Safety controller synthesis using human generated trajectories: Nonlinear dynamics with feedback linearization and differential flatness

The aim of the safety controller synthesis problem is to synthesize a feedback controller that results in closed-loop trajectories that meet certain criteria, namely, the state or output trajectories terminate in a Goal set without entering an Unsafe set. We propose a formal method for synthesizing such a controller using finitely many human generated trajectories. The main theoretical idea behind our results is the concept of trajectory robustness, which is established using the theory of approximate bisimulation. Approximate bisimulation has been used to establish robustness (in the L
_∞
sense) of execution trajectories of dynamical systems and hybrid systems, resulting in trajectory-based safety verification procedures. The work reported in this paper builds on our earlier work where the dynamics of the system is assumed to be affine linear. We extend the existing results to special classes of nonlinear dynamical systems, feedback linearizable and differentially flat systems. For both cases, we present some examples where it is possible to synthesize the controller using human generated trajectories, which are obtained through interactive computer programs with graphical interface (computer games).