Sliding mode controller-observer pair for p53 pathway.

A significant loss of p53 protein, an anti-tumour agent, is observed in early cancerous cells. Induction of small molecules based drug is by far the most prominent technique to revive and maintain wild-type p53 to the desired level. In this study, a sliding mode control (SMC) based robust non-linear technique is presented for the drug design of a control-oriented p53 model. The control input generated by conventional SMC is discontinuous; however, depending on the physical nature of the system, drug infusion needs to be continuous. Therefore, to obtain a smooth control signal, a dynamic SMC (DSMC) is designed. Moreover, the boundedness of the zero-dynamics is also proved. To make the model-based control design possible, the unknown states of the system are estimated using an equivalent control based, reduced-order sliding mode observer. The robustness of the proposed technique is assessed by introducing input disturbance and parametric uncertainty in the system. The effectiveness of the proposed control scheme is witnessed by performing trials, revealing that the sustained level of p53 can be achieved by controlled drug administration. Moreover, a comparative quantitative analysis shows that both controllers yield similar performance. However, DSMC consumes less control energy.