scholarly journals Controllability of Semilinear Systems with Multiple Variable Delays in Control

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1955
Author(s):  
Jerzy Klamka
Keyword(s):  
Control Systems ◽  
Time Variable ◽  
Multiple Time ◽  
Variable Delays ◽  
Finite Dimensional ◽  
Multiple Variable ◽  
Variable Point ◽  
Admissible Controls ◽  
Point Delays ◽  
Controllability Conditions

In the paper semilinear, finite-dimensional, control systems with multiple time variable point delays in admissible controls are considered. Using Rothe’s fixed-point theorem, sufficient controllability conditions are formulated. The results of the paper are generalization to many time variable delays in control, of the results published recently.

Controllability of dynamical systems. A survey

2013 ◽  
Vol 61 (2) ◽  
pp. 335-342 ◽  
Author(s):  
J. Klamka
Keyword(s):  
Dynamical Systems ◽  
Control Theory ◽  
Systems Theory ◽  
Control Systems ◽  
Canonical Form ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Dynamical Control ◽  
Time Invariant ◽  
Admissible Controls

Abstract The main objective of this article is to review the major progress that has been made on controllability of dynamical systems over the past number of years. Controllability is one of the fundamental concepts in the mathematical control theory. This is a qualitative property of dynamical control systems and is of particular importance in control theory. A systematic study of controllability was started at the beginning of sixties in the last century, when the theory of controllability based on the description in the form of state space for both time-invariant and time-varying linear control systems was worked out. Roughly speaking, controllability generally means, that it is possible to steer a dynamical control system from an arbitrary initial state to an arbitrary final state using the set of admissible controls. It should be mentioned, that in the literature there are many different definitions of controllability, which strongly depend on a class of dynamical control systems and on the other hand on the form of admissible controls. Controllability problems for different types of dynamical systems require the application of numerous mathematical concepts and methods taken directly from differential geometry, functional analysis, topology, matrix analysis and theory of ordinary and partial differential equations and theory of difference equations. In the paper we use mainly state-space models of dynamical systems, which provide a robust and universal method for studying controllability of various classes of systems. Controllability plays an essential role in the development of modern mathematical control theory. There are various important relationships between controllability, stability and stabilizability of linear both finite-dimensional and infinite-dimensional control systems. Controllability is also strongly related to the theory of realization and so called minimal realization and canonical forms for linear time-invariant control systems such as the Kalmam canonical form, the Jordan canonical form or the Luenberger canonical form. It should be mentioned, that for many dynamical systems there exists a formal duality between the concepts of controllability and observability. Moreover, controllability is strongly connected with the minimum energy control problem for many classes of linear finite dimensional, infinite dimensional dynamical systems, and delayed systems both deterministic and stochastic. Finally, it is well known, that controllability concept has many important applications not only in control theory and systems theory, but also in such areas as industrial and chemical process control, reactor control, control of electric bulk power systems, aerospce engineering and recently in quantum systems theory.

scholarly journals Fault Detection for Wireless Networked Control Systems with Stochastic Uncertainties and Multiple Time Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Lina Rong ◽  
Chengda Yu ◽  
Pengfei Guo ◽  
Hui Gao
Keyword(s):  
Fault Detection ◽  
Control Systems ◽  
Time Delays ◽  
Networked Control Systems ◽  
Networked Control ◽  
Linear Matrix ◽  
Multiple Time ◽  
Multiple Time Delays ◽  
System States ◽  
Stochastic Uncertainties

The fault detection problem for a class of wireless networked control systems is investigated. A Bernoulli distributed parameter is introduced in modeling the system dynamics; moreover, multiple time delays arising in the communication are taken into account. The detection observer for tracking the system states is designed, which generates both the state errors and the output errors. By adopting the linear matrix inequality method, a sufficient condition for the stability of wireless networked control systems with stochastic uncertainties and multiple time delays is proposed, and the gain of the fault detection observer is obtained. Finally, an illustrated example is provided to show that the observer designed in this paper tracks the system states well when there is no fault in the systems; however, when fault happens, the observer residual signal rises rapidly and the fault can be quickly detected, which demonstrate the effectiveness of the theoretical results.

Analysis of networked control systems with drops and variable delays

Automatica ◽  
2007 ◽  
Vol 43 (12) ◽  
pp. 2054-2059 ◽  
Author(s):  
Matías García-Rivera ◽  
Antonio Barreiro
Keyword(s):  
Control Systems ◽  
Networked Control Systems ◽  
Networked Control ◽  
Variable Delays

Chatter Stability Analysis of the Variable Speed Face-Milling Process

2000 ◽  
Vol 123 (4) ◽  
pp. 753-756 ◽  
Author(s):  
Sridhar Sastry, ◽  
Shiv G. Kapoor, ◽  
Richard E. DeVor, and ◽  
Geir E. Dullerud
Keyword(s):  
Discrete System ◽  
Milling Process ◽  
Face Milling ◽  
Solution Technique ◽  
Dimensional System ◽  
Multiple Time ◽  
Time Varying ◽  
Variable Speed ◽  
Finite Dimensional ◽  
Industrial Grade

In this study, a solution technique based on a discrete time approach is presented to the stability problem for the variable spindle speed face-milling process. The process dynamics are described by a set of differential-difference equations with time varying periodic coefficients and time delay. A finite difference scheme is used to discretize the system and model it as a linear time varying (LTV) system with multiple time delays. By considering all the states over one period of speed variation, the infinite dimensional periodic time-varying discrete system is converted to a finite dimensional time-varying discrete system. The eigenvalues of the state transition matrix of this finite dimensional system are then used to propose criteria for exponential stability. Predicted stability boundaries are compared with lobes generated by numerical time-domain simulations and experiments performed on an industrial grade variable speed face-milling testbed.

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