Continuous State Space Model Research Articles

Continuous time state space modeling of panel data by means of sem

Maximum likelihood parameter estimation of the continuous time linear stochastic state space model is considered on the basis of largeN discrete time data using a structural equation modeling (SEM) program. Random subject effects are allowed to be part of the model. The exact discrete model (EDM) is employed which links the discrete time model parameters to the underlying continuous time model parameters by means of nonlinear restrictions. The EDM is generalized to cover not only time-invariant parameters but also the cases of stepwise time-varying (piecewise time-invariant) parameters and parameters varying continuously over time according to a general polynomial scheme. The identification of the continuous time parameters is discussed and an educational example is presented.

Predictive Control of Air Temperature in Greenhouses

This paper describes a new method for improving the control of air temperature in greenhouses. The proposed controller is an extended version of the generalized predictive controller (GPC). The prediction of air temperature is facilitated by a continuous time stochastic state space model identified for the heat dynamics of the greenhouse. A simulation study illustrates that the proposed GPC gives a more active controller with less control error than the implemented PID controller.

Quality assessment models for initial production process control based on stochastic differential equations

It is of great importance to assess an initial production process prior to the regular mass-production. For this purpose, many statistical methods have been proposed for practical use. In this paper, we propose two stochastic models for an assessment method of the initial production process control: a Markov process model and a Markov approximation model. These models are continuous state space models and formulated by applying mathematical techniques of stochastic differential equations. Based on each model, we derive several quantitative assessment measures for initial production process control.

A continuous state space model of multiple service, multiple resource communication networks

The merging of telephone and computer networks is introducing multiple resources into networks, and information is becoming increasingly distributed across the network. Related services are being integrated onto a single network rather than being offered on separate uncoordinated networks. We focus upon communication networks that integrate multiple services using multiple resources. In previous work, such networks have been modeled by multidimensional Markov chains with product form distributions. We approximate the distribution on the original discrete state space by a similar product form distribution on a continuous state space. We consider access control of such a system and prove that the resulting optimal coordinate-convex control policy is convex. Based on this result, we suggest an algorithm for ending a near-optimal policy for the discrete problem that has much less complexity than existing methods for finding optimal or near-optimal policies.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Determining the stability and realizability of a type of identified power system linear dynamic equivalent model

Abstract The linear multi-input multi-output dynamic equivalent system model for power system studies is often required to be stable and realizable. The stability and realizability may be checked after the continuous state space model has been obtained, but it will result in excessive computing time for model identification. This paper gives the conditions on the poles of an autoregression model for checking its stability and realizability. Along with the assumption of output decoupling, application of these conditions can greatly reduce the computing time for model identification.

Recent Advances in Longitudinal Methodology

It is common to all types of longitudinal data that one observes some social unit from at least two points in time. With such data several opportunities for analysis arise that are not present in cross-sectional data, for example, to study change processes and to account for unobserved variables in a more robust manner. There are many types of longitudinal data. I review some recent advances in analyzing two types: event histories and panel data. In Part I of this article I focus on seven recent advances in analyzing event history data: (i) techniques for dealing with unobserved explanatory variables, (ii) peculiarities of various sampling frames, (iii) time-aggregation bias, (iv) discrete time methods, (v) estimation procedures such as those based on Cox's partial likelihood, (vi) local hazard-rate models, and (vii) continuous state space models. In Part II of the article I focus on recent advances in analyzing panel data, with an emphasis on how panel data allows one better to take account of unobserved variables in the types of static relationships usually estimated with cross-sectional data.

An optimal control approach to dynamic routing in networks

This paper explores the application of optimal control theory to the problem of dynamic routing in networks. The approach derives from a continuous state space model for dynamic routing and an associated linear optimal control problem with linear state and control variable inequality constraints. The conceptual form of an algorithm is presented for finding a feedback solution to the optimal control problem when the inputs are assumed to be constant in time. The algorithm employs a combination of necessary conditions, dynamic programming, and linear programming to construct a set of convex polyhedral cones which cover the admissible state space with optimal controls. An implementable form of the algorithm, along with a simple example, is presented for a special class of single destination networks.

Some New Transformation Algorithms in the Identification of Continuous-Time Multivariable Systems Using Discrete Identification Methods

A procedure for the identification of linear continuous multivariable systems is shown which is based on a discrete identification method and suitable transformation algorithms. Both, the structural and the parametric identification are performed from samples of input and output data, and are based on the discrete input-output model. A new method for the deduction of a state-space model from the identified input-output model is proposed. The method is based on a recursive formula by which construction and inversion of the auxiliary matrix is avoided. The discrete state-space model is transformed into the continuous state-space model using methods based on the fundamental matrix logarithm and its approximations. Four different algorithms for computation of the matrix logarithm function are proposed. For the derivation of the control matrix and the transmission matrix, also four different approaches are shown: the step-invariant, the rampinvariant, the bilinear and the combined approach. The proposed procedure is very efficient when sequences of steps or rectangular pulses can be used as test functions in the identification procedure. If normal operating records of the plant are used, the method is less efficient. The applicability of the proposed procedure for systems simplification is also discussed. Finally, an application of this procedure to a simulated continuous process, using different transformation methods is given.