An optimal linear-quadratic digital tracker for analog neutral time-delay systems

^** Email: shtsai{at}mail.ncku.edu.tw In this paper, an optimal hybrid tracking control problem forcontinuous neutral time-delay systems is formulated and studied.An optimal linear integral quadratic cost function that hasa high-gain property is used for tracking control specification.Two interpolation methods are applied to directly convert theoriginal analog neutral time-delay system into an equivalentdigital retarded time-delay system, and meanwhile convert thecontinuous-time quadratic cost function into a discretized form.Then, an extended state vector is constructed for an associateextended discrete-time optimal control problem without timedelay. Using the standard discrete-time linear-quadratic optimalcontrol theory and an indirect digital redesign technique witha predictive feature, an effective digital tracker is designedfor the original analog neutral time-delay system. An exampleis finally given for illustrating the effectiveness of the newtracker design method.     

Fuzzy impulsive control of chaotic systems based on TS fuzzy model

Combining Takagi–Sugeno (TS) fuzzy model and impulsive control, a new approach to control chaotic systems, namely fuzzy impulsive control, is proposed in this paper. The rigorous stability analysis of the proposed method is given. The effectiveness of the approach is tested on Chua’s circuit, Chen’s system and Rössler’s system.     

Stability and chaos in a class of 2-dimensional spatiotemporal discrete systems

This paper is concerned with a class of 2-dimensional spatiotemporal discrete systems (2d spatiotemporal discrete systems), or 2-dimensional and 2-directional discrete systems (2d-2D discrete systems). Some sufficient conditions for this system to be stable and some illustrative examples for this system to be chaotic in the sense of Devaney and of Li-Yorke are derived and discussed.     

Multiple firing coherence resonances in excitatory and inhibitory coupled neurons

The impact of inhibitory and excitatory synapses in delay-coupled Hodgkin–Huxley neurons that are driven by noise is studied. If both synaptic types are used for coupling, appropriately tuned delays in the inhibition feedback induce multiple firing coherence resonances at sufficiently strong coupling strengths, thus giving rise to tongues of coherency in the corresponding delay-strength parameter plane. If only inhibitory synapses are used, however, appropriately tuned delays also give rise to multiresonant responses, yet the successive delays warranting an optimal coherence of excitations obey different relations with regards to the inherent time scales of neuronal dynamics. This leads to denser coherence resonance patterns in the delay-strength parameter plane. The robustness of these findings to the introduction of delay in the excitatory feedback, to noise, and to the number of coupled neurons is examined. Mechanisms underlying our observations are revealed, and it is suggested that the regularity of spiking across neuronal networks can be optimized in an unexpectedly rich variety of ways, depending on the type of coupling and the duration of delays.