Abstract-

SUMMARYWe consider general discrete-time nonlinear systems (of arbitrary nonlinear growth) with time-varying input delays and design an explicit predictor feedback controller to compensate the input delay. Such results have been achieved in continuous time, but only under the restriction that the delay rate is bounded by unity, which ensures that the input signal flow does not get reversed, namely, that old inputs are not felt multiple times by the plant (because on such subsequent occasions, the control input acts as a disturbance). For discrete-time systems, an analogous restriction would be that the input delay is non-increasing. In this work, we do not impose such a restriction. We provide a design and a global stability analysis that allow the input delay to be arbitrary (containing intervals of increase, decrease, or stagnation) over an arbitrarily long finite period of time. Unlike in the continuous-time case, the predictor feedback law in the discrete-time case is explicit. We specialize the result to linear time-invariant systems and provide an explicit estimate of the exponential decay rate. Carefully constructed examples are provided to illustrate the design and analytical challenges.

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In this study, we design a state predictor-based output feedback controller that compensates for unavoidable time-varying network delays in networked control systems (NCSs) over Wi-Fi networks. We model time-varying network delays as timevarying input delays of NCSs over Wi-Fi networks. The designed controller consists of a linear quadratic regulator (LQR), a full-order observer, and a time-varying stepahead state predictor. The state predictor plays a key role in compensating for the time-varying input delay by providing the LQR with an estimation of future states ahead by the current network delay time. The time-varying network delays are acquired in real time by measuring the time differences between sent and received control data packets. We verify the stability and compensation performance of the designed controller by performing extensive experiments for an NCS in which a rotary inverted pendulum is controlled over Wi-Fi networks.