Augmented invariance control for systems with smoothness constraints

Abstract

In many applications, the controlled dynamical system is subject to constraints, e.g. to enforce a desired performance. There are various methods, which guarantee the enforcement of such constraints. They do, however, not provide satisfactory solutions if the system state has to exhibit certain smoothness properties. This work presents a novel method of designing a control input, which guarantees the adherence to constraints as well as a desired smoothness of the system state. The control scheme is implemented as an add-on to an existing task dependent control law. Augmentation of the dynamical system achieves a desired smoothness of the state whereas methods from invariance control are utilized to guarantee constraint enforcement.

Shared invariance control for constraint satisfaction in multi-robot systems

“…This assumption is imposed for convenience of notation and poses no additional restrictions on the systems, because the relative degree may be increased, if necessary, by augmented invariance control as introduced for general systems by Kimmel et al (2016) and for robotic systems by Jähne and Hirche (2017). Note that for robotic systems with position constraints, for example, the assumption is naturally fulfilled as the relative degree equals two for all agents.…”