Control of Positive Systems with an Unknown State-Dependent Power Law Input Delay and Input Saturation

TL;DR

This paper develops a control method for positive systems with unknown, state-dependent delays and saturation, demonstrated on a biological model to improve treatment outcomes.

Contribution

It introduces a novel control law that compensates for unknown delays and saturation in positive systems, with stability analysis and practical biological application.

Findings

Controller achieves stable reference tracking

Numerical simulations show improved performance

Application to a human coagulation model demonstrates potential clinical benefits

Abstract

This paper is motivated by a class of positive systems with an input that is subject to an unknown state-dependent power law delay as well as saturation. For example, biological networks have non-negative protein concentration states. Mass action kinetics in these systems result in power law behavior, while complex interactions cause signal propagation delays. Incomplete network characterization makes delay state-dependence unknown. Manipulating network activity via modulated protein concentrations to attain desired performance is restricted by upper-bounds on concentration actuator authority. Here, an innovative control law exploits system dynamics to compensate for control domain restrictions. A Lyapunov stability analysis establishes that the reference tracking error of the closed-loop system is uniformly ultimately bounded. Numerical simulations on a human coagulation model show controller efficacy and better performance compared to the relevant literature. This example application steps toward personalized, closed-loop treatments for trauma coagulopathy, which currently has 30% mortality with open-loop clinical approaches.