Ensuring safety for sampled data systems: An efficient algorithm for filtering potentially unsafe input signals

A common design pattern in cyber-physical systems features a continuous plant and a discrete controller in a feedback loop. Sampled data analysis attempts to take into consideration both the continuous and discrete time elements of such a design. In this paper we adapt an earlier algorithm for efficient ellipsoidal approximation of robust sampled data finite horizon viability kernels to compute capture basins for systems with linear dynamics. Using these capture basins, we construct a hybrid automaton which can verify and if necessary modify an exogenous input signal to ensure safety. The hybrid automaton can be run online in the controller so that it can handle exogenous input signals arriving in real time, such as might be generated by human-in-the-loop control. The technique is demonstrated on a six dimensional nonlinear longitudinal model of a quadrotor with a human pilot in the loop. The capture basins' robustness is used to handle the model nonlinearity in a sound fashion.