Showing papers on "State vector published in 1996"

Replicated resource management system for managing resources in a distributed application and maintaining a relativistic view of state

Abstract: A method and apparatus for accessing resource objects contained in a distributed memory space in a communications network, including dividing the distributed memory space into a plurality of memory pools, each pool containing a collection of resource objects, providing a plurality of resource manager objects, each resource manager object having an associated set of memory pools and a registry of network unique identifiers for the resource objects in those pools, and accessing a given resource object via its network identifier. Another aspect of the invention is to provide a relativistic view of state of a plurality of objects, each object generating a state vector representing that object's view of its own state and the state of all other objects, each object sending its state vector to other objects, and each object maintaining a state matrix of the state vectors.

Geometry of stochastic state vector reduction

Abstract: The state space of a quantum mechanical system is a complex projective space, the space of rays in the associated Hilbert space. The state space comes equipped with a natural Riemannian metric (the Fubini-Study metric) and a compatible symplectic structure. The operations of ordinary quantum mechanics can thus be reinterpreted in the language of differential geometry. It is interesting in this spirit to scrutinize the probabilistic assumptions that are brought in at various stages in the analy­sis of quantum dynamics, particularly in connection with state vector reduction. A promising approach to understanding reduction, studied recently by a number of authors, involves the use of nonlinear stochastic dynamics to modify the ordinary linear Schrodinger evolution. Here we use stochastic differential geometry to give a systematic geometric formulation for such stochastic models of state vector collapse. In this picture, the conventional Schrodinger evolution, which corresponds to the unitary flow associated with a Killing vector of the Fubini -Study metric, is replaced by a more general stochastic flow on the state manifold. In the simplest example of such a flow, the volatility term in the stochastic differential equation for the state trajectory is proportional to the gradient of the expectation of the Hamiltonian. The conservation of energy is represented by the requirement that the actual process followed by the expectation of the Hamiltonian, as the state evolves, should be a martingale. This requirement implies the existence of a nonlinear term in the drift vector of the state process, which is always oriented opposite to the direction of in­ creasing energy uncertainty. As a consequence, the state vector necessarily collapses to an energy eigenstate, and a martingale argument can be used to show that the probability of collapse to a given eigenstate, from any particular initial state, is, in fact, given by precisely the usual quantum mechanical probability.

Approximate Data Assimilation Schemes for Stable and Unstable Dynamics

Abstract: Two suboptimal data assimilation schemes for stable and unstable dynamics are introduced. The first scheme, the partial singular value decomposition filter, is based on the most dominant singular modes of the tangent linear propagator. The second scheme, the partial eigendecomposition filter, is based on the most dominant eigenmodes of the propagated analysis error covariance matrix. Both schemes rely on iterative procedures like the Lanczos algorithm to compute the relevant modes. The performance of these schemes is evaluated for a shallow-water model linearized about an unstable Bickley jet. The results are contrasted against those of a reduced resolution filter, in which the gains used to update the state vector are calculated from a lower-dimensional dynamics than the dynamics that evolve the state itself. The results are also contrasted against the exact results given by the Kalman filter. These schemes are validated for the case of stable dynamics as well. The two new approximate assimilation schemes are shown to perform well with relatively few modes computed. Adaptive tuning of a modeled trailing error covariance for all three of these low-rank approximate schemes enhances performance and compensates for the approximation employed.

Track-to-track fusion with dissimilar sensors

Abstract: An analysis is described of a kinematic state vector fusion algorithm when tracks are obtained from dissimilar sensors. For the sake of simplicity, it is assumed that two dissimilar sensors are equipped with nonidentical two-dimensional optimal linear Kalman filters. It is shown that the performance of such a track-to-track fusion algorithm can be improved if the cross-correlation matrix between candidate tracks is positive. This cross-correlation is introduced by noise associated with target maneuver that is common to the tracking filters in both sensors and is often neglected. An expression for the steady state cross-correlation matrix in closed form is derived and conditions for positivity of the cross-correlation matrix are obtained. The effect of positivity on performance of kinematic track-to-track fusion is also discussed.

Best choice of coordinate system for tracking coordinated turns

Abstract: A standard approach to tracking is to use the extended Kalman filter (EKF) applied to a nonlinear state-space model. We compare two conceivable choices of state variables for modeling civil aircrafts. One where Cartesian velocities are used and one where absolute velocity and heading angle are used. In both choices, Cartesian coordinates are used for position and angular velocity for turning. It is shown that the latter state vector always performs better. This is proven by considering the linearization error made in the extended Kalman filter applied either to a time-continuous model or a discretized model. The result is supported by a Monte Carlo simulation study.

Linear quantum state diffusion for non-Markovian open quantum systems

Abstract: We demonstrate the relevance of complex Gaussian stochastic processes to the stochastic state vector description of non-Markovian open quantum systems. These processes express the general Feynman-Vernon path integral propagator for open quantum systems as the classical ensemble average over stochastic pure state propagators in a natural way. They are the coloured generalization of complex Wiener processes in quantum state diffusion stochastic Schrodinger equations.

Uncertain map making in natural environments

Abstract: Building on previous work on incremental natural scene modelling for mobile robot navigation, we focus in this paper on the problem of representing and managing uncertainties. The environment is composed of ground regions and objects. Objects (e.g., rocks) are represented by an uncertain state vector (location) and a variance-covariance matrix. Their shapes are approximated by ellipsoids. Landmarks are defined as objects with specific properties (discrimination, accuracy) that permit to use them for robot localization and for anchoring the environment model. Model updating is based on an extended Kalman filter. Experimental results are given that show the construction of a consistent model over tens of meters.

Method for automatic costate calculation

Abstract: A method for the automatic calculation of costates using only the results obtained from direct optimization techniques is presented. The approach exploits the relation between the time-varying costates and certain sensitivities of the variational cost function, a relation that also exists between the Lagrangian multipliers obtained from a direct optimization approach and the sensitivities of the associated nonlinear-programming cost function. The complete theory for treating free, control-constrained, interior-point-constrained, and state-constrained optimal control problems is presented. As a numerical example, a state-constrained version of the brachistochrone problem is solved and the results are compared to the optimal solution obtained from Pontryagin's minimum principle. The agreement is found to be excellent. Nomenclature / = right-hand side of state equations ge = control equality constraints gi = control inequality constraints he = state equality constraints hi = state inequality constraints J = cost function M = interior-point constraints m = dimension of control vector u N = total number of nodes minus 1 = total number of subintervals n — dimension of state vector x PWC = set of piecewise continuous functions t = time tf = final time ti = nodes along the time axis to = initial time u = control vector x = state vector Xf = final state Xi = state vector at node £/ Xo = initial state \(t) = costate A/ = Lagrangian multiplier associated with differential constraints along subinterval / Hi - Lagrangian multiplier associated with state constraints at node i (Ti = Lagrangian multiplier associated with control constraints along subinterval / <£ = cost function if} j. = boundary conditions at final time •00 = boundary conditions at initial time

Discrete-time model reference adaptive control of nonlinear dynamical systems using neural networks

Abstract: A multilayer discrete-time neural net (NN) controller is presented for the direct model reference adaptive control of a class of multi-input multi-output (MIM0) nonlinear dynamical systems. The nonlinear dynamical system is assumed to be controllable and its state vector is available for measurement. The NN controller exhibits learning-while-functioning features instead of learning-then-control so that control is immediate with no explicit learning phase needed. The tracking error between the output of a nonlinear plant and an ideal linear model converges within a very short time. Persistence of excitation (PE) is not needed, linearity in the parameters is not required, and certainty equivalence is not used. This overcomes several limitations of standard adaptive control. The novel weight tuning paradigm for the NN controller is based on the well-known delta rule but includes a modification to the learning rate parameter plus a correction term. It guarantees tracking as well as bounded NN weights in non-i...

An LQ Approach to Active Control of Vibrations in Helicopters

Abstract: In this paper, Linear Quadratic (LQ) optimal control concepts are applied for the active control of vibrations in helicopters. The study is based on an identified dynamic model of the rotor. The vibration effect is captured by suitably augmenting the state vector of the rotor model. Then, Kalman filtering concepts can be used to obtain a real-time estimate of the vibration, which is then fed back to form a suitable compensation signal. This design rationale is derived here starting from a rigorous problem position in an optimal control context. Among other things, this calls for a suitable definition of the performance index, of nonstandard type. The application of these ideas to a test helicopter, by means of computer simulations, shows good performances both in terms of disturbance rejection effectiveness and control effort limitation. The performance of the obtained controller is compared with the one achievable by the so called Higher Harmonic Control (HHC) approach, well known within the helicopter community.

On neurodynamics with limiter function and linsker's developmental model

Abstract: The limiter function is used in many learning and retrieval models as the constraint controlling the magnitude of the weight or state vectors. In this paper, we developed a new method to relate the set of saturated fixed points to the set of system parameters of the models that use the limiter function, and then, as a case study, applied this method to Linsker's Hebbian learning network. We derived a necessary and sufficient condition to test whether a given saturated weight or state vector is stable or not for any given set of system parameters, and used this condition to determine the whole regime in the parameter space over which the given state is stable. This approach allows us to investigate the relative stability of the major receptive fields reported in Linsker's simulations, and to demonstrate the crucial role played by the synaptic density functions.

Optimal Preview Control of a Two-dof Vehicle Model Using Stochastic Optimal Control Theory

Abstract: SUMMARY An optimal preview control algorithm is applied to a two degree of freedom(dof) vehicle model travelling with constant velocity on a randomly profiled road. The road roughness is modelled as a homogeneous random process being the output of a linear first order filter to white noise. The input from the road irregularity is assumed to be measured at some distance in front of the vehicle and this measured infonnation is utilized by the active controller to prepare the system for the ensuing input. The preview control algorithm is obtained by minimizing a quadratic performance index and by describing the average behaviour of the system by the covariance matrix of the vehicle response state vector. Results are presented for full state feedback and significant improvements in sprung mass acceleration, suspension working space and road holding are observed.

Power system state estimation: ANN application to bad data detection and identification

Abstract: The state estimation problem in power systems consists of four distinct basic operations: hypothesis structure; estimation; detection; identification. This paper solves this problem based on a proposed artificial neural network (ANN) scheme. The state estimation/bad data detection and identification (SE/BDDI) process is conducted via a two-stages (cascaded) neural network. The first stage is devoted to the estimation of the system states, using the raw measurements and network information. The second stage projects the estimated state vector, resulting from the first stage, onto the set of measurements that originates the estimated state vector. The neural computing is followed by a bad data detection block that detects and identifies the presence of bad data, if any. Bad data replacement is also suggested to enhance the state estimator reliability. Theoretical results are illustrated by means of a simple power network example.

Effect of Common Process Noise on Two-Sensor Track Fusion

Abstract: In a multisensor environment for surveillance systems, each sensor tracks multiple targets. It is assumed that sensors are equipped with optimal Kalman filters for target tracking. These tracks are correlated because the common process noise resulting from target maneuver enters the estimate of the state vector of the target being tracked. To obtain better quality tracks, the tracks from each sensor are associated using the nearest neighbor criterion for track matching and then kinematic track fusion is performed using the matched tracks. For this purpose, the cross-correlation matrix between tracks is introduced in the test statistic to test the hypothesis that the two tracks originated from the same target. It is shown that the probability distribution of correct track association is increased if the cross-covariance matrix introduced in the test statistic is positive. Necessary and sufficient conditions for the existence, uniqueness, and positivity of the cross-covariance matrix are derived. In addition, an expression for the steady-state cross-covariance matrix is obtained, which is shown to be a function of the parameters of the two filters associated with the candidate tracks being fused. It is shown that for two identical sensors, if the cross-covariance matrix is to be positive definite, certain restrictions on steady-state performance of the individual Kalman filters must be placed. Other measures of performance on the effect of cross correlation on kinematic track fusion are also discussed.

Nonlinear model reduction with application to rapid thermal processing

Abstract: The proper orthogonal decomposition, also called snapshot method, is a nonlinear model order reduction method where reduction of the size of the state space is achieved using a singular value decomposition of a matrix of snapshots of the state vector. This method has been shown to work well for a simple lumped physical model of a rapid thermal processing chamber. Although a substantial reduction of the number of states is achieved, some numerical computations still need to be performed in the high-dimensional state which is computationally expensive. In this paper we demonstrate how this can be avoided using aggregation of terms, resulting in a significant model simulation speed improvement.

Linear quadratic regulator for structure under on-line predicted future seismic excitation

Abstract: A predictive-adaptive (PA) control algorithm has been developed for a structure under a seismic excitation. This algorithm analyses information of an observed seismic excitation, estimates future structural responses and determines the control force for the structure, based on the linear quadratic regulator. That is, at a given moment t k : (1) seismic excitation information is converted to an autoregressive model, which forms the state equation for the excitation; (2) the identification model is combined with the structural model to build a state equation in an augmented space; (3) the weighted quadratic norm of the state vector and the future control force is formed as a cost function for estimating future responses; (4) the Ricatti equation is solved to find the optimum value of the cost function; and (5) the optimum gain matrix is obtained, and the control force is determined. The PA algorithm is not restricted to one type of control system, but can be applied to both an active driver system and an active tendon system. Its effectiveness is confirmed by numerical experiments for 1DOF and 3DOF structural models under sine and seismic excitations.

Maximum-likelihood symbol detection for RLL-coded data

Abstract: Parallel ML processing of an analog signal in a RLL-coded channel in which (1) vectors for a current state of the channel and the next state of the channel are computed using Walsh transform vector coefficients of the analog signal; (2) current state vectors and next state vectors and values of vectors precomputed in analog matched filters are used to generate vector scalar products which are compared against preselected threshold values for generating binary decision outputs that are used in digital sequential finite state machines to generate ML symbol decisions; and (3) ML symbol decisions are fed back and used to subtract the intersymbol interference value of the current state vector from the vector of the next state to transform the next state vector into an updated current state vector.

Chatter free variable structure perturbation estimator on the torque control of flexible robot joints with disturbance and parametric uncertainties

Abstract: A perturbation estimator using the theory of variable-structure systems is designed to enhance the robustness of a pole-placement controller design in the control of joint torque. In its ideal form, the pole-placement design using feedback-linearization technique achieves desired performance in nonlinear time-varying systems. However, its performance deteriorates rapidly with the presence of disturbance and parametric uncertainties, referred to as perturbation. The estimate generated by the proposed perturbation estimator is incorporated as an additional input to rectify the uncertainties in the nominal control model of the pole-placement design. The proposed scheme requires neither the measurement of the time derivative of state vector nor the precise knowledge of system parameters, but rather the bounds on system perturbation. Chatter and the adverse effects of conservative bounds on system perturbation, often encountered in conventional sliding-mode control (SMC), are alleviated for the controlled plant by this scheme.

Moment Equations for Non-Linear Systems Under Renewal-Driven Random Impulses with Gamma-Distributed Interarrival Times

Abstract: The moment equations technique is devised for non-linear dynamic systems subjected to random trains of impulses driven by an ordinary renewal point process with gamma-distributed integer parameter interarrival times (Erlang process) Since the renewal point process has not independent increments the state vector of the system, consisting of the generalized displacements and velocities, is not a Markov process Based on the fact that for this class of renewal processes the renewal events are every kth Poisson events (k - being the integer parameter of the gamma distribution) the renewal impulse process is recast in such a way as to express it in terms of the stationary Poisson counting process This results in the introduction of additional state variables, for which the stochastic equations are also formulated The resulting state vector augmented by the additional variables is now a Markov vector process

Computer system for simulating physical processes

Abstract: To simulate physical processes, state vectors for each of multiple voxels are stored in a memory along with a representation for each of multiple facets that are sized and oriented independently of the size and orientation of the voxels and, in combination, represent one or more surfaces. Each state vector includes multiple entries, each of which corresponds to a number of elements at a particular momentum state of multiple possible momentum states at a voxel. Interaction operations that model interactions between elements of different momentum states are performed on the state vectors, and surface interaction operations that model interactions between a facet and elements at one or more voxels near the facet are performed on the representations of facets. Finally, move operations that reflect movement of elements to new voxels are performed on the state vectors.

A theory on sequence spaces and shift register generators

Abstract: As a unified approach to the description of various shift register generators, the concept of sequence space is introduced and its properties are examined. A sequence space refers to a vector space whose elements are sequences satisfying the relation specified by a characteristic polynomial. In support of the sequence space, two bases-the elementary basis and the primary basis-are defined, and the polynomial expression of the sequence is defined as a tool for mathematical manipulations within the sequence space. Based on these definitions, various properties of sequence spaces such as sequence subspaces and minimal sequence spaces are investigated and summarized in terms of properties and theorems. The developed sequence theory is then applied to the description of the behaviors of shift register generators (SRGs). An SRG is represented by the state transition matrix, and the relevant SRG sequences are uniquely determined by this state transition matrix and the initial state vector. For an SRG, it is shown how to identify the sequence space generated by the SRG sequences with a fixed initial state vector (or the SRG space), and further, how to find the largest-dimensional sequence space that can be obtained by varying the initial state vectors (or the SRG maximal space). Conversely, for a given sequence space, it is shown how to find the minimum-sized SRGs that can generate the sequence space (or the basic SRGs). Finally, it is shown that the two typical SRGs-simple SRG and modular SRG-are special cases of basic SRGs that can generate the primary and the elementary bases, respectively.

Method for airbourne transfer alignment of an inertial measurement unit

Abstract: A method for determining the initial conditions for an inertial measurementnit (IMU) of a second vehicle launched from a wing of a first vehicle is provided. The method includes the steps of defining a state vector x as including (a) the rotation ζ of the computed coordinate axes with respect to the real coordinate axes of the second vehicle and (b) the projection δα along the Z axis of the first vehicle of the rotation of the second vehicle from its nominal coordinate axes to its real coordinate axes. A measurement z is defined as the projection δβ of a rotation angle β, along the Z axis of the first vehicle, between the nominal coordinate axes and a current computed coordinate axes. The method also includes the steps of estimating x over time with a Kalman filter, wherein the projection δβ is the measurement vector and the state vector x changes only due to random noise and processing x to produce the attitude about the Z axis of the first vehicle.

A neural network architecture for static security mapping in power systems

Abstract: In this paper a neural network based architecture, which combines supervised and unsupervised learning for the static security assessment of power systems, is presented. The proposed method allows the on-line security evaluation of a possible outage simply by considering the position of the neuron activated by the pre-fault state vector in an output map, allowing an easy and immediate view of the contingency risks. The mapping capabilities of two unsupervised neural networks, SOM (self-organising map) and CCA (curvilinear component analysis), are compared. Numerical tests, carried out on a study system, are presented and discussed.

Suboptimality of Cascaded and Federated Kalman Filters

Abstract: Cascaded and Federated Filters are seldom optimal in the sense of the centralized Kahnan filter, yet no correct method of assessing their statistical performance has been used except for limited simulation testing. This paper develops the proper covariance(and mean) analysis algorithms for assessing the suboptimality of these implementations. “Dual state” suboptimal analysis is used to model the real world(truth) state vector along with the implemented “stacked” state vector of the first and second filters of the Cascaded filter approach(or the implemented “stacked” state vector of the parallel bank of local filters and following master filter of the Federated filter approach). Differences between the real world model and the stacked implemented filter models can then be statistically assessed. A number of specific examples relating to GPS/INS navigation are shown to illustrate the usefulness of the resulting statistical analysis algorithms. An novel approach for evaluating the dynamic lag of a GPS only(no INS) filter is also included.

Collision operators in physical process simulation

Abstract: A computer implemented method for simulating a physical process (100). The method includes storing in a memory a state vector (106) for each of a number of voxels. Each state vector includes a plurality of integers, each of which corresponds to a particular momentum state of a number of possible momentum states at a voxel and represents the number of elements having the particular momentum state. The method also includes performing interaction operations (108) that model interactions between elements of different momentum states and include interaction rules that operate on a subset of the integers of a state vector. The interaction rules comprise a collision operator that transfers between integers representing a first set of momentum states and integers representing a second set of momentum states. Finally, the method includes performing move operations (114) on the state vectors that reflect movement of elements to new voxels.

Methods and systems for designing and making signal-processor circuits with internal companding, and the resulting circuits

Abstract: Electrical filter or signal processor circuits are provided with internal companding for reduced sensitivity to noise while input-output response is as conventionally specified. In the continuous-time case, for a specified circuit described by state equations with a state vector x(t), state equations are derived of an equivalent companding circuit having a state vector w(t)=G(t) x(t), where G(t) is a suitably chosen matrix (12). G(t) may be chosen for instantaneous or syllabic companding of the state vector. A corresponding technique applies to discrete-time circuits.

Parameter identification of vector-controlled induction machines

Abstract: This paper describes the identification of electromagnetic time constants and stator resistance for field oriented induction motor drives. The model of an induction motor at standstill in terms of state representation is discussed. A direct continuous-time identification from the standstill time-domain test data is based on the parametrized observer state vector. In a laboratory configuration the stator resistance is influenced by the non-linear inverter gain function. Two categories of current responses to voltage steps and to pseudo random binary sequences are examined. The current transients indicate saturation effects. Parameter estimates of a linear machine model are determined using least squares algorithms. Simulation and experimental studies are carried out in a Matlab software environment. Corresponding results obtained for two induction motor drives of different power ratings are included.