Towards the development of an efficient nonlinear controller for ART and cART against HIV infection.

The Human Immuno-deficiency Virus (HIV) is responsible for attacking the CD4+ T cells present in human blood and causes the human immune system to become vulnerable for numerous contagious and opportunistic diseases. It is hence pertinent to curb the spread of HIV infection using anti-HIV drugs. This study integrates sigmoid function with conventional sliding mode control and incorporate it within the framework of multi-objective optimal model predictive controller to reduce the impact of HIV infection through anti-retro-viral therapy. The proposed algorithm is designed using a deterministic HIV-human immune system model that also includes the dynamics of cytotoxic T-lymphocytes precursor and effector cells. The research work provides the detailed design of nonlinear sigmoid based SMC controller and its Lyapunov theory based stability analysis. This designed controller is then integrated within the framework of MPC. Simulation level dosage bounds derived from the considered reference values for anti-HIV drug dosage has been realized to explicate and understand the relationship between administered dosage and control inputs. To validate the superior performance of the proposed controller, the results are compared to that of recently proposed nonlinear backstepping, state-feedback and synergetic controllers. Lastly, the proposed control algorithm is also evaluated using a three-state, three-input HIV model to examine its applicability to combination anti-retro-viral therapy (cART). The simulations demonstrate that the proposed sigmoid SMC-MPC framework can regulate the modeled drug inputs while simultaneously improving the simulated CD4+ T-cell response and suppressing viral load. The results are intended to demonstrate the algorithmic performance of the proposed nonlinear control framework within the considered mathematical models. Importantly, this study is simulation-based and does not constitute a clinical treatment strategy or a recommendation for automated administration of anti-retro-viral drugs. The simulations are performed using MATLAB/Simulink. The observations and results presented in this study are also analyzed to substantiate the need of nonlinear feedback controllers to limit the amount of administered treatment burden to effectively and efficiently curb HIV advancement. Results showed that the proposed hybrid sigmoid SMC-MPC approach effectively lowered the initial drug dosage requirements by 30%. Whereas, the reduction in final steady state dosage has been reduced by upto 70% while reducing the convergence time of viral load by 14%. Similarly, the convergence time of healthy CD4+ T cell count, to the desired reference level, has been reduced by 26.8%. These results indicate favorable algorithmic performance within the considered simulation framework.