be tuned and therefore can be efficiently solved by using a two-dimensional search method combining with convex optimisation algorithms. To be able to obtain directly an output feedback control matrix from the derived condition, they propose an appropriate combination between a state transformation with a choice of a special form of the free-weighting matrices. The feasibility and effectiveness of the derived results are illustrated through five numerical examples.