MS16.2: Control and Synchronization in Nonlinear Systems

Fourier series-based method of control optimization effectively tackles the optimal control problem in non-smooth mechanical systems characterized by discontinuities from dry friction or impacts. However, the current optimization procedure employs evolutionary algorithm, which may not ensure enhanced system efficiency with an increasing number of harmonics K. To address this limitation, this paper introduces a developed, iterative approach to the method. The aim is to maintain, at least, non-decreasing quality of solutions in successive iterations during the optimization procedure. The proposed approach is tested on a discontinuous capsule drive, and a comparative analysis is conducted with the previous approach (non-iterative). It is anticipated that this work will enable progress in control optimization of systems, for which typical approaches cannot be utilized.

While safety is often critical for nonlinear systems, guaranteeing safety should not hinder their performance drastically. Various approaches have been considered in the literature to achieve both safety and performance for nonlinear systems by means of control, and the use of safety filters has been gaining traction thanks to its flexibility. The safety filter safeguards an already well-tuned performance-based controller by minimal intervention only when necessary such that a safety constraint is satisfied. A convenient tool to establish this safety constraint is control barrier functions (CBFs), which provide the formal safety guarantees for the underlying nonlinear dynamics through a Lyapunov-like condition. The accuracy of the CBF-based safety constraint may reduce in the presence of uncertainty in the system model such as external disturbances. In this manuscript, we discuss the design steps of a robust safety filter, which leads to an easy-to-implement and easy-to-interpret control scheme to provide safety for nonlinear systems under uncertainty. We take a worst-case type of approach to accommodate bounded disturbances, and we use a modification to mitigate the unnecessary conservativeness. Concepts are demonstrated and evaluated on a example with a swing.

This talk discusses the synchronization problem in time-varying networks of nonlinear QUAD systems. In particular, we attempt to derive a sufficient condition for synchronization without using information about the possible network structures in a case where at least one system is directly connected to all other systems in the network, even if not simultaneously. Defining one system that can connect with all other systems as the target system and focusing on the synchronization error between the system and other systems, we consider the synchronization problem as the stability problem of the origin of the synchronization error dynamics. Then, we derive a sufficient condition for synchronization in the form of linear matrix inequalities. The obtained condition uses information on only the possible degree of node corresponding to each system but does not require information about the entire graph structure. The validity of the obtained condition will be illustrated with a numerical example in this talk.