This paper studies a new class of instantaneous and non-instantaneous impulsive boundary value problem involving the generalized $\psi$-Caputo fractional derivative with a weight. Depending on critical point theorems and some properties of $\psi$-Caputo-type fractional integration and differentiation, the variational construction and multiplicity result of solutions are established.

In this paper, we propose an output feedback flight tracking control scheme for helicopter attitude and altitude systems with unmeasured states under full state constraints. Firstly, a state observer is constructed based on the measured output signals, which is proven to be rigorous since all states are constrained within the desired and assigned scopes. Secondly, the flight tracking controller is built using the state estimations with the full state constraints control method. Then, the Barrier Lyapunov function method is adopted to guarantee the stability of the composite closed-loop nonlinear error systems. Meanwhile, the linear matrix inequality technology is applied to calculate the gains of the state observer. Finally, a numerical simulation example is provided to confirm the reasonableness of the full state constraint output feedback flight tracking control method.