Showing papers on "State vector published in 1986"

Estimation, Prediction, and Interpolation for ARIMA Models with Missing Data

Abstract: We show how to define and then compute efficiently the marginal likelihood of an ARIMA model with missing observations. The computation is carried out by using the univariate version of the modified Kalman filter introduced by Ansley and Kohn (1985a), which allows a partially diffuse initial state vector. We also show how to predict and interpolate missing observations and obtain the mean squared error of the estimate.

Stochastic dynamical reduction theories and superluminal communication.

Abstract: In theories which describe the reduction of the state vector as a physical process, the possibility exists, for certain experiments, of predictions which differ from those of quantum theory. These are ``interrupted reduction interference'' experiments, characterized by an interaction which triggers the reduction, followed rapidly (before the reduction is completed) by a measurement of interference between the superposed states that make up the state vector (possible examples: double Stern-Gerlach experiment, two-slit neutron interference). We consider the general class of stochastic reduction theories, and ask whether they allow superluminal communication by means of such experiments. We show that, if the state vector that precedes reduction is precisely reproducible, then superluminal communication can occur in certain circumstances, unless the off-diagonal elements of the density matrix decay exponentially, with a universal time constant. We also show, in that case, that no state vector ever reduces in a finite time, so such a theory is not satisfactory. However, superluminal communication can be avoided if reduction is triggered only in irreproducible state vectors, of such complexity that prior to reduction the ``effective'' density matrix, constructed from the ensemble of such state vectors and traced over the variables outside the experimenter's control, is diagonal. Then predictions are identical to those of quantum theory for ``interrupted reduction interference'' experiments and thus apparently for all experiments. The lesson of this paper is that the ``effective'' density matrix must always be used to make physical predictions in dynamical reduction theories. This supplies a resolution of the problem of reconciling state-vector reduction with relativity: even if the reduction dynamics is not relativistically invariant, its experimental predictions are. It also implies that the ``effective'' entropy increases during a measurement, but remains constant during reduction, which is the reverse of a common dictum.

Identification of nonlinear system parameters in joints using the force-state mapping technique

Abstract: A procedure is presented for identifying the potentially strong nonlinear properties of structural members, such as joints, by expressing the force transmitted by the member as a function of its mechanical state. By explicitly including position and rate dependent effects, the surface of transmitted force versus state, the force-state map, has distinct, unique, superposable features for common structural nonlinearities, even those which appear to indicate hysteresis on a force-stroke presentation. An analysis is performed on the influence of true memory effects, transient response, and uncertainty in the measurements and system mass on the precision of the procedure. The successful identification of simulated data verifies the accuracy of the identification algorithm. Tests are then conducted on three actual joint models, with incomplete state measurements typical of an actual testing environment. The ability of the procedure to estimate the complete state vector and to analyze and reconstruct the measured nonlinear characteristics is demonstrated.

A note on optimal control of generalized state-space (descriptor) systems

Abstract: Linear time-invariant systems of the form E dx/dt = Ax + Bu are considered, where E is a square matrix, which may be singular, and B is a rectangular matrix having full column rank. It is assumed that for any ‘admissible’ initial state x(0−), any control vector u(t) yields one and only one state vector x(t). The problem is this: find a control vector u(t) that will drive the system from an ‘admissible’ initial state x(0−) to a fixed final state xf , in a fixed time tf while minimizing some cost functional $. Only elementary matrix and variational techniques are used. Necessary conditions are derived for the existence of minima of J; the problem of finding sufficient conditions of the existence of minima of J is not considered. It is shown that in many cases the necessary conditions for the existence of minima of J yield a two-point boundary-value problem consisting of a system of ordinary differential equations containing only elements of, x(t) and the boundary conditions prescribed at 0− and tf . If some...

Realization of bilinear stochastic systems

Abstract: This note considers the problem of realization of bilinear stochastic systems (BLSR) First an explicit statement for the BLSR problem is presented Next a realization algorithm is developed In this algorithm the state vector is picked as a basis in the subspace obtained by projecting an appropriately defined past vector onto an appropriately defined future vector Also, the realization algorithm involves solving a matrix nonlinear equation which is akin to the algebraic Riccati equation, except for one additional term

Optimization of multistage processes described by differential-algebraic equations

Abstract: The paper describes an algorithm for the computation of optimal design and control variables for a multistage process, each stage of which is described by a system of nonlinear differential-algebraic equations of the form: $$f(t,\dot x(t),x(t),u(t),v) = 0$$ where t is the time, x(t) the state vector, \(\dot x(t)\) its time derivative, u(t) the control vector, and v a vector of design parameters. The system may also be subject to end-point or interior-point constraints, and the switching times may be explicitly or implicitly defined. Methods of dealing with path constraints are also discussed.

Assimilation of Altimeter Data into Ocean Models

Abstract: The problem of assimilating satellite altimeter data into an ocean model is considered for the case in which the ocean currents are weak, so that they can be represented by a superposition of linear Rossby waves, and the altimeter measurements are exact and available everywhere. The state of the model at each instant is represented by a state vector, and the process of assimilating data is represented by the projection of this vector onto the surface made up of all the model states consistent with the observations. The projection and the evolution of the model between assimilating each batch of data may be represented by a matrix operator, whose eigenvalues characterize the convergence properties of the scheme. The possibility of using altimeter observations of the ocean surface to determine the deeper structure of the ocean is investigated. It is found to be limited by the phase separation that develops over each assimilation cycle between modes of the ocean with the same horizontal wavenumber b...

Suppose the State Vector Is Real: The Description and Consequences of Dynamical Reduction

Abstract: Probably sometime you have said “the wave function of the electron” when you might have said “the wave function of an ensemble of identically prepared electrons” or “the wave function describing my knowledge of the electron.” You might also have said “the wave funotion of the many universes, each containing the electron, but only one containing me” or “the wave function describing all possible experiments I might do upon the electron if I wanted to.” Perhaps you were just saving your breath. Then again, perhaps, deep in the physics psyche (the classical part), there is the belief, hope, or yearning that quantum theory describes an individual physical system in nature. However, quantum.theory unaltered does not do this. Schrodinger made the point most clearly in his famous “cat paradox” paper:’ in the quantum theory description of a measuremefit, the Schrodidger unitary evolution leaves the state vector in a superposition of macroscopically distinguishable states (e.g., “cat-alive” plus “catdead”), whereas in nature, the apparatus is left in one of those states (e.g., “cat-alive”). Fifty years ago, Schrodinger wrote:’

Estimating the plant state from the compensator state

Abstract: For the system \dot{w} = Sw where w = (x\over{z}) , this note states and proves necessary and sufficient conditions under which a) z is an estimate of a linear function of x (i.e., z estimates Tx ), or b) a linear function of z is an estimate of x (i.e., Vz estimates x ). The mapping T has been used previously by the authors to compute the estimator-controller form of a compensator whose state vector z had the same dimension as the plant state vector x .

Linear guidance laws for space missions

Abstract: A general analysis of guidance laws is presented along with a review of the propagation of state perturbations. Linearized guidance laws are derived for fixed and variable time of arrival, and for the Shuttle phasing and height guidance maneuvers. In general, six interrelated partials are involved in each guidance law. These partials relate the maneuver delta velocity and time of flight to perturbations in initial position, velocity, and time. The partials can be expressed as a function of a single fundamental guidance partial, which relates the maneuver to the final position perturbation, and the partials from the upper row of the augmented time transition matrix (augmented with the dynamical state vector). Guidance can be interpreted as a form of offset targeting. PACE trajectories involve a series of coast phases separated by maneuvers. The maneuvers can be derived by imposing sufficient guidance constraints to uniquely define the maneuver. The guidance constraints can be imposed on the maneuver, postmaneuyer trajectory, or some combination thereof. Impulsive maneuvers may be assumed for many space missions. The impulsive maneuvers can be computed exactly or with a linearized model. The linearized model could be used for real-time software because trajectory perturbations are generally small, but a more likely use is in preflight covariance analysis. The linear model contains guidance matrices for up- dating through the maneuvers, and transition matrices for up- dating through the coasting phases. This paper presents two general techniques for solving the linear guidance problem. Most applications of linearized guidance laws have been based on fixed- and variable-time-of-arrival guidance.1'4 Many other linearized laws can be introduced by imposing dif- ferent constraints on the maneuver and postmaneuver trajec- tory.5'6 Some general properties of linearized guidance laws were established by Cicolani.7 A general solution to the linear guidance problem was proposed by Tempelman5 by introduc- ing a generalized linear constraint equation. This paper at- tempts to define some general techniques for establishing the relationship between the maneuver and the perturbations in position, velocity, and time using a more intuitive approach than presented in Ref. 5. Fixed- and variable-time-of-arrival guidance laws are reviewed to demonstrate the techniques and to serve as an introduction to more complicated maneuvers, such as the Shuttle phasing and height maneuvers.

Study of a homotopy continuation method for early orbit determination with the Tracking and Data Relay Satellite System (TDRSS)

Abstract: A recent mathematical technique for solving systems of equations is applied in a very general way to the orbit determination problem. The study of this technique, the homotopy continuation method, was motivated by the possible need to perform early orbit determination with the Tracking and Data Relay Satellite System (TDRSS), using range and Doppler tracking alone. Basically, a set of six tracking observations is continuously transformed from a set with known solution to the given set of observations with unknown solutions, and the corresponding orbit state vector is followed from the a priori estimate to the solutions. A numerical algorithm for following the state vector is developed and described in detail. Numerical examples using both real and simulated TDRSS tracking are given. A prototype early orbit determination algorithm for possible use in TDRSS orbit operations was extensively tested, and the results are described. Preliminary studies of two extensions of the method are discussed: generalization to a least-squares formulation and generalization to an exhaustive global method.

Infinite-Dimensional Bilinear Realizations of Nonlinear Dynamical Systems

Abstract: Publisher Summary This chapter discusses the infinite-dimensional bilinear realizations of nonlinear dynamical systems The chapter provides an overview of the state of knowledge in the field, from the viewpoint of the Nachbin School of holomorphy, and provides suggestions for further research along the same lines The chapter focuses on the linear function space realizations of a dynamical system characterized by a state vector x t , governed by the state evolution equation The Fourier-Borel duality and bilinear realizations of control systems are described in the chapter The chapter also discusses the analytic evolution equations in Banach spaces such as nuclear, Hilbert-Schmidt, compact and L P in the sense of Dwyer and Dineen, and to real-analytic functions Finite-dimensional linear, bilinear and linearly controlled analytic systems have been studied

Stabilizing Partially Observable Uncertain Linear Systems

Abstract: We consider linear systems which involve no stochastic element, but whose state equations depend on time-varying unknown parameters. This parameter uncertainty is not complete because we know that the parameters are constrained to lie within known bounded intervals. The objective is to choose a dynamic observer and a feedback on the state vector of this observer guaranteing uniform asymptotic stability for all admissible variations of the parameters of this control law.

Design of a reduced-order adaptive observer

Abstract: A reduced-order implicit adaptive observer for a single-input single-output time-invariant nth-order linear system is considered. A state vector described in observable canonical form is explicitly parameterised in terms of the unknown system parameters and the filtered input and output vectors. For parameter estimation, a least-square-type adaptation scheme that can afford an arbitrarily fast exponential convergence is proposed.

Parallel 3-action type optimum regulator

Abstract: PURPOSE:To obtain an effective state variable vector even in case the mean value of disturbance is not equal to zero and also unknown, by transmitting said variable vector in parallel through a proportional feedback a time average feedback element and a trend feedback element respectively. CONSTITUTION:An optimum control input vector (20) is obtained from a state equation (1), where (t): time, t0: initial time point, (x): n-dimensional state vector, (u): r-dimensional control input vector, (w): m-dimensional disturbance and a disturbance vector w(t) supposed as the normal white noise respectively. The 1st, 2nd and 3rd terms of the right member of the equation 20 are attained by the proportional feedback of the state variable vector, the time average feedback of the state variable vector and the trend feedback of the state variable vector respectively. Then the sum of these vectors of feedbacks is obtained and used as a control input vector to attain the equation 20. When an optimum regulator is obtained based on the equation 20, P, I, D and K are decided by equations 21, 22, 23 and 24 respectively.

Computer-aided design of multivariable stochastic control systems with a-priori prescribed dynamical properties

Abstract: This paper presents a computer-aided procedure for designing multivariable controllers which simultaneously achieve a variety of desired design goals in stochastic, unity feedback, linear multivariable systems. The multivariable control system simultaneously ensures: 1) decoupling closed-loop design using linear estimation state variable feedback in combination with feedforward compensator, 2) complete and arbitrary closedloop pole placement which implies desired transient performance as well as closed-loop stability, 3) steady-state output rejection of nondecreasing deterministic part of stochastic disturbances with non-zero mean values, and 4) optimal steady-state estimation of plant's state vector using Kalman filter. In the design procedure the polynomial matrix approach in s-domain is used. The overall multivariable stochastic control problem is divided into two equivalent problems: stochastic state Kalman filtering and deterministic control of the state estimation and output feedback. The considerations are illustrated by a numerical example for simplified version of the ship possitionnig control system.

Injection State Vector Estimation from Flight Data Analysis of a Spinning Apogee Stage

Abstract: In the present paper, a procedure is presented to estimate the injection state vector from the data of a single-axis velocity encoder and Horizon Crossing Sensors mounted on a spinning apogee stage together with Inertial Navigation System information at the separation of previous stage The attitude information is obtained through a new global approach using only horizon crossing sensors The inertial pitch angle is obtained from local pitch angle history by separating the low frequency component due to translational motion The yaw angle is derived from the pattern of dynamical coupling of the pitch and yaw motions in frequency domain The attitude information is combined with the output of a single axis velocity encoder and trajectory information is generated The test results obtained from present approach are com-pared with a dynamics simulator and it is established that the injection point can be estimated with an accuracy sufficient for preliminary orbit determination