The position-force tracking issue of an object being moved by collaborative Multiple Flexible-Joint arms, facing dynamic uncertainties, model nonlinearities, and unknown perturbations is studied in this paper. Toward this end, an adaptive control scheme applying the function approximation technique is suggested, enabling the object to track the reference trajectory. This capability arises from the universal approximation property of the FAT-based approaches. Herein, the q-Bernstein-Schurer operators are exploited to disturbances/uncertain dynamic approximations. Since the parameters of the system are not exactly recognized, adaptive rules are suggested for tuning the coefficients of the operator. The Lyapunov stability analysis guarantees uniformly ultimately bounded stability of all the error signals. Two Flexible-Joint manipulators transporting a rigid object are employed to validate the theoretical achievements. The state-of-the-art Chebyshev Neural Network approximator is also used to compare the suggested methodology. The outcomes exhibit the usefulness of the presented approach, handling the system even in the incidence of uncertainties and disturbances needless to the system’s state feedback for function approximation with a low computational burden.

Modeling the tumor behavior in the host organ as function of time and radiation dose has been a major study in the previous decades. Here the effort in estimation of cancerous and normal cell proliferation and growth in glioblastoma multiform (GBM) tumor is presented. This paper introduces a new mathematical model in the form of differential equation of tumor growth. The model contains dose delivery amount in the treatment scheme as an input term. It also can be utilized to optimize the treatment process in order to increase the patient survival period. Gene expression programming (GEP) as a new concept is used for estimating this model. The LQ model has also been applied to GEP as an initial value, causing acceleration and improvement of the algorithm estimation. The model shows the number of the tumor and normal brain cells during the treatment process using the status of normal and cancerous cells in the initiation of treatment, the timing and amount of dose delivery to the patient, and a coefficient that describes the brain condition. A critical level is defined for normal cell when the patient's death occurs. In the end the model has been verified by clinical data obtained from previous accepted formulae and some of our experimental resources. The proposed model helps to predict tumor growth during treatment process in which further treatment processes can be controlled.

In this article a brief story of mathematical model for one of the most lethal tumor, GBM, is considered, and it tries to reduce the amount of dose delivery to the patient by using genetic algorithm (GA). Since this tumor kills many of its patients, lots of efforts have been done in the previous decades in order to cure this cancer or at least increase its patients' lifetime. Most of previous models have not been associated with a treatment term but in this investigation the latest model of the tumor which contains the input term of radiotherapy has been utilized. This paper shows a new optimization solution on the latest model of GBM and reduces the total dose received by the patient while he or she has the same lifetime.

In this paper, a Szasz-Favard-Mirakyan operator is exploited for chaos synchronization of a master-slave system. The universal approximation feature asset lets in Szasz-Favard-Mirakyan operators for approximating uncertainties, including un-modeled dynamics and disturbances. The above subject is considered in detail in this investigation. It is confirmed that the synchronization/approximation errors are uniformly bounded and stable if the Szasz-Favard-Mirakyan operators are applied as the regressors. Additionally, it has been presumed that the synchronization’s error rate is not available, and an observer will be designed for its estimation. The Duffing–Holmes oscillator is examined as the computer-generated chaotic framework with the target of examining the functioning of the recommended synchronization observer-based controller. The outcomes are compared with an effective approximation-based control strategy. Unlike Chebyshev Neural Network approximators in which the system’s inputs states are needed to define the regressor vector and approximate uncertainties, the suggested Szasz-Favard-Mirakyan operators–based strategy is independent of the system states for constructing the regressor vector.