scholarly journals Approximate Prediction-Based Control Method for Nonlinear Oscillatory Systems with Applications to Chaotic Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-21
Author(s):  
Thiago P. Chagas ◽  
Pierre-Alexandre Bliman ◽  
Karl H. Kienitz
Keyword(s):  
Continuous Time ◽  
Control Method ◽  
Nonlinear Dynamical Systems ◽  
System Response ◽  
Free System ◽  
Nonlinear Dynamical ◽  
Oscillatory Systems ◽  
Continuous Time Systems ◽  
Estimation Precision ◽  
Time Systems

The approximate Prediction-Based Control method (aPBC) is the continuous-time version of the well-known Prediction-Based Chaos Control method applied to stabilize periodic orbits of nonlinear dynamical systems. The method is based on estimating future states of the free system response of continuous-time systems using the solution from the Runge-Kutta implicit method in real time. Some aspects of aPBC are evaluated in the present work, particularly its robustness to low future states estimation precision is exemplified.

DESIGNING HOPF BIFURCATIONS INTO NONLINEAR DISCRETE-TIME SYSTEMS VIA FEEDBACK CONTROL

2004 ◽  
Vol 14 (07) ◽  
pp. 2283-2293 ◽  
Author(s):  
GUILIN WEN ◽  
DAOLIN XU
Keyword(s):  
Feedback Control ◽  
Center Manifold ◽  
Control Method ◽  
Nonlinear Dynamical Systems ◽  
Critical Conditions ◽  
Hopf Bifurcations ◽  
Control Law ◽  
Nonlinear Dynamical ◽  
Weak Resonance ◽  
Time Systems

Hopf bifurcations lead to limit circles that exhibit oscillatory behaviors in nonlinear dynamical systems. Building a specified limit circle into nonlinear systems by control enables us to achieve preferred dynamical performance in the systems. This paper reports a general control method for generating a variety of specified Hopf bifurcations at a desired parameter location. The proposed control law is applicable to nonresonance, weak resonance, strong resonance, or degenerate cases. It allows us to flexibly operate and manipulate the control of Hopf bifurcations. The discrete washout filters are used for the feedback controller. The feedback control gains are derived from the critical conditions and stability conditions of Hopf bifurcations by means of the center manifold method and normal form technique. Numerical experiments indicate that the control method is effective.

Mixed Method of Routh and ISE Criterion Approaches for Reduced-Order Modeling of Continuous-Time Systems

1984 ◽  
Vol 106 (4) ◽  
pp. 353-356 ◽  
Author(s):  
Chyi Hwang
Keyword(s):  
Mixed Method ◽  
Continuous Time ◽  
Reduced Order Model ◽  
System Response ◽  
Order Model ◽  
Reduced Order ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Continuous Time Systems ◽  
Time Systems

A mixed method using the advantages of Routh approximation method and integral-squared-error criterion is proposed for obtaining stable reduced-order models for high-order continuous-time systems. The reduced-order model tends to approximate the transient portion of the system response in the sense of minimum mean-squared-error, while the steady-state portion is matched exactly. Instead of actually evaluating time responses of the system and the reduced-order model, a matrix formula is used to calculate the integral-squared-error from the error transfer function.

scholarly journals Application of the Preview Control Method to the Optimal Tracking Control Problem for Continuous-Time Systems with Time-Delay

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Fucheng Liao ◽  
Haishan Xu
Keyword(s):  
Time Delay ◽  
Control Problem ◽  
Continuous Time ◽  
Tracking Control ◽  
Control Method ◽  
Reference Signal ◽  
Preview Control ◽  
Optimal Tracking ◽  
Continuous Time Systems ◽  
Time Systems

This paper considers the application of the preview control method to the optimal tracking control problem for a class of continuous-time systems with state and input delays. First, through a transformation, the system is transformed into a nondelayed one. Then, the tracking problem of the time-delay system is transformed into one of a nondelayed system via processing of the reference signal. We then apply preview control theory to derive an augmented system for the nondelayed system and design a controller with preview function assuming that the reference signal is previewable. Finally, we obtain the optimal control law of the augmented error system and thus obtain that of the original system by letting the preview length of the reference signal go to zero. Numerical simulations are provided to illustrate the effectiveness and validity of our conclusions.

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