Photovoltaic (PV) system generates energy that varies with the variation in environmental conditions such as temperature and solar radiation. To cope up with the ever increasing demand of energy, the PV system must operate at maximum power point (MPP), which changes with load as well as weather conditions. This paper proposes a nonlinear backstepping controller to harvest maximum power from a PV array using DC-DC buck converter. A regression plane is formulated after collecting the data of the PV array from its characteristic curves to provide the reference voltage to track MPP. Asymptotic stability of the system is proved using Lyapunov stability criteria. The simulation results validate the rapid tracking and efficient performance of the controller. For further validation of the results, it also provides a comparison of the proposed controller with conventional perturb and observe (P&O) and fuzzy logic-based controller (FLBC) under abrupt changes in environmental conditions.

Background: Recently proposed brain-tumor treatment strategies prioritize fast reduction of tumor cell population while often neglecting the radiation or chemotherapeutic drug dosage requirements to achieve it. Moreover, these techniques provide chemotherapy based treatment strategies, while ignoring the toxic side effects of the drugs employed by it. Methods: This study updates the recently proposed brain-tumor system dynamics by incorporating radiotherapy along with chemotherapy to simultaneously initiate both therapies for a more comprehensive and effective response against tumor proliferation. Afterwards, based on the upgraded system dynamics, this study proposes a novel multi-input sigmoid-based smooth synergetic nonlinear controller with the aim to reduce the dosage requirements of both therapies while keeping the overall system response robust and efficient. The novelty of this study lies in the combination of radiotherapy and chemotherapy inputs in a way that prioritizes patients health and well-being, while integrating advanced synergetic control technique with a sigmoid function based smoothing agent. Results: The proposed method reduced baseline radiation and chemo drug dosages by 57% and 33% respectively while effectively suppressing tumor growth and proliferation. Similarly, the proposed controller reduced the time required for complete tumor mitigation by 60% while reducing the radiation and chemotherapeutic drug intensity by 93.8% and 21.3% respectively. Conclusions: This study offers significant improvement in tumor treatment methodologies by providing a safer, less riskier brain-tumor treatment strategy that has promising potential to improve survival rates against this menacing health condition so that the affected patients may lead a healthier and better quality of life.

Sliding mode control (SMC) is a robust nonlinear control framework that enforces system trajectories onto predefined manifolds, providing strong robustness guarantees against uncertainties. However, SMC inherently introduces unwanted transients or chattering in system state trajectories, which may cause issues especially for sensitive applications such as regulation of drug administration. This paper proposes a multi-input smooth sliding mode control (MISSMC) strategy that combines radiotherapy and chemotherapy for a nonlinear tumor–immune dynamical system described by ordinary differential equations. The closed-loop system is first analyzed to establish key qualitative properties: all state variables remain positive and bounded, the sliding surfaces exhibit asymptotic convergence, and explicit analytical upper bounds on the cumulative therapy doses are derived under clinically motivated constraints. On this basis, a smooth hyperbolic-tangent sliding manifold and associated control law are designed to regulate the radiation and drug infusion rates. While the use of a hyperbolic-tangent smoothing function effectively suppresses chattering, it introduces a small steady-state error due to the presence of a boundary layer. To address this limitation, integral action is incorporated into the sliding surfaces, ensuring asymptotic convergence of tumor state and reducing residual steady-state error, while enhancing robustness against model uncertainties and parameter variations. Numerical simulations, based on a brain-tumor case study, show that the proposed smooth SMC markedly suppresses transient overshoots in both states and control inputs, while preserving effective tumor reduction. Compared with a conventional (non-smooth) SMC scheme, the MISSMC controller reduces baseline radiation and chemotherapy intensities on average by roughly 70%. Similarly, MISSMC lowers the overall cumulative doses on average by about 40%, without degrading the therapeutic outcome. The resulting integral smooth SMC framework therefore offers a rigorous nonlinear-systems approach to designing combined radio-chemotherapy protocols with guaranteed positivity, boundedness, and asymptotic stabilization of the closed-loop system, together with explicit bounds on the control inputs.

Nonlinear biological systems exhibit complex interactions, uncertain parameters, and strong treatment-dependent dynamics, making mathematical modeling and control essential for designing reliable therapeutic intervention strategies. This study proposes a multi-input adaptive smooth sliding mode control (AMIS-SMC) framework for regulating combined radiotherapy and chemotherapy in a nonlinear tumor–immune dynamical system described by ordinary differential equations. The proposed controller integrates a hyperbolic tangent smoothing mechanism with adaptive parameter-estimation laws to compensate for uncertainty in tumor and healthy-cell growth dynamics. In this way, the method explicitly links biological-system modeling, feedback control, treatment-dose management, and parameter adaptation within a single mathematically analyzable framework. Fundamental closed-loop properties are established analytically, including positivity and boundedness of all biological state variables, asymptotic convergence of the sliding surfaces, and explicit upper bounds on the administered radiation and chemotherapeutic drug dosages. Lyapunov-based stability analysis is used to guarantee boundedness of the closed-loop signals and convergence of the sliding manifold. Numerical simulations based on a brain-tumor case study demonstrate that the proposed AMIS-SMC algorithm achieves rapid tumor suppression while administering substantially lower treatment intensities than conventional and integral SMC approaches. Under nominal conditions, the proposed controller reduces cumulative radiation and chemotherapy dosages while maintaining effective tumor mitigation. Under mismatched parameter conditions, AMIS-SMC consistently drives the tumor-cell population toward the desired equilibrium across all tested scenarios, whereas conventional and integral SMC show limited adaptability. Statistical analysis using Mann–Whitney U and Fisher’s tests further indicates that AMIS-SMC provides an effective mathematical-control and treatment-management strategy for tumor suppression in a simplified nonlinear tumor–immune biological system under parameter uncertainty.