Simulation studies on the design of optimum PID controllers to suppress chaotic oscillations in a family of Lorenz-like multi-wing attractors

Abstract

Abstract:Multi-wing chaotic attractors are highly complex nonlinear dynamical systems with higher number of index-2 equilibrium points. Due to the presence of several equilibrium points, randomness and hence the complexity of the state time series for these multi-wing chaotic systems is much higher than that of the conventional double-wing chaotic attractors. A real-coded Genetic Algorithm (GA) based global optimization framework has been adopted in this paper as a common template for designing optimum Proportional-Integral-Derivative (PID) controllers in order to control the state trajectories of four different multi-wing chaotic systems among the Lorenz family viz. Lu system, Chen system, Rucklidge (or Shimizu Morioka) system and Sprott-1 system. Robustness of the control scheme for different initial conditions of the multi-wing chaotic systems has also been shown.

Towards a global controller design for guaranteed synchronization of switched chaotic systems

“…Synchronize two identical unified chaotic systems with arbitrary switching in the key parameter α. iii. Synchronize both switched and non-switched variants for arbitrary initial conditions of the master and slave unlike [38], [39]. iv.…”

“…The other popular software package YALMIP [13] gives more flexibility in implementing the LMIs and hence is widely used in the control community. Simulation and optimization based optimal controller design has been previously investigated in Das et al [38] with a particular choice of initial conditions for establishing synchronization amongst two chaotic systems or the suppression of chaotic oscillation in highly complex systems [39], without the consideration of switching. But such synchronization is not theoretically guaranteed for all possible initial conditions.…”

Evolving chaos: Identifying new attractors of the generalised Lorenz family

“…Previous exploration reveals that simple structures of chaotic systems with only product nonlinearity (without an explicit transcendental term), as a natural successor of Lorenz family of attractors [6], [20]- [22], is capable of generating sufficiently complex chaotic motions in the phase space. The GP searches for new chaotic system state expressions while maximising the LLE obtained from time delay embedding of a single time series [23] as a candidate solution.…”

The Application of Zhang-Gradient Method for Iterative Learning Control

“…Recently, Zhang-gradient method has shown their powerful performance in solving online timevarying control problem (See [16][17][18][19][20]). The Zhang-gradient method is based on an indefinite errormonitoring function (See [20]), but the gradient dynamics method is usually designed from a norm or square-based energy function.…”