Approximation-free Quantitative Prescribed Performance Control of Unknown Strict-feedback Systems

Abstract

Prescribed performance control (PPC) has been proved to be a powerful tool which seeks transient performance for tracking errors. Unfortunately, the existing PPC schemes only can qualitatively design transient performance, while they cannot quantitatively set the convergence time and meanwhile minimize overshoot. In this article, we propose a new quantitative PPC strategy for unknown strict-feedback systems, capable of quantitatively designing convergence time and minimizing overshoot. Firstly, a new quantitative prescribed performance mechanism is proposed to impose boundary constraint on tracking errors. Then, back-stepping is used to exploit virtual controllers and actual controller based on Nussbaum Function, without requiring any prior knowledge of system unknown dynamics. Compared with the existing methodologies, the main contribution of this paper is that it can guarantee predetermined convergence time and zero overshoot for tracking errors, and meanwhile there is no need of any fuzzy/neural approximation. Finally, compared simulation results are given to validate the effectiveness and advantage.

Segmented hybrid event‐triggered control for underactuated autonomous underwater vehicles with an asymmetrical prescribed performance constraint

“…To achieve the predefined transient and steady state performance of the AUV trajectory tracking, the tracking errors $$$ {\alpha}_e,\left(\alpha =\rho, \theta, \psi \right) $$$ are required to be fulfilled the constraint $$$ \underset{\_}{\alpha }(t)\le {\alpha}_e(t)\le \overline{\alpha}(t) $$$. Inspired by References 20 and 25, the asymmetric boundary functions (ABFs) are designed as: $$$$ \left\{\begin{array}{l}\overline{\alpha}(t)=\left({p}_{\alpha }(t)-{p}_{\infty}^{\alpha}\right)\kern0.2em \operatorname{sign}\kern0.2em \left({\alpha}_e(0)\right)+{p}_{\alpha }(t){\overline{\Lambda}}_{\alpha}\\ {}\underset{\_}{\alpha }(t)=\left({p}_{\alpha }(t)-{p}_{\infty}^...$$…”

“…As a result, the conservative design approach used in the former may lead to unnecessary overshooting due to excessive control gains, even though the tracking error does not exceed the preset boundary layer. To mitigate design conservatism and minimize overshoot of tracking error, a promising asymmetrical prescribed performance control (APPC) method was implemented in References 20 and 25. This approach provides a predefined quantitative specification of tracking behavior and addresses the limitations of traditional funnel‐based PPC schemes.…”