Lifted Digital Redesign of Prediction-Based Digital Controller for Hybrid Chaotic System

Abstract

Tracking a periodic orbit of a chaotic attractor has been a considerable challenge since it often encounters numerical sensitivity. In this paper, a lifted prediction-based low-gain digital controller obtained from a predesigned high-gain analog controller is developed and applied to the hybrid chaotic system. The new proposed digital tracker with a relatively longer sampling time is insensitive to numerical errors and performs better than the one developed via the existing prediction-based digital redesign method. The Chen and Chua attractors are used as illustrative examples to demonstrate the effectiveness of the proposed lifted digital redesign method.

Realization of causal current output-based optimal full/reducedorder observer and tracker for the linear sampled-data system with a direct transmission term

“…Ignoring these limitations will result in an undesirable performance in the form of large overshoot or long setting time or even unstable processing; (v) direct digital design of discrete‐time and sampled‐data controllers for a multivariable continuous‐time system with an existing well‐performed analog controller may encounter difficulties in determining the sampling period and hybrid control specifications for the multivariable continuous‐time system to be designed. For example, the inter‐sampling behavior, that is, the state matching of the digitally controlled sampled‐data system and the theoretically well‐designed continuous‐time system at any instant between each relatively long sampling period, is not considered ; and (vi) some well‐designed methodologies for the continuous‐time system cannot or extremely difficult to be directly extended to the digital design of discrete‐time system. For example, without solving the eigenvalues and eigenvectors of the system matrix, the multistage continuous‐time optimal pole‐placement design to optimally move the poles outside the sector region (hatched) in Figure (a) in the s‐plane to the desired hatched sector and keep those original poles of the open‐loop system lie within the sector invariant cannot be directly extended in the digital control case for the corresponding common region of a circle and a logarithmic spiral in the z‐plane (hatched in Figure (b)).…”