Decentralized Fuzzy Control of Nonlinear Interconnected Dynamic Delay Systems via Mixed $H_2/\!H_\infty$ Optimization With Smith Predictor

Each subsystem of a nonlinear interconnected dynamic delayed system is approximated by a weighted combination of L transfer function delayed systems (TFDSs). The H
₂
-norm of the difference between the transfer function of a reference model and the closed-loop transfer function of the kth TFDS of subsystem i is then minimized to obtain a suitable frequency response without incurring oscillating and sluggish phenomena. Because of the existence of the disturbance at the output of the kth TFDS, which is not only large but also contains various frequency components, the H
_∞
-norm of the weighted sensitivity function between the output disturbance and its corresponding output of the kth TFDS is simultaneously minimized to reduce its effect. Furthermore, with proper selection of weighted sensitivity functions, certain specific modes of the output disturbance can be eliminated. Finally, two simulations are performed; one is the simulation of our designed TFDSs with different delays or nonminimum phases, and the other is the simulation of an internet-based intelligent space for the trajectory tracking of a car-like wheeled robot system. We demonstrate the effectiveness and efficiency of the proposed control. The main contributions of this paper are twofold. First, the control can simultaneously attain robust performance through the mixed H
₂
/H
_∞
optimization with a Smith predictor and achieve the robust stability via L
₂
^N
stable with finite gain. Second, fuzzy observer is not needed.