Adaptive control in nonlinear dynamics

Sinha, Sudeshna; Ramaswamy, Ramakrishna; Rao, J. Subba

doi:10.1016/0167-2789(90)90020-p

Cited by 144 publications

(45 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Over the last few decades the control of both periodic and chaotic oscillations in dynamical systems and the stabilization of unstable dynamics have been topics of intense research interest from both theoretical and experimental points of view [87,94,95,96,97,98]. Several existing methods [94,95,96,99,100] stabilize fixed points by changing accessible internal parameters of a given system.…”

Section: Targeting and Controlmentioning

confidence: 99%

See 1 more Smart Citation

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

View full text Add to dashboard Cite

When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete suppression of oscillations, formally termed amplitude death (AD). Oscillations of the entire system cease as a consequence of the interaction, leading to stationary behavior. The fixed points that the coupling stabilizes can be the otherwise unstable fixed points of the uncoupled system or can correspond to novel stationary points. Such behaviour is of relevance in areas ranging from laser physics to the dynamics of biological systems. In this review we discuss the characteristics of the different coupling strategies and scenarios that lead to AD in a variety of different situations, and draw attention to several open issues and challenging problems for further study.

show abstract

Section: Targeting and Controlmentioning

confidence: 99%

“…Several existing methods [94,95,96,99,100] stabilize fixed points by changing accessible internal parameters of a given system. In many natural systems, internal parameters are typically not accessible or at any rate cannot be tuned.…”

Section: Targeting and Controlmentioning

confidence: 99%

Amplitude death: The emergence of stationarity in coupled nonlinear systems

2012

View full text Add to dashboard Cite

show abstract

“…Sinha [5] extended the adaptive algorithm of literature [4] to multiple parameters and high dimensional nonlinear systems. In the condition of the dynamic behavior changes caused by a sudden disturbance of system parameters suffered, the adaptive control algorithm [6] proposed by Sinha for the perturbed system restoring to the initial dynamic behavior is significantly effective, and that in any case, recovery time and control stiffness into the results of linear inverse relationship (in terms of weak stiffness), effectively control system to the equilibrium point or limit cycle state. But the above two methods are not suitable to control the movement state of the system to an unstable orbit, and the size of the control stiffness is not easy to determine, the range of the initial value of the disturbed parameters is also limited.…”

Section: Control Theory Of Chaotic Motionmentioning

confidence: 99%

“…But the above two methods are not suitable to control the movement state of the system to an unstable orbit, and the size of the control stiffness is not easy to determine, the range of the initial value of the disturbed parameters is also limited. Based on the literature [5,6], a parameter adaptive control algorithm based on reference model is proposed by Vassiliadis [7], a discrete deterministic nonlinear dynamic system model is established. The control forms of the parameters adaptive are presented, and the coupling style between the system and the model is considered.…”

Section: Control Theory Of Chaotic Motionmentioning

confidence: 99%

Research on the adaptive control method with continuous feedback parameters for controlling of chaotic motion

Wu¹

2015

Proceedings of the 4th International Conference on Mechatronics, Materials, Chemistry and Computer Engineering 2015

View full text Add to dashboard Cite

Abstract. Although the feed system of CNC machine tool is a certain dynamic system, the chaotic motion often occurs because of the function of the nonlinear factors.The dynamic model of the feed system with nonlinear spring force and nonlinear friction force is numerically simulated by using the adaptive control method with continuous feedback parameters. It can be seen that when the system is in chaotic vibration state, the adaptive feedback control is applied, and the different target orbital period are given，that is the different time delay values τ .With the adjustment of the intensity of the control signalσ , the chaotic vibration can be entered into the quasi periodic state in a short time.

show abstract

“…To solve the problem introduce the error equations subtracting (18) from (17) el = e2 e2 = -plel -e: -pe2 + ( q -qm) cos wt -3~1 2 1~e 1 + 'U (20) where el = X I -xlm and e2 = 2 2 -~2~. According to the design procedure of the previous section assume that the value of parameter q is known.…”

Section: = U ( Y F ? T )mentioning

confidence: 99%