This research introduces a fractional high-order sliding mode control (FHOSMC) method that utilises an inverse integral fractional order, $0<\beta <1$, as the high order on the FHOSMC reaching law, exhibiting a novel contribution in the related field of study. The application of the proposed approach into a bioreactor system via diffeomorphism operations demonstrates a notable improvement in the management of the bioreactor dynamics versus classic controllers. The numerical findings highlight an improved precision in tracking reference signals and an enhanced plant stability compared to proportional–integral–derivative (PID) controller implementations within challenging disturbance scenarios. The FHOSMC effectively maintains the biomass concentration at desired levels, reducing the wear of the system as well as implementation expenses. Furthermore, the theoretical analysis of the convergence within time indicates substantial potential for further enhancements. Subsequent studies might focus on extending this control approach to bioreactor systems that integrate sensor technologies and the formulation of adaptive algorithms for real-time adjustments of $\beta$-type fractional-orders.

The trajectory tracking problem of underactuated unmanned surface vehicles (USVs) with unknown physical parameters arising from hydrodynamic effects is addressed using a robust control strategy based on a sliding-mode dynamic neural network identifier. To handle the unknown physical parameters, a dynamic neural network identifier with a novel structure is developed, enabling the construction of an equivalent mathematical model of the USV dynamics. To compensate for the underactuated nature of the system, a coordinate transformation is introduced. Using this transformation, together with the proposed identifier, a nonsingular sliding-mode controller is designed. Lyapunov-based analysis establishes finite-time convergence of the neural weight estimation errors to zero and convergence of the identification errors to a bounded neighborhood of zero. Furthermore, once the identification errors enter this bounded region, they asymptotically converge to zero. In addition, the closed-loop stability analysis guarantees finite-time convergence of the tracking errors. The effectiveness of the proposed identifier–controller framework is validated through simulation studies that incorporate explicit actuator saturation constraints and external disturbances to emulate realistic operating conditions. These results demonstrate the practical applicability of the proposed control strategy, as the commanded inputs remain within the physical limits of the propulsion system. Comparative results with a state-of-the-art model-based super-twisting controller show that the proposed approach achieves comparable tracking performance while eliminating the need for prior knowledge of the system’s dynamic parameters.

En este trabajo, se presenta el diseño de un control adaptable por modelo de referencia para un vehículo aéreo no tripulado sujeto a variaciones en su carga útil, de modo que la masa del vehículo y sus momentos de inercia se consideran parámetros inciertos en su dinámica. El diseño del controlador considera el análisis del modelo subactuado de la dinámica del vehículo aéreo, el cual puede descomponerse en tres subsistemas independientes. Para cada subsistema se propone un modelo de referencia y utilizando el formalismo de Lyapunov se obtiene la ley de control por realimentación para estabilizar al vehículo junto con una regla de adaptación que ajusta en línea los parámetros inciertos. Esto resulta en un esquema de control tipo backstepping con capacidades de adaptación. El análisis de estabilidad, también garantiza la convergencia de los estados de cada subsistema a los de su correspondiente modelo de referencia. Para evaluar el desempeño del controlador propuesto se realizaron simulaciones numéricas en MATLAB Simulink.

A novel structure for a Robust Dynamic Neural Network Identifier (RDNNI) based on sliding modes is proposed for the online identification of nonlinear second-order systems. A stability analysis using Lyapunov theory demonstrates that both the neural weight estimation errors and the sliding surface converge to zero in finite. Most of the identification schemes based on dynamic neural networks reported in the literature only assure the asymptotic convergence of the synaptic weights and the identification process. There exist some works which modifies the identifier structure to guarantee the finite time convergence of the identification process. However, all these schemes have the limitation that identification errors converge to a region around the origin because of the upper boundaries introduced by the system disturbances. Compared these types of dynamic neural network identifiers found in the literature, the proposed identifier combines the non-singular terminal sliding mode surface with the synaptic weights’ adaptation laws to guarantee that the identification errors converge to zero in a finite time. To evaluate the performance of the developed structure, a simulation is conducted for the identification of a Duffing oscillator, together with a series of experimental tests to identify the dynamics of depth and yaw in an unmanned underwater vehicle. Finally, a quantitative comparison of the identification performance with a recently introduced State-Input Affine Differential Neural Network (SIADNN) identifier demonstrates the superior performance of the proposed design, both in simulations and in real-time experiments.