DESIGN OF THE STATE OBSERVER WITH D-STABILITY FOR UNCERTAIN SYMMETRIC CIRCULANT COMPOSITE SYSTEMS

2005 ◽  
Vol 08 (02n03) ◽  
pp. 193-208
Author(s):  
MAN LIU ◽  
YOU ZHANG ◽  
YUAN-WEI JING ◽  
SI-YING ZHANG
Keyword(s):  
Uncertain Systems ◽  
Composite System ◽  
Uncertain System ◽  
Original System ◽  
State Observer ◽  
Pole Assignment ◽  
The State ◽  
Special Structure ◽  
Composite Systems ◽  
Decentralized Observer

The design of the state observer for a kind of uncertain symmetric circulant composite systems based on regional pole assignment is studied. The "decentralized observer gain matrices" have been obtained by taking use of the special structure of the system. The central observer gain matrix for such a system has the same block symmetric circulant structure as the original system and can be constructed by the "decentralized observer gain matrices." Thus, the problem of designing state observer for such an uncertain system with n·N dimensions based on regional pole assignment can be transformed into the subproblems for N/2+1 or (N + 1)/2 uncertain systems with n dimensions. The central D-stabilizable state observer is also a symmetric circulant composite system. And the design of the observer makes best use of the advantage of interconnections of the system.

The Analysis and Synthesis of Vibrating Systems

1954 ◽  
Vol 58 (526) ◽  
pp. 703-719 ◽  
Author(s):  
R. E. D. Bishop
Keyword(s):  
Composite System ◽  
Frequency Equation ◽  
Computational Effort ◽  
Analytical Treatment ◽  
Principal Mode ◽  
Oscillatory Systems ◽  
Composite Systems ◽  
Analysis And Synthesis ◽  
Simple Systems ◽  
Vibrating Systems

SummaryComplicated oscillatory systems may be broken down into component “ sub-systems ” for the purpose of vibration analysis. These will generally submit more readily to analytical treatment. After an introduction to the concept of receptance, the principles underlying this form of analysis are reviewed.The dynamical properties of simple systems (in the form of their receptances) may be tabulated. By this means the properties of a complicated system may be found by first analysing it into convenient sub-systems and then extracting the properties of the latter from a suitable table. A catalogue of this sort is given for the particular case of conservative torsional systems with finite freedom.The properties of the composite system which may be readily found in this way are (i) its receptances and (ii) its frequency equation. Tables are given of expressions for these in terms of the receptances of the component sub-systems. All of the tables may easily be extended. The tabulated receptances may also be used for determining relative displacements during free vibration in any principal mode.A method of presenting information on the vibration characteristics of machinery, which is effectively due to Carter, is illustrated by means of an example. More general adoption by manufacturers of this method (which requires no more computational effort than must normally be made) would lead to enormous savings of labour in calculating natural frequencies of composite systems.

scholarly journals A Control Approach Based on Observers of State and Uncertainty for a Class of Takagi–Sugeno Fuzzy Models

2021 ◽  
Vol 25 (3) ◽  
pp. 317-325
Author(s):  
Jun Zhao ◽  
Hugang Han ◽  
◽  
Keyword(s):  
Control System ◽  
Control Systems ◽  
Fuzzy Model ◽  
State Observer ◽  
The State ◽  
State Information ◽  
Control Approach ◽  
Fuzzy Models ◽  
Takagi Sugeno ◽  
Stable Control

Although the Takagi–Sugeno fuzzy model is effective for representing the dynamics of a plant to be controlled, two main questions arise when using it just as other models: 1) how to deal with the gap, which is referred to as uncertainty in this study, between the model and the concerned plant, and how to estimate the state information when it cannot be obtained directly, especially with the existence of uncertainty; 2) how to design a controller that guarantees a stable control system where only the estimated state is available and an uncertainty exists. While the existing studies cannot effectively observe the state and the resulting control systems can only be managed to be uniformly stable, this study first presents a state observer capable of precisely estimating the state regardless of the existence of uncertainty. Then, based on the state observer, an uncertainty observer is derived, which can track the trajectory of uncertainty whenever it occurs in a real system. Finally, a controller based on both observers is presented, which guarantees the asymptotic stability of the resulting control system.

A New Algorithm for Computing the Ergodic Probability Vector for Large Markov Chains

1990 ◽  
Vol 4 (1) ◽  
pp. 89-116 ◽  
Author(s):  
Ushlo Sumita ◽  
Maria Rieders
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
State Space ◽  
The State ◽  
Special Structure ◽  
Probability Vector ◽  
Rank Reduction ◽  
Replacement Process ◽  
Novel Algorithm

A novel algorithm is developed which computes the ergodic probability vector for large Markov chains. Decomposing the state space into lumps, the algorithm generates a replacement process on each lump, where any exit from a lump is instantaneously replaced at some state in that lump. The replacement distributions are constructed recursively in such a way that, in the limit, the ergodic probability vector for a replacement process on one lump will be proportional to the ergodic probability vector of the original Markov chain restricted to that lump. Inverse matrices computed in the algorithm are of size (M – 1), where M is the number of lumps, thereby providing a substantial rank reduction. When a special structure is present, the procedure for generating the replacement distributions can be simplified. The relevance of the new algorithm to the aggregation-disaggregation algorithm of Takahashi [29] is also discussed.

scholarly journals Selective Finite Memory Structure Filtering Using the Chi-Square Test Statistic for Temporarily Uncertain Systems

2019 ◽  
Vol 9 (20) ◽  
pp. 4257 ◽  
Author(s):  
Pyung Soo Kim
Keyword(s):  
Uncertain Systems ◽  
Estimation Error ◽  
Uncertain System ◽  
Aircraft Engine ◽  
Memory Structure ◽  
Conditional Density ◽  
Test Statistic ◽  
Chi Square ◽  
Chi Square Test ◽  
Finite Memory

In this paper, a finite memory structure (FMS) filtering with two kinds of measurement windows is proposed using the chi-square test statistic to cover nominal systems as well as temporarily uncertain systems. First, the simple matrix form for the FMS filter is developed from the conditional density of the current state given finite past measurements. Then, one of the two FMS filters, the primary FMS filter or the secondary FMS filter, with different measurement windows is operated selectively according to the presence or absence of uncertainty, to obtain a valid estimate. The primary FMS filter is selected for the nominal system and the secondary FMS filter is selected for the temporarily uncertain system, respectively. A declaration rule is defined to indicate the presence or absence of uncertainty, operate the suitable one from two filters, and then obtain the valid filtered estimate. A test variable for the declaration rule is developed using a chi-square test statistic from the estimation error and compared to a precomputed threshold. In order to verify the proposed selective FMS filtering and compare with the existing FMS filter and the infinite memory structure (IMS) filter, computer simulations are performed for a selection of dynamic systems including a F404 gas turbine aircraft engine and an electric motor. Simulation results confirm that the proposed selective FMS filtering works well for nominal systems as well as temporarily uncertain systems. In addition, the proposed selective FMS filtering is shown to be remarkably better than the IMS filtering for the temporarily uncertain system.

scholarly journals Structural Balance Control of Complex Dynamical Networks Based on State Observer for Dynamic Connection Relationships

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Zilin Gao ◽  
Yinhe Wang ◽  
Jiang Xiong ◽  
Yong Pan ◽  
Yuanyuan Huang
Keyword(s):  
Balance Control ◽  
Lyapunov Stability Theory ◽  
State Observer ◽  
The State ◽  
Complex Dynamical Networks ◽  
Complex Dynamical Network ◽  
Dynamical Networks ◽  
Structural Balance ◽  
Practical Applications ◽  
Coupled Subsystems

This paper investigates the observer-based structural balance control for a class of complex dynamical networks. Generally speaking, a complete complex dynamical network is composed of two coupled subsystems, which are called node subsystem (NS) and connection relationship subsystem (CS), respectively. Similar to synchronization and stabilization of networks, the structural balance is another phenomenon of networks and determined by the state of connection relationships. However, it is not feasible to design the controller for the CS directly because the states of the connection relationships are difficult to be measured accurately in practical applications. In order to solve this problem, a state observer for the CS has been designed. Thus, the structural balance controller in the CS can be directly designed by using the estimation information of the state observer. Then, with the help of the Lyapunov stability theory, it is proved that the CS can asymptotically track a given structural balance matrix under the influence of the observer-based controller. Finally, the results derived from this paper are demonstrated by performing a numerical example.

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