MS16.4: Control and Synchronization in Nonlinear Systems

The path-following control of automated vehicles is analyzed in the presence of large disturbances. The global dynamics of three controller variations are analyzed using phase portraits, illustrating the domain of attraction of stable path-following, the presence of possible steady state solutions and the transient response of the system. A globally stable control law is proposed, which removes all unwanted steady state solutions, guaranteeing stable path-following regardless of initial conditions and disturbances.

We consider the problem of optimizing the interconnection graphs of complex networks to enhance synchronization. In instances where traditional optimization methods prove impractical due to uncertain or unknown node dynamics, we advocate for a data-driven approach that exploits available datasets containing pertinent examples. We consider two representative case studies, one featuring linear and the other nonlinear node dynamics. We explored different design strategies and discovered that the most effective ones either rely on using knowledge from examples close to a specific Pareto front or employ a combination of a neural network and a genetic algorithm. Notably, these strategies exhibit statistically superior performance compared to the best examples within the datasets.

This note focuses on the analysis of emergent behaviors in networks of dynamical systems, where their interations are of activation-type locally and inhibitory-type in the long-range. Such interplay between activation and inhibition is reminiscent of the classical formula for oscillations in lumped systems, i.e., local positive feedback and long-range negative feedback. Dominance tools are used for the analysis of the resulting behavior, obtaining certificates in the form of linear matrix inequalities which allows to study the existence of emergent static pattern or oscillations in the network. A numerical example illustrates the proposed approach.

Extremum-seeking control is a purely data-based performance optimization strategy for dynamical systems. Typical extremum seeking approaches rely on applying perturbations to tunable system parameters and measuring the corresponding system output, to determine a suitable search direction aimed at optimizing steady-state performance. While in practical applications performing measurements may be costly or time-consuming, these measurement data are typically discarded after a single parameter update step. To make more efficient use of these valuable data, we propose a novel extremum-seeking control approach that uses the data to construct an online approximation of the system’s steady-state performance map, instead of discarding them. By using this approximation to determine the search direction and update step size whenever the approximation is deemed sufficiently accurate, the total number of measurements needed to optimize performance is significantly reduced, as shown in an illustrative example.