Safety Verification of Output Feedback Controllers for Nonlinear Systems
Provides a method to recover safety guarantees for nonlinear systems when only output measurements are available, addressing a practical limitation in control theory.
The paper derives a bound on the distance between state-feedback and output-feedback trajectories for a class of nonlinear systems, showing it converges to zero with observer gain, enabling safety verification under output feedback and control saturation.
A high-gain observer is used for a class of feedback linearisable nonlinear systems to synthesize safety-preserving controllers over the observer output. A bound on the distance between trajectories under state and output feedback is derived, and shown to converge to zero as a function of the gain parameter of an observer. We can therefore recover safety properties under output feedback and control saturation constraints by synthesizing a controller as if the full state were available. We specifically design feedback linearising controllers that satisfy certain properties, such as stability, and then construct the associated maximal safety-invariant set, namely the largest set of all initial states that are guaranteed to produce safe trajectories over a given (possibly infinite) time horizon.