This paper studies the problem of global state regulation with stability for time-delay nonlinear systems with unknown control directions. Using a dynamic gain-based approach for counteracting time-delay nonlinearity and the Nussbaum-gain function for dealing with unknown control directions, we develop a dynamic state feedback control strategy that solves the problem. A novel construction of Lyapunov-Krasovskii functionals is presented and plays a key role in handling nonlinearity with delayed states and unknown control directions simultaneously. The proposed dynamic state feedback compensators are shown to guarantee: i) global asymptotic convergence of the system state to the origin; and ii) global boundedness of the resulted closed-loop systems

Adaptive control of general nonlinear systems with nonlinear parameterization is studied in this paper. Under the assumptions that the system has stable free dynamics and satisfies controllability-like conditions characterized by the Lie brackets of affine vector fields, it is proved that there exist L_gV-type adaptive controllers that not only asymptotically regulate the state of the nonlinearly parameterized system but also guarantee global stability of the closed-loop system. The design of L_gV-type adaptive controllers is also included. Applications of the proposed adaptive control scheme are presented, including an interesting case of a DC-microgrid with PV and battery system.

This paper aims to present an approach to address the atom rearrangement problem by developing Convolutional Neural Network (CNN) models. These models predict the coordinates for atom movements while ensuring collision-free transitions and filling all vacancies in the target array. The process begins with designing a cost function for the assignment problem that incorporates constraints to prevent collisions and guarantee vacancy filling. We then build and train CNN models using datasets for three different grid sizes: $10\times 10,13\times 13,\mathrm{and}21\times 21$. Our models achieve high accuracy in predicting atom positions, with individual position accuracies of 99.63%, 98.93%, and 97.24%, respectively, for the aforementioned grid sizes. Despite limitations in training larger models due to hardware constraints, our approach demonstrates significant improvements in speed and accuracy. The final section of the paper presents detailed accuracy results and calculation times for each model, highlighting the potential of CNN-based methods in optimizing atom rearrangement processes.