Optimal State Filter Research Articles

Optimal state filters for networked iterative learning control systems with data losses and noises

SummaryData losses and noises in both forward and feedback channels significantly impact the convergence of networked iterative learning control (ILC) systems. To address this issue, this article considers a class of linear time‐invariant objects controlled by proportional ILC controllers, an optimal state filter is then designed at the ILC controller side that aims to guarantee the convergence of the input transmitted by ILC controllers. First, two data transmission processes are introduced to account for the effects of data losses and noises. Second, a filtering model is established utilizing only the object information and the aforementioned data transmission processes. Third, the optimal state filter is designed on the basis of the orthogonal projection principle. This filtered state facilitates the acquisition of actual output errors, thus improving the convergence of the input transmitted by ILC controllers. Simulation results demonstrate the effectiveness of the proposed state filters.

Optimal state filter from sequential unknown input reconstruction: Application to distributed state filtering

SummaryThis paper generalizes Kalman filtering with an intermittent unknown input problem to be left invertible discrete‐time stochastic linear systems with zero, one, or more structural delays. Contrary to the state filtering–based system inversion where the unknown input vector is reconstructed with a time delay that is equal to the structural delay of the plant, we propose an optimal state filtering by reconstructing some linear combinations of the unknown input vector with a time delay less than the structural delay. Designed under a sequential unknown input decoupling constraint, which has never been previously studied in the literature, all presented filters are very computationally efficient. The proposed state filtering is used to solve the autonomous distributed state filtering problem in large‐scale networked control systems when the unknown input vector represents interactions between subsystems and when each subsystem receives intermittent information about the interaction from unreliable networks. The stochastic stability conditions of the extended intermittent unknown input Kalman filter are established when the arrival binary sequence of packet dropouts follows a random Bernoulli process.

Optimal mean-square state and parameter estimation for stochastic linear systems with Poisson noises

This paper presents the mean-square state and parameter estimation problem for stochastic linear systems with unknown multiplicative and additive parameters over linear observations, where unknown parameters are considered Poisson processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. The obtained optimal filter for the extended state vector also serves as the optimal identifier for the unknown parameters. Performance of the designed optimal state filter and parameter identifier is verified for both, stable and unstable, stochastic linear systems and compared against the mean-square estimator designed for polynomial systems with white Gaussian noises.

A framework for globally optimal state estimation for systems with unknown inputs (I): transformation approach

In this paper, a globally optimal state estimation is addressed in light of the conventional Luenberger observer-type filter. This paper is the first part of a comprehensive extension of an original work by Hsieh, with the main aim being to develop a transformation-based filtering framework for global unbiased minimum-variance state estimation (GUMVSE) for systems with unknown inputs that affect both the system and the output. The main contributions of this paper are (i) a complete optimal solution for the GUMVSE is addressed, where both the globally optimal state filter and predictor are presented, and (ii) additional insights for implementing the globally optimal state filter are highlighted via the proposed decorrelation constraint. Compared with existing results, the proposed globally optimal filter has the most general filter form among all transformation-based globally optimal filters in the sense that it does not use any specific unknown input transformation matrix in the derivation. A simulation example is given to illustrate the usefulness of the proposed results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society

Optimal filtering over linear observations with unknown parameters

This paper presents the optimal filtering and parameter identification problem for linear stochastic systems over linear observations with unknown parameters, where the unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. The resulting filtering system is bilinear in state and linear in observations. The obtained optimal filter for the extended state vector also serves as the optimal identifier for the unknown parameters. Performance of the designed optimal state filter and parameter identifier is verified for both, positive and negative, parameter values.

Optimal State Filtering and Parameter Identification for Linear Stochastic Time-Delay Systems

This paper presents the optimal joint state filtering and parameter identification problem for linear stochastic time-delay systems with unknown parameters. The original identification problem is reduced to the optimal filtering problem for incompletely measured polynomial (bilinear) time-delay system states over linear observations with an arbitrary, not necessarily invertible, observation matrix, where the unknown parameters are considered standard Wiener processes and incorporated as additional states in the extended state vector. The obtained solution is based on the designed optimal filter for incompletely measured bilinear time-delay states over linear observations, taking into account that the optimal filter for the extended state vector also serves as the optimal identifier for the unknown parameters. In the example, performance of the designed optimal state filter and parameter identifier is verified for a linear time-delay system with an unknown multiplicative parameter over linear observations. Both, stable and unstable, linear systems are examined.

Optimal state filtering and parameter identification for linear systems

AbstractThis paper presents the optimal filtering and parameter identification problem for linear stochastic systems with unknown multiplicative and additive parameters over linear observations, where unknown parameters are considered Wiener processes. The original problem is reduced to the filtering problem for an extended state vector that incorporates parameters as additional states. The obtained optimal filter for the extended state vector also serves as the optimal identifier for the unknown parameters. Performance of the designed optimal state filter and parameter identifier is verified for both stable and unstable linear uncertain systems. Copyright © 2007 John Wiley & Sons, Ltd.

Optimal state filtering of controllable systems with random structure

The problem of optimal filtering in stochastic differential systems with random structure whose switches are generated by a special class of Markov jump processes is considered. The equations of the conditional expectation and conditional probability density function of the signal process are obtained. Numerical methods for solving the corresponding analogues of the Fokker-Planck-Kolmogorov and Zakai equations are proposed.