Passive feedback control for nonlinear systems

Abstract: Dynamical systems can be used to model a broad class of physical processes, and conservation laws give rise to system properties like passivity or port-Hamiltonian structure. An important problem in practical applications is to steer dynamical systems to prescribed target states, and feedback controllers combining a regulator and an observer are a powerful tool to do so. However, controllers designed using classical methods do not necessarily obey energy principles, which makes it difficult to model the controller-plant interaction in a structured manner. In this paper, we show that a particular choice of the observer gain gives rise to passivity properties of the controller that are independent of the plant structure. Furthermore, we state conditions for the controller to have a port-Hamiltonian realization and show that a model order reduction scheme can be deduced using the framework of nonlinear balanced truncation. In addition, we propose a novel passivity preserving discrete gradient scheme for the time discretization of passive systems. To illustrate our results, we numerically realize the controller using the policy iteration and compare it to a controller where the observer gain is given by the extended Kalman filter.