Adaptive Control for Compartmental Dynamical Systems with Disturbance Rejection Guarantees

Compartmental system models involve dynamic states whose values are nonnegative. These models are widespread in biological and physiological sciences and play a key role in understanding these processes. In this paper, we develop a direct adaptive control framework for compartmental dynamical systems with exogenous bounded disturbances. The proposed framework is Lyapunov-based and guarantees partial asymptotic stability of the closed-loop system, that is, asymptotic stability with respect to part of the closed loop system states associated with the plant dynamics. The remainder of the states associated with the adaptive gains are shown to be Lyapunov stable. Finally, in the case of bounded energy L₂ disturbances the proposed approach guarantees a non-expansivity constraint on the closed-loop input-output map.