A Method of Finding Discrete Controls for Switched Dynamical Systems by Applying Continued Fractions

2021 ◽  
Vol 24 (2) ◽  
pp. 175-183
Author(s):  
S. M. Khryashchev
Keyword(s):  
Control Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Continued Fractions ◽  
Control Method ◽  
Initial State ◽  
Final State ◽  
Control Goal ◽  
Controllability Of Systems ◽  
And Control

Control systems with a finite number of control settings are considered. It is assumed that any polysystem operates in continuous time and control switchings occur at some certain discrete time instants. A control goal is to transfer a polysystem from an initial state to a final state. Controllability of systems switched in discrete time is studied. Controls are constructed by using the theory of generalized multicomponent continued fractions and the congruences theory. Applications of the proposed control method to specific systems are discussed.

Intervention Time in Target-Oriented Chaos Control

2021 ◽  
Vol 31 (09) ◽  
pp. 2150134
Author(s):  
Juan Segura
Keyword(s):  
Discrete Time ◽  
Chaos Control ◽  
Control Method ◽  
Single Species ◽  
Positive Equilibrium ◽  
Population Stability ◽  
Determine Parameter ◽  
And Control ◽  
Parameter Values ◽  
Proportional Feedback

The timing of interventions plays a central role in managing and exploiting biological populations. However, few studies in the literature have addressed its effect on population stability. The Seno equation is a discrete-time equation that describes the dynamics of single-species populations harvested according to the proportional feedback method at any moment between two consecutive censuses. Here we study a discrete-time equation that generalizes the Seno equation by considering the management and exploitation of populations through the target-oriented chaos control method. We investigate the combined effect of timing, targeting, and control on population stability, focusing on global stability. We prove that high enough control values create a positive equilibrium that attracts all positive solutions. We also prove that it is possible to determine parameter values to stabilize the controlled populations at any preset population size. Finally, we investigate the parameter combinations for which the management and exploitation are optimized in different scenarios.

Markov chains and generalized continued fractions

1992 ◽  
Vol 29 (04) ◽  
pp. 838-849 ◽  
Author(s):  
Thomas Hanschke
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Wide Class ◽  
Stochastic Models ◽  
Continuous Time ◽  
Continued Fractions ◽  
Invariant Measures ◽  
Continuous Time Markov Chains ◽  
Generalized Continued Fractions

This paper deals with a class of discrete-time Markov chains for which the invariant measures can be expressed in terms of generalized continued fractions. The representation covers a wide class of stochastic models and is well suited for numerical applications. The results obtained can easily be extended to continuous-time Markov chains.

Harmony search optimization for robust pole assignment in union regions for synthesizing feedback control systems

2017 ◽  
Vol 40 (6) ◽  
pp. 1956-1969 ◽  
Author(s):  
Junchang Zhai ◽  
Liqun Gao ◽  
Steven Li
Keyword(s):  
Control Systems ◽  
Discrete Time ◽  
Continuous Time ◽  
Search Algorithm ◽  
Harmony Search ◽  
Pole Assignment ◽  
Harmony Search Algorithm ◽  
Time System ◽  
Feedback Control Systems ◽  
Time Systems

This paper is concerned with robust pole assignment optimization for synthesizing feedback control systems via state feedback or observer-based output feedback in specified union regions using the harmony search algorithm. By using exact pole placement theory and the harmony search algorithm, robust pole assignment for linear discrete-time systems or linear continuous-time systems in union regions can be converted into a global dynamical optimization problem. The robust measured indices are derived for robust union region stability constraints and a robust [Formula: see text] performance. For the nonlinear, robust measured indices, a set of dynamic poles and the corresponding feedback controllers can be obtained by global dynamic optimization based on the harmony search algorithm and the idea of robust exact pole assignment. One key merit of the proposed approach is that the radius or the position of the sub-regions can be arbitrarily specified according to the transient performance request. Furthermore, the eigenstructure of the closed-loop system matrix can be optimized with better robustness for the proposed approach. Finally, the simulation results for a discrete-time system and a continuous-time system demonstrate the effectiveness and superiority of the proposed method.

Discrete-time approximationsfor continuous-time Markoviancontrol systems

1984 ◽  
Vol 16 (1) ◽  
pp. 15-16
Author(s):  
A. Hordijk ◽  
F. A. Van Der Duyn Schouten
Keyword(s):  
Decision Theory ◽  
Discrete Time ◽  
Continuous Time ◽  
Time System ◽  
Time Approximation ◽  
Discrete Time Systems ◽  
Discrete Time Approximation ◽  
And Control ◽  
Time Systems ◽  
Continuous Time System

The method of discrete-time approximation is widespread in control and decision theory. However, little attention has been paid to the conditions on parameters and control under which the discrete-time systems come close to the continuous-time system.

Markov chains and generalized continued fractions

1992 ◽  
Vol 29 (4) ◽  
pp. 838-849 ◽  
Author(s):  
Thomas Hanschke
Keyword(s):  
Markov Chains ◽  
Discrete Time ◽  
Wide Class ◽  
Stochastic Models ◽  
Continuous Time ◽  
Continued Fractions ◽  
Invariant Measures ◽  
Continuous Time Markov Chains ◽  
Generalized Continued Fractions

This paper deals with a class of discrete-time Markov chains for which the invariant measures can be expressed in terms of generalized continued fractions. The representation covers a wide class of stochastic models and is well suited for numerical applications. The results obtained can easily be extended to continuous-time Markov chains.

Discrete-Time H2-Optimal Control for Hydraulic Position Control Systems

2007 ◽  
Author(s):  
Yang Lin ◽  
Yang Shi ◽  
Richard Burton
Keyword(s):  
Optimal Control ◽  
Control Systems ◽  
Discrete Time ◽  
Ad Hoc ◽  
Position Control ◽  
Experimental Studies ◽  
Design Procedure ◽  
Design Parameters ◽  
Practical Applications ◽  
And Control

Hydraulic position control systems play an important role in industrial automation. This paper explores the application of discrete-time H2-optimal control for a hydraulic position control system (HPCS). By minimizing the H2-norm of the system, the discrete-time robust H2-optimal control both stabilizes the plant and minimizes the root-mean-square of the servo position error simultaneously. The intuitive nature of this advanced approach helps to manage the selection of design parameters, whereas, classical methods provide less insight into strategies for parameter selection and control design. Additionally, the powerful ability to address disturbances and uncertainty in the robust H2-optimal design offers a more direct alternative to the ad hoc and iterative nature of classical methods for the hydraulic servo position system. Computer simulations illustrate the design procedure and the effectiveness of the proposed method. Experimental studies which employ the H2-optimal control on a hydraulic positioning system are also conducted and the results show that the method is suitable for practical applications.

Bandgap Structures of SH-Wave in a One-Dimensional Phononic Crystal with Viscoelastic Interfaces

2017 ◽  
Vol 09 (07) ◽  
pp. 1750102 ◽  
Author(s):  
Yuhang Li ◽  
Xiaoliang Zhou ◽  
Zuguang Bian ◽  
Yufeng Xing ◽  
Jizhou Song
Keyword(s):  
Periodic Structure ◽  
Phononic Crystal ◽  
Adhesive Layer ◽  
Phononic Crystals ◽  
Sh Wave ◽  
Initial State ◽  
Final State ◽  
One Dimensional ◽  
Adhesive Layers ◽  
And Control

Phononic crystal is an artificial periodic structure with the ability to regulate and control the wave propagation of particular frequencies and has been widely used in many applications. The adhesive layer bonding different constituents in the periodic structure of phononic crystals is usually a viscoelastic material, which has frequency-dependent material properties. In this paper, an analytical model based on the transfer matrix method is developed to study the bandgap structures of SH-wave (a shear wave with the propagation direction normal to the motion plane) in a one-dimensional phononic crystal consisting of two different elastic constituents bonded by the viscoelastic adhesive layer. The results show that the viscosity of the adhesive layer has a significant influence on the bandgap structure at the region of high frequency. The effects of various material parameters of the viscoelastic adhesive layer such as the relaxation time, the final-state modulus and the initial-state modulus are systematically studied. These results are very helpful in the practical design of phononic crystals involving the viscoelastic adhesive layers.

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