Prescribed performance under input saturation for uncertain strict-feedback systems: A switching control approach

Abstract

We consider the problem of achieving prescribed performance metrics on the output tracking error, for uncertain strict-feedback systems, while satisfying inelastic control input constraints in the form of magnitude saturation. Inspired by the prescribed performance control (PPC) methodology, we propose a switching control strategy comprised of two operational units: a traditional PPC and a Safety Controller. The former enforces the output error to evolve strictly inside a user-defined performance envelope that incorporates all the desired performance characteristics. However, in the presence of input saturation this envelope can be easily violated, leading to PPC instability. On the other hand, the Safety Controller enables the safe escaping, thus avoiding the appearance of this internal instability phenomenon. We prove that the closed-loop system solution is complete and non-zeno. Furthermore, we show that the tracking error evolves inside a modified performance envelope, guaranteeing a prescribed minimum convergence rate and a controlled maximum steady-state error. Simulation studies clarify and verify the theoretical findings.