Neural Network Adaptive Control of Systems with Input Saturation

In the application of adaptive flight control, significant issues arise due to limitations on the plant inputs, such as actuator displacement limits. The concept of utilizing a modified reference model to prevent an adaptation law from "seeing" this system-input characteristic is described. The method allows correct adaptation while the plant input is saturated. To apply the method, estimates of actuator positions must be found. However, the adaptation law can correct for errors in these estimates. A theorem of boundedness for all system signals is included for a single hidden layer neural network adaptive law. The domain of attraction is also discussed. 1. Background In recent years, several theoretical developments have given rise to the use of artificial Neural Networks (NNs) for adaptive control of nonlinear systems. The use of NN adaptive flight control has been demonstrated in piloted hardware-in-the-loop simulation and flight test on the X-36 aircraft. This approach has been utilized to enable a single controller to handle multiple versions of guided munitions, and to replace traditional reusable launch vehicle gain tables. Input saturation implies that either a position or rate limit has been exceeded. Input saturation presents a significant problem for adaptive control, because in causes an adaptation law to be “tricked” by unexpected effects a behavior analogous to integrator windup in a linear controller. However, unlike an integrator designed for a selected linear response, it may be possible for an adaptive law to function properly (as designed) during finite periods of input saturation. One approach used is to avoid saturation altogether by either command or feedback signal adjustment. This has been demonstrated in an adaptive control setting. A second approach involves slowing or halting adaptation as saturation is entered. A common ad-hoc approach for most adaptive control methods is to simply stop adaptation completely when any input saturates. Another approach to the problem of adaptive control with input displacement saturation is augmenting the error signal. These methods apply to Model Reference Adaptive Control (MRAC), with an early result given by without a stability proof. For this method, the effect of the saturation nonlinearity on the reference model tracking error is removed by adding a signal derived from the actual plant input to the error signal . The method described below was originally motivated by the application in, and is most closely related to the method in, except that it relies on a modification to the reference model. As a result, it is not limited to saturation nonlinearities, linear plants, or linear reference models. The method described is also similar to Anti-Windup Bumpless Transfer (AWBT) theory for non-adaptive controllers, specifically the Hanus conditioning technique which also includes the concept of a miss-match between commanded and actual plant input. 2. Pseudo-Control Hedging Architecture The method described here is termed Pseudo-Control Hedging (PCH). The purpose of the method is to prevent the adaptive element of an adaptive control system from adapting to selected plant input characteristics. The specific case of PCH applied to an adaptive control architecture that includes an approximate dynamic inversion is illustrated in Figure 1. Reference Model Plant Approximate Dynamic Inversion Adaptation Law Neural Network rm rm x x & ,