Analysis and Control of Perturbed Density Systems

The paper investigates dynamical systems for which the derivative of a positive-definite function along the solutions of these systems depends on a density function. In turn, such dynamical systems are called density systems. The density function influences the solutions of these systems by determining the density of the space in which systems evolve. It can also describe regions where there are no system solutions. The density function is used to design a new adaptive control law for systems with unknown parameters and disturbances, where we formulate control goals such as stabilization within given bounded or semi-bounded sets. All theoretical results and conclusions are illustrated by numerical simulations and experiments, and are also compared with existing methods.