The dynamic model of mobile wheelchair technology requires developing and implementing an intelligent control system to improve protection, increasing performance efficiency, and creating precise maneuvering in indoor and outdoor spaces. This work aims to design a robust tracking control algorithm based on a reference model for operating the kinematic model of powered wheelchairs under the variation of system parameters and unknown disturbance signals. The control algorithm was implemented using the pole placement method in combination with the sliding mode control (PP-SMC) approach. The design also adopted a neural network approach to eliminate system uncertainties from perturbations. The designed method utilized the sinewave signal as an essential input signal to the reference model. The stability of a closed-loop control system was achieved by adopting the Goa reaching law. The performance of the proposed tracking control system was evaluated in three scenarios under different conditions. These included assessing the tracking under normal operation conditions, considering the tracking performance by changing the dynamic system's parameters and evaluating the control system in the presence of uncertainties and external disturbances. The findings demonstrated that the proposed control method efficiently tracked the reference signal within a small error based on mean absolute error (MAE) measurements, where the range of MAE was between 0.08 and 0.12 in the presence of uncertainties or perturbations.

This investigation focuses on solitary wave solutions and dynamic analysis of the complex coupled Maccari system. We employ the new extended hyperbolic function method to establish bright-wave and dark-wave profiles of the model. The resulting solutions include hyperbolic, trigonometric, and exponential-type functions. Furthermore, we explore the model's dynamical characteristics via multiple perspectives, including phase portrait analysis, quasi-periodic and chaotic patterns, sensitivity analysis and Lyapunov exponent. The analysis validates the robustness of the new extended hyperbolic function method on one hand and extends the understanding of complex wave structures in Maccari's system on the other hand.

Cancer is a complex group of diseases characterized by uncontrolled cell growth that can spread throughout the body, leading to serious health issues. Traditional treatments mainly include chemotherapy, surgery, and radiotherapy. Although combining different therapies is becoming more common, predicting how these treatments will interact and what side effects they may cause, such as gastrointestinal or neurological problems, can be challenging. This research applies optimal control theory (OCT) to create precise and personalized treatment plans for cancer patients. OCT helps identify the most effective doses of chemotherapy and immunotherapy by forecasting how various treatment combinations will impact tumor growth and the immune response over time. It optimizes the integration of chemotherapy with immunotherapy to minimize side effects while maximizing therapeutic benefits. The study proposes a model for managing malignant tumors using a mix of immunotherapy, vaccines, and chemotherapy. The aim is to develop the best treatment plan that reduces new tumor growth while keeping healthy cells stable. It also takes into account individual differences among patients, including variations in tumor biology and immune responses in both younger and older individuals. To do this, we compared different optimal control strategies: interior point optimization (IPOPT), an open-source tool for nonlinear optimization; state-dependent Riccati equation (SDRE), which adapts linear control methods for nonlinear situations; and approximate sequence Riccati equation (ASRE), a globally optimal feedback control approach for nonlinear systems. The optimization criterion showed that the proposed work achieved a cost value of 52.3573 for IPOPT, compared with 52.424 for both SDRE and ASRE. For $\mathrm{C}\mathrm{D}{8}^{+}$ T cells, the proposed method maintained a consistent value of 1.6499 for continuous (C) and dosed (D) across all techniques. Tumor cell counts had a C value of 0.0007 for IPOPT, compared with 0.0006 for ISDRE and ASRE, with D values remaining at 0 across all methods. This comparison demonstrates the successful use of control theory techniques and highlights their potential for developing personalized and effective treatment strategies for complex cancer cases. By optimizing treatment schedules and dosages, OCT can help minimize the side effects of cancer therapies, thereby enhancing patients' overall quality of life.