Distributed Coordination of Asymmetric Compartmental Systems Under Time-Varying Inputs and Its Applications

Abstract

In this paper, we present new distributed coordination for a set-point regulation of asymmetric compartmental systems under periodically time-varying external inputs. The feature of the proposed coordination is to adjust system parameters, which is directly related to interflow rate among compartments and outflow rate to environment. In contrast to symmetric compartmental systems, there is a difficulty in analysis resulted from a property of compartmental matrix in the asymmetric cases; however, we solve the problem by designing an appropriate coordination range of the system parameters. In order to compensate the time-varying effect in the inputs, we assume that the structure of the inputs is a finite Fourier series, and show that the coordination of the system parameters should have the same structure with the same frequencies. The remainder of the coordination is to determine coefficients of the Fourier series of the system parameters. We develop a distributed update law for obtaining the coefficients. We apply the distributed coordination to water irrigation systems and water distribution systems, and show the effectiveness of the proposed distributed coordination schemes through numerical simulations.