Constrained Control of Semilinear Fractional-Order Systems: Application in Drug Delivery Systems

This paper proposes an approach to control fractional-order semilinear systems which are subject to linear constraints. The design procedure consists of two stages. First, a linear state-feedback control law is proposed to prestabilize the system in the absence of constraints. The stability and convergence properties are proved using Lyapunov theory. Then, a constraint-handling unit is utilized to enforce the constraints at all times. In particular, we use the Explicit Reference Governor (ERG) scheme. The core idea behind ERG is, first, to translate the linear constraints into a constraint on the value of the Lyapunov function, and then to manipulate the auxiliary reference such that the Lyapunov function is smaller than a threshold value at all times. The proposed method is applied in a drug delivery system to control the drug concentration, and its performance is assessed through extensive simulation results.