Viability kernel based control approach for a flight simulator model

An approach for the application of differential game theory to control a realistic flight simulator model is presented. In the context of aircraft control safe operation must be ensured particularly under external disturbances (e.g. wind). The application of viability theory enables a determination of envelopes (viability kernels) in which safe operation is guaranteed. Here, a state-feedback control law can be derived based on a viability kernel which keeps the dynamic system within a set of safe states. So far, our solver implementation on a supercomputer allows us to compute viability kernels for general nonlinear dynamic systems in up to seven state dimensions. Unfortunately, the mathematical model of the flight simulator consists of about one hundred differential equations. Therefore, the following procedure is used to enable the application of the viability kernel based control. First, a reduced model of the flight simulator model is derived for the calculation of the viability kernel in up to seven state dimensions. Then, the optimal controls are determined through the evaluation of the precomputed viability kernel using the reduced model. In order to apply the optimal controls to the flight simulator model a Nonlinear Dynamic Inversion (NDI) control architecture is used. This NDI controller contains two cascaded control loops with modified reference models of relative degree one. Numerical experiments in a cruise flight condition using different wind disturbances suggest that the proposed control procedure keeps the considered states of the flight simulator model within the viability kernel.