Fuzzy Adaptive Zero-Error-Constrained Tracking Control for HFVs in the Presence of Multiple Unknown Control Directions

This article attempts to realize zero-error constrained tracking for hypersonic flight vehicles (HFVs) subject to unknown control directions and asymmetric flight state constraints. The main challenges of reaching such goals consist in that addressing multiple unknown control directions requires novel conditional inequalities encompassing the summation of multiple Nussbaum integral terms, and in that the summation of conditional inequality may be bounded even when each term approaches infinity individually, but with opposite signs. To handle this challenge, novel Nussbaum functions that are designed in such a way that their signs keep the same on some periods of time are incorporated into the control design, which not only ensures the boundedness of multiple Nussbaum integral terms but preserves that velocity and altitude tracking errors eventually converge to zero. Fuzzy-logic systems (FLSs) are exploited to approximate model uncertainties. Asymmetric integral barrier Lyapunov functions (IBLFs) are adopted to handle the fact that the operating regions of flight state variables are asymmetric in practice, while ensuring the validity of fuzzy-logic approximators. Comparative simulations validate the effectiveness of our proposed methodology in guaranteeing convergence, smoothness, constraints satisfaction, and in handling unknown control directions.