Sychronisation of Chua's Oscillator via the State Observer Technique

2003 ◽  
Vol 40 (1) ◽  
pp. 36-44
Author(s):  
Xiaogen Yin ◽  
Y. J. Cao
Keyword(s):  
Control Theory ◽  
Control Systems ◽  
Chaotic Dynamics ◽  
State Observer ◽  
Dynamical Behaviour ◽  
Simple Approach ◽  
Nonlinear Circuit ◽  
Third Order ◽  
Rich Variety ◽  
Chua’S Oscillator

Chua's oscillator is a simple autonomous third-order nonlinear circuit with a rich variety of dynamical behaviour. This paper presents a simple approach to synchronisation of Chua's oscillators using a state observer in control theory, which can be used as an interesting example for educational purposes in control systems, showing the students a simple way of coping with chaotic dynamics.

Control Theory and Decision Making in Organisations A Reconnaissance

1970 ◽  
Vol 3 (3) ◽  
pp. T46-T48 ◽  
Author(s):  
G. L. Mallen
Keyword(s):  
Control Theory ◽  
Control Systems ◽  
Decision Process ◽  
Transfer Functions ◽  
Social Systems ◽  
Simulation Methods ◽  
Industrial Dynamics ◽  
Simulation Approach ◽  
Decision Systems ◽  
Classical Control

Differences between the domains of application of classical control theory and applied cybernetics are examined. It is suggested that a unifying concept for the understanding of both simple mechanical control systems and complex social systems is that of the decision process. Simple decision systems are equated to those for which transfer functions can be specified. Complex systems demand a simulation approach. No prescriptive organisational control theory based on simulation methods yet exists but one is required and is seen to be emerging from such diverse fields as artificial intelligence and Industrial Dynamics.

scholarly journals Control solutions in mechatronics systems

2005 ◽  
Vol 18 (3) ◽  
pp. 379-394
Author(s):  
Radu-Emil Precup ◽  
Stefan Preitl
Keyword(s):  
Fuzzy Control ◽  
Control Systems ◽  
Third Order ◽  
Fuzzy Controllers ◽  
Real World Application ◽  
Conventional Solution ◽  
Extended Symmetrical Optimum Method ◽  
Theoretical Results ◽  
Iterative Feedback ◽  
Fuzzy Solutions

This paper presents control solutions dedicated to a class of controlled plants widely used in mechatronics systems, characterized by simplified mathematical models of second-order and third-order plus integral type. The conventional control solution is focused on the Extended Symmetrical Optimum method proposed by the authors in 1996. There are proposed six fuzzy control solutions employing PI-fuzzy controllers. These solutions are based on the approximate equivalence in certain conditions between fuzzy control systems and linear ones, on the application of the modal equivalence principle, and on the transfer of results from the continuous-time conventional solution to the fuzzy solutions via a discrete-time expression of the controller where Prof. Milic R. Stojic's book [1] is used. There is performed the sensitivity analysis of the fuzzy control systems with respect to the parametric variations of the controlled plant, which enables the development of the fuzzy controllers. In addition, the paper presents aspects concerning Iterative Feedback Tuning and Iterative Learning Control in the framework of fuzzy control systems. The theoretical results are validated by considering a real-world application.

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.

CPS Security

2015 ◽  
pp. 119-139
Keyword(s):  
Information Security ◽  
Control Theory ◽  
Control Systems ◽  
Distributed System ◽  
Cyber Physical Systems ◽  
Physical Systems ◽  
Secure Control ◽  
Structured Information ◽  
Specialized Experts ◽  
And Control

Information security can be efficiently provided by the sound structured information and a set of specialized experts in the field of IT and CPS. The interconnection among the systems in the CPS imposes a new challenge in providing security to CPS. A concise study of CPS security is given in this chapter. The problem of secure control systems is also indentified and defined. The way the information security and control theory guards the system is explored. The security of CPSs can be enhanced using a particular set of challenges, which are also described later in this chapter. The resistance to malicious events is strengthening as cyber physical systems are part of critical structures. The CPSs are time sensitive in nature, unlike the distributed system where a little amount of delay is acceptable.

Determination of Nonchaotic Behavior for Some Classes of Polynomial Jerk Equations

2020 ◽  
Vol 30 (08) ◽  
pp. 2050117
Author(s):  
Marcelo Messias ◽  
Rafael Paulino Silva
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Simple Form ◽  
Chaotic Dynamics ◽  
Third Order ◽  
Algebraic Criterion

In this work, by using an algebraic criterion presented by us in an earlier paper, we determine the conditions on the parameters in order to guarantee the nonchaotic behavior for some classes of nonlinear third-order ordinary differential equations of the form [Formula: see text] called jerk equations, where [Formula: see text] is a polynomial of degree [Formula: see text]. This kind of equation is often used in literature to study chaotic dynamics, due to its simple form and because it appears as mathematical model in several applied problems. Hence, it is an important matter to determine when it is chaotic and also nonchaotic. The results stated here, which are proved using the mentioned algebraic criterion, corroborate and extend some results already presented in literature, providing simpler proofs for the nonchaotic behavior of certain jerk equations. The algebraic criterion proved by us is quite general and can be used to study nonchaotic behavior of other types of ordinary differential equations.

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