Robust p53 recovery using chattering free sliding mode control and a gain-scheduled modified Utkin observer

p53 protein plays an essential role in protecting the genomic integrity of mammalian cells. A drastic decrease in the amount of p53 protein has been observed in cancerous cells. By using Nutlin-based small molecule drugs, the concentration of p53 can be restored to the desired level. This paper presents the drug-dosage design for p53 pathway, based on a control-oriented nonlinear model. A chattering free sliding mode control (CFSMC) strategy is employed to track the desired trajectory of p53 concentration for both of its dynamic behaviors, i.e., sustained and oscillatory responses. A gain-scheduled modified Utkin observer (GSMUO) is designed for robust state reconstruction and disturbance estimation. The simulation results show that CFSMC and GSMUO exhibit desired robustness and performance properties in the presence of parametric variations, an input disturbance and measurement noise. Moreover, a comprehensive simulation study, along with a detailed quantitative analysis is performed to compare CFSMC-GSMUO with four different techniques: a sliding mode control (SMC) with an equivalent control based sliding mode observer (SMO) and GSMUO, respectively, and a dynamic sliding mode control (DSMC) with SMO and GSMUO, respectively. The analysis demonstrates that the tracking error and utilization of the control energy is the least in the case of CFSMC-GSMUO as compared to its counterparts.