Validation of adaptive control laws using optimization and trajectory sensitivity

In this paper it is proposed an easy-to-use verification and validation method for adaptive control laws that relies on time domain simulations. The problem is set as a trajectory falsification problem that is the search of closed loop trajectories that, starting from a set of admissible initial conditions, reach a set of unsafe states. The falsification is placed as a nonlinear optimization problem whose decision variables are the initial condition of the states and the uncertain parameters of the system. The falsification is performed iteratively using the local gradient of the sensitivity function derived from a linearized model of the system trajectory. The sensitivity function allows computing updated values for the initial condition and for the system parameters such that the updated system trajectory get closer to the user defined unsafe set. A detailed Model Reference Adaptive Control law falsification example applied to an F16 aircraft model is presented to highlight the efficacy of the approach.