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On the effects of time-delay on precision degradation in fixed point transformation-based adaptive control

Time delay effects frequently occur in remote control when the signals of observation “travel” from the location of the sensor to that of the controller and the control commands “propagate” from the controller to the drives and/or effectors. Another frequent reason for working with time-delay is the computational time needed by the digital controllers whenever the solution of a continuous control task is realized (and necessarily approximated) by digital controllers operating with discrete time resolution. In several cases the information so travels in the form of “packages” along some communication network that the various packages may have different traveling time and the delay cannot be precisely estimated. In other cases the time need of the signal propagation can be known in advance. Both the traditional model-based controllers as well as the adaptive controllers designed for strongly nonlinear systems the use of the Lyapunov function-based approach is a prevailing technique. It has been extended to time-delayed systems by the use of the Lyapunov-Krasovskii functional. As an alternative of the Lyapunov function-based design the “Fixed Point Transformation-based Adaptive Control” was elaborated that generally so works on the basis of an approximate initial model that it always has to take into consideration fresh observations. The appearance of time-delay to some extent makes the available observed signal “obsolete”, therefore it may degrade the precision of the adaptive controller. The present paper is the 1st report on systematic investigations on this degradation effect in the case of a strongly nonlinear system under delayed control. The simulations reveal that tis novel approach may be applicable to delayed systems, too.