Adaptive pseudo inverse control for a class of nonlinear asymmetric and saturated nonlinear hysteretic systems

This paper aims at eliminating the asymmetric and saturated hysteresis nonlinearities by designing hysteresis pseudo inverse compensator and robust adaptive dynamic surface control &#x0028 DSC &#x0029 scheme. The &#x201C pseudo inverse &#x201D means that an on-line calculation mechanism of approximate control signal is developed by applying a searching method to the designed temporary control signal where the true control signal is included. The main contributions are summarized as: 1&#x0029 to our best knowledge, it is the first time to compensate the asymmetric and saturated hysteresis by using hysteresis pseudo inverse compensator because the construction of the true saturated-type hysteresis inverse model is very difficult; 2&#x0029 by designing the saturated-type hysteresis pseudo inverse compensator, the construction of true explicit hysteresis inverse and the identifications of its corresponding unknown parameters are not required when dealing with the saturated-type hysteresis; 3&#x0029 by combining DSC technique with the tracking error transformed function, the &#x201C explosion of complexity &#x201D problem in backstepping method is overcome and the prespecified tracking performance is achieved. Analysis of stability and experimental results on the hardware-in-loop platform illustrate the effectiveness of the proposed adaptive pseudo inverse control scheme.