In this paper, we present a fractional sliding mode controller based on a robust $P{I}^{\alpha }$ observer for fractional systems with bounded disturbances. This controller is introduced to achieve closed-loop Mittag–Leffler stability for uncertain fractional systems; meanwhile, the robust $P{I}^{\alpha }$ observer is designed such that a ${\mathcal{L}}_2$ stability is obtained via quadratic Lyapunov functions and the tuning is achieved with linear matrix inequality approach. The performance and stability of the proposed controller are analysed and demonstrated through a generalised $n\alpha$-differentiator. Finally, to illustrate the effectiveness of the proposed approach a comparative analysis against the fractional Super-Twisting is carried out.

Kinesthetic Motor Imagery (MKI) has been demonstrated to be a robust paradigm for Brain-Computer Interfaces (BCI). In this paper we present the characterization of KMI paradigm of three tasks of wrist and forearm of the right arm using Hurst exponent and variogram, preceding for ICA to map signals into source space. The results show high persistency an average of 0.76 ± 0.07 for KMI Pronation/Supination (PS), 0.82 ± 0.05 for KMI Flexion-Extension). (FE), and 0.90 ± 0.02 for KMI Abduction-Adduction (AA We found a significant difference between the three KMI tasks, useful for multimodal command in BCI.

Constrained nonlinear optimization plays a fundamental role in engineering design due to the presence of irregular feasible regions and interacting nonlinear restrictions. This study evaluates the performance of the Plant Growth Optimization (PGO) algorithm in a constrained nonlinear benchmark problem. The algorithm was implemented in MATLAB^® and assessed using a fixed external penalty formulation for constraint handling. Performance was analyzed through convergence dynamics, constraint evolution, dispersion across 20 independent runs, and computational efficiency. A comparative study was conducted against Particle Swarm Optimization (PSO), Genetic Algorithms (GA), and Differential Evolution (DE) under identical experimental conditions. Results show that PGO achieves stable convergence within 87 generations, consistently attaining a feasible solution near the constraint boundary with low dispersion across runs. Statistical validation using the Friedman test (${\chi }^2=32.45$, $p<0.001$) confirmed significant performance differences among algorithms, while post-hoc Wilcoxon tests indicated comparable performance between PGO and DE and significant differences relative to PSO and GA. These findings demonstrate that PGO provides a balanced compromise between robustness, convergence stability, and computational efficiency, supporting its suitability for constrained nonlinear engineering optimization tasks.

In this article we apply a polyadic approach to obtain very explicit description of a novel kind of wavelets on the ring of finite adèles, \(\mathbb{A}_{f}\), which are also eigenfunctions of a Vladimirov-type pseudodifferential operator on \(L^2(\mathbb{A}_{f})\). As an accompaniment, we solve the Cauchy problem for a certain pseudodifferential equation.