APC framework improves nonlinear control under asymmetric actuator constraints

A new paper from Saurabh Kumar, Shashi Ranjan Kumar, and Abhinav Sinha (arXiv:2608.15375) tackles a persistent challenge in control engineering: keeping nonlinear systems stable and safe when actuators have asymmetric limits on magnitude, rate, and time-varying output constraints. Traditional approaches rely on algebraic clipping or post-design saturation compensation, which can introduce instability or degrade performance. The authors propose Admissibility-Preserving Control (APC), a realization-centered framework that embeds actuator constraints directly into a continuously differentiable dynamic system called the Admissibility-Preserving Input Realization (APIR). This design treats the actuator set as forward invariant, meaning the physical input never violates limits, while maintaining user-selectable regularity and interpretable tuning parameters.

The APC architecture integrates the APIR with recursive backstepping, treating the realized plant input as an additional state. Crucially, this eliminates the need for an input-to-state stability (ISS) assumption on the uncontrolled plant. Instead, nonlinear drift terms are compensated recursively under an explicit compatibility condition between desired motion, available control authority, and APIR interior gain. The framework extends to time-varying output-safe tracking using a smooth asymmetric logarithmic barrier coordinate and associated Lyapunov function, and to simultaneous magnitude and rate constraints via a cascaded APIR. Rigorous Lyapunov and invariance analyses confirm regional asymptotic tracking, forward invariance of admissible sets, and boundedness of all closed-loop signals. Numerical studies illustrate the benefits for systems like robotic manipulators and autonomous vehicles, where asymmetric actuator constraints are common and safety is critical.