Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
Browse
4 results
Search Results
Article Citation - WoS: 1Citation - Scopus: 1No-Regret and Low-Regret Control for a Weakly Coupled Abstract Hyperbolic System(Wiley, 2025) Louafi, Meriem; Messaoudi, Mohammed; Abdeljawad, Thabet; Jarad, FahdThis paper explores an optimal control problem of weakly coupled abstract hyperbolic systems with missing initial data. Hyperbolic systems, known for their wave-like phenomena and complexity, become even more challenging with weak coupling between subsystems. The study introduces no-regret and low-regret control strategies to handle missing information and achieve optimal performance. By deriving the Euler-Lagrange optimality system, it characterizes these control approaches in the context of weak coupling. Additionally, the paper establishes the existence and uniqueness of a no-regret and low-regret control, emphasizing the influence of uncertain coupling parameters. These findings are optimal control strategies for abstract weakly coupled hyperbolic systems under uncertainty. Finally, as highlighted in our conclusion, future research could explore integrating memory effects through fractional derivatives to improve the modeling of viscoelasticity, diffusion with memory, and wave damping.Article Citation - WoS: 173Citation - Scopus: 173On the Fractional Optimal Control Problems With a General Derivative Operator(Wiley, 2021) Baleanu, Dumitru; Jajarmi, AminThis paper deals with a general form of fractional optimal control problems involving the fractional derivative with singular or non-singular kernel. The necessary conditions for the optimality of these problems are derived and a new numerical method is designed to solve these equations effectively. Simulation results indicate that the proposed method works well and provides satisfactory results with regard to accuracy and computational effort. Comparative results also verify that a particular case with Mittag-Leffler kernel improves the performance of the controlled system in terms of the transient response compared to the other fractional- and integer-order derivatives.Article Citation - WoS: 14Citation - Scopus: 18Optimal Control of Nonlinear Dynamical Systems Based on a New Parallel Eigenvalue Decomposition Approach(Wiley, 2018) Baleanu, Dumitru; Jajarmi, AminThis manuscript aims to investigate a new approach based on the modal series method and eigenvalue decomposition technique to solve a class of nonlinear optimal control problems. For this purpose, a sequence of decoupled linear two-point boundary value problems is solved iteratively instead of solving the coupled nonlinear two-point boundary value problem derived from the maximum principle. The convergence analysis of the suggested technique is also investigated. In addition, the problem that needs to be solved at each iteration is composed of lower-order decoupled subproblems; hence, they can be solved in parallel. Thus, the new scheme has a parallel computing property improving its computational effectiveness. Numerical simulations and comparative results show that the proposed approach is efficient and provides satisfactory results.Article Citation - WoS: 28Citation - Scopus: 34Optimal Chemotherapy and Immunotherapy Schedules for a Cancer-Obesity Model With Caputo Time Fractional Derivative(Wiley, 2018) Arshad, Sadia; Baleanu, Dumitru; Akman Yildiz, TugbaThis work presents a new mathematical model to depict the effect of obesity on cancerous tumor growth when chemotherapy and immunotherapy have been administered. We consider an optimal control problem to destroy the tumor population and minimize the drug dose over a finite time interval. The constraint is a model including tumor cells, immune cells, fat cells, and chemotherapeutic and immunotherapeutic drug concentrations with the Caputo time fractional derivative. We investigate the existence and stability of the equilibrium points, namely, tumor-free equilibrium and coexisting equilibrium, analytically. We discretize the cancer-obesity model using the L1 method. Simulation results of the proposed model are presented to compare three different treatment strategies: chemotherapy, immunotherapy, and their combination. In addition, we investigate the effect of the differentiation order alpha and the value of the decay rate of the amount of chemotherapeutic drug to the value of the cost functional. We find out the optimal treatment schedule in case of chemotherapy and immunotherapy.