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Abstract Tuberculosis (TB) is a contagious disease which can easily be disseminated in a society. A five state Susceptible, exposed, infected, recovered and resistant (SEIRs) epidemiological mathematical model of TB has been considered along with two non‐linear controllers: State Feedback (SFB) and Synergetic controllers have been designed for the control and prevention of the TB in a population. Using the proposed controllers, the infected individuals have been reduced/controlled via treatment, and susceptible individuals have been prevented from the disease via vaccination. A mathematical analysis has been carried out to prove the asymptotic stability of proposed controllers by invoking the Lyapunov control theory. Simulation results using MATLAB/Simulink manifest that the non‐linear controllers show fast convergence of the system states to their respective desired levels. Comparison shows that proposed SFB controller performs better than Synergetic controller in terms of convergence time, steady state error and oscillations.

Abstract Destruction of β‐cells in pancreas causes deficiency in insulin production that leads to diabetes in the human body. To cope with this problem, insulin is either taken orally during the day or injected into the patient's body using artificial pancreas (AP) during sleeping hours. Some mathematical models indicate that AP uses control algorithms to regulate blood glucose concentration (BGC). The extended Bergman minimal model (EBMM) incorporates, as a state variable, the disturbance in insulin level during medication due to either meal intake or burning sugar by engaging in physical exercise. In this research work, EBMM and proposed finite time robust controllers are used, including the sliding mode controller (SMC), backstepping SMC (BSMC) and supertwisting SMC (second‐order SMC or SOSMC) for automatic stabilisation of BGC in type 1 diabetic patients. The proposed SOSMC diminishes the chattering phenomenon which appears in the conventional SMC. The proposed BSMC is a recursive technique which becomes robust by the addition of the SMC. Lyapunov theory has been used to prove the asymptotic stability of the proposed controllers. Simulations have been carried out in MATLAB/Simulink for the comparative study of the proposed controllers under varying data of six different type 1 diabetic patients available in the literature.

Lack of insulin production by pancreas causes high blood glucose level (BGL) in the diabetic patients. For their treatment, manual insulin intake is possible only during the day timings but not feasible during the night when the patient is sleeping. Artificial pancreas (AP) is used for the automatic regulation of BGL by continuous injection of insulin. The nonlinear Bergman's Minimal Model (BMM) considers fixed meal disturbance which may actually vary continuously during medication due to meal intake or by doing exercise. This variation has been taken into account by the Extended Bergman's Minimal Model (EBMM). In this paper, two nonlinear: Terminal Synergetic and State Feedback Linearization based controllers have been proposed for AP to regulate BGL using EBMM. Asymptotic stability of the proposed controllers has been proved using Lyapunov theory. Comparison of the proposed controllers with each other and that with PID controller has been done using MATLAB/Simulink. White noise has been added as the disturbance to further analyze the output performance of the proposed controllers. The Terminal Synergetic controller which performs better than others, has also been implemented on the data of six Type 1 diabetic patients available in the literature.

Diabetes Mellitus Type 1 happens when our immune system destroys beta cells in our pancreas due to which it fails to produce enough insulin; a hormone which allows sugar/glucose to enter in its cells in order to produce energy. To cope with failure of pancreas, artificial ones are used to inject the required amount of insulin in the body. Controllers are used for automatic balancing of blood glucose-insulin level. Bergman's minimal model (BMM) is a physiologically verified model representing this phenomenon. In a recent research BMM is extended to more generic form with an extended state of the system, dealing with the disturbance to the blood glucose level caused by meal intake during medication. In this research paper, we have used BMM along with its extended model and proposed three nonlinear controllers: Integral Backstepping (IBS) Controller, Backstepping (BS) Controller and Fuzzy Logic Controller (FLC), for the automatic stabilization of the blood glucose level in Diabetes Mellitus Type 1 patients. The integral action is integrated with Backstepping technique; resulting in reducing steady-state error by significant amount. A mathematical analysis has been done to prove the asymptotic stability of the proposed controllers for the both models using Lyapunov theory. For showing the tracking behavior of the proposed controllers with their respective models to the desired blood-glucose output, simulation results have been performed and discussed using MATLAB/Simulink. Comparison results of the both systems show that the proposed controllers performs far better than the ones given in the literature.