scholarly journals Parameter and State Estimator for State Space Models

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Ruifeng Ding ◽  
Linfan Zhuang
Keyword(s):  
State Space ◽  
State Equation ◽  
The State ◽  
Parameter Estimates ◽  
Identification Algorithm ◽  
State Variables ◽  
Input Output ◽  
State Estimator ◽  
Output Data ◽  
Canonical State

This paper proposes a parameter and state estimator for canonical state space systems from measured input-output data. The key is to solve the system state from the state equation and to substitute it into the output equation, eliminating the state variables, and the resulting equation contains only the system inputs and outputs, and to derive a least squares parameter identification algorithm. Furthermore, the system states are computed from the estimated parameters and the input-output data. Convergence analysis using the martingale convergence theorem indicates that the parameter estimates converge to their true values. Finally, an illustrative example is provided to show that the proposed algorithm is effective.

Non Linear State and Parameters Estimation in Chemical Processes: Analysis and Improvement of Three Estimation Structures Applied to a CSTR

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Héctor Botero ◽  
Hernán Álvarez
Keyword(s):  
Parameter Estimation ◽  
Chemical Process ◽  
Chemical Processes ◽  
The State ◽  
Convergence Speed ◽  
Parameters Estimation ◽  
State Variables ◽  
Input Output ◽  
On Line ◽  
Linear State

This paper proposes a new composite observer capable of estimating the states and unknown (or changing) parameters of a chemical process, using some input-output measurements, the phenomenological based model and other available knowledge about the process. The proposed composite observer contains a classic observer (CO) to estimate the state variables, an observer-based estimator (OBE) to obtain the actual values of the unknown or changing parameters needed to tune the CO, and an asymptotic observer (AO) to estimate the states needed as input to the OBE. The proposed structure was applied to a CSTR model with three state variables. With the proposed structure, the concentration of reactants and other CSTR parameters can be estimated on-line if the reactor and jacket temperatures are known. The procedure for the design of the proposed structure is simple and guarantees observer convergence. In addition, the convergence speed of state and parameter estimation can be adjusted independently.

Stability analysis of continuous-time linear systems consisting of n subsystems with different fractional orders

2012 ◽  
Vol 60 (2) ◽  
pp. 279-284 ◽  
Author(s):  
M. Busłowicz
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
State Equation ◽  
The State ◽  
Natural Order ◽  
State Variables ◽  
The Stability ◽  
Derivatives Of ◽  
Fractional Orders ◽  
Time Linear

Abstract. The stability problem of continuous-time linear systems described by the state equation consisting of n subsystems with different fractional orders of derivatives of the state variables has been considered. The methods for asymptotic stability checking have been given. The method proposed in the general case is based on the Argument Principle and it is similar to the modified Mikhailov stability criterion known from the stability theory of natural order systems. The considerations are illustrated by numerical examples.

scholarly journals A Stochastic and State Space Model for Tumour Growth and Applications

2009 ◽  
Vol 10 (2) ◽  
pp. 117-138 ◽  
Author(s):  
Wai-Yuan Tan ◽  
Weiming Ke ◽  
G. Webb
Keyword(s):  
State Space ◽  
Stochastic System ◽  
Tumour Growth ◽  
Deterministic Model ◽  
State Space Model ◽  
Tumour Cells ◽  
The State ◽  
System Model ◽  
State Variables ◽  
Space Model

We develop a state space model documenting Gompertz behaviour of tumour growth. The state space model consists of two sub-models: a stochastic system model that is an extension of the deterministic model proposed by Gyllenberg and Webb (1991), and an observation model that is a statistical model based on data for the total number of tumour cells over time. In the stochastic system model we derive through stochastic equations the probability distributions of the numbers of different types of tumour cells. Combining with the statistic model, we use these distribution results to develop a generalized Bayesian method and a Gibbs sampling procedure to estimate the unknown parameters and to predict the state variables (number of tumour cells). We apply these models and methods to real data and to computer simulated data to illustrate the usefulness of the models, the methods, and the procedures.

Short-Term Oil Price Forecasting Based on State Space Model

2011 ◽  
Vol 403-408 ◽  
pp. 2530-2534
Author(s):  
Wei Qi Li ◽  
Lin Wei Ma ◽  
Ya Ping Dai ◽  
Dong Hai Li
Keyword(s):  
State Space ◽  
Likelihood Function ◽  
State Space Model ◽  
The State ◽  
Oil Price ◽  
Filter Method ◽  
Parameter Estimates ◽  
Price Forecasting ◽  
Short Term ◽  
Space Model

In competitive petroleum markets, oil price forecasting has always been an important strategic tool for oil producers and consumers to predict market behavior. In this study, we researched the monthly crude oil price in the period between 1988 and 2009. Firstly, we present a state space model to represent oil price system. Secondly, we determine the parameter estimates of the state space model for oil price through a faster algorithm to compute the likelihood function. Lastly, we use the Kalman filter method to estimate the next three months’ oil price and compare it with the econometric structure model as a benchmark. Empirical results indicate that the state space model performs well in terms of some standard statistics indices, and it may be a promising method for short-term oil price forecasting.

scholarly journals Hysteresis-Based Current Control Approach by Means of the Theory of Switched Systems

2021 ◽  
Vol 11 (19) ◽  
pp. 9175
Author(s):  
Malte Thielmann ◽  
Florian Hans
Keyword(s):  
State Space ◽  
Switched Systems ◽  
Multiple Equilibria ◽  
Current Control ◽  
The State ◽  
Voltage Source ◽  
Voltage Source Converter ◽  
Reference Trajectory ◽  
State Variables ◽  
Control Approach

In this paper, a novel hysteresis-based current control approach is presented. The basis of the developed control approach is the theory of switched systems, in particular, the system class of switched systems with multiple equilibria. The proposed approach guarantees the convergence of the state trajectory into a region around a reference trajectory by selective switching between the individual subsystems. Here, the reference trajectory is allowed to be time varying, but lies within the state space spanned by the subsystem equilibria. Since already published approaches only show convergence to a common equilibrium of all subsystems, the extension to the mentioned state space is a significant novelty. Moreover, the approach is not limited to the number of state variables, nor to the number of subsystems. Thus, the applicability to a large number of systems is given. In the course of the paper, the theoretical basics of the approach are first explained by referring to a trivial example system. Then, it is shown how the theory can be applied to a practical application of a voltage source converter that is connected to a permanent-magnet synchronous motor. After deriving the limits of the presented control strategy, a simulation study confirms the applicability on the converter system. The paper closes with a detailed discussion about the given results.

scholarly journals Noise control with Kalman filter for active headrest

2021 ◽  
Vol 39 (5) ◽  
pp. 937-944
Author(s):  
Lei WANG ◽  
Kean CHEN ◽  
Jian XU ◽  
Wang QI
Keyword(s):  
Kalman Filter ◽  
Noise Control ◽  
Active Noise Control ◽  
Noise Signal ◽  
State Equation ◽  
The State ◽  
Convergence Speed ◽  
State Variables ◽  
Gradient Based ◽  
Convergence Performance

A control strategy with Kalman filter (KF) is proposed for active noise control of virtual error signal for active headset. Comparing with the gradient based algorithm, KF algorithm has faster convergence speed and better convergence performance. In this paper, the state equation of the system is established on the basis of virtual error sensing, and only the weight coefficients of the control filter are considered in the state variables. In order to ensure the convergence performance of the algorithm, an online updating strategy of KF parameters is proposed. The fast-array method is also introduced into the algorithm to reduce the computation. The simulation results show that the present strategy can improve the convergence speed and effectively reduce the noise signal at the virtual error point.

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