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Dissipativity properties have proven to be very valuable for systems analysis and controller design. With the rising amount of available data, there has, therefore, been an increasing interest in determining dissipativity properties from (measured) trajectories directly, while an explicit model of the system remains undisclosed. Most existing approaches for data-driven dissipativity, however, guarantee the dissipativity condition only over a finite-time horizon and provide weak or no guarantees on robustness in the presence of noise. In this article, we present a framework for verifying dissipativity properties from measured data with desirable guarantees. We first consider the case of input-state measurements, where we provide computationally attractive conditions in the presence of process noise. We extend this approach to input–output data, where similar results hold in the noise-free case, and finally provide results for the case of noisy input–output trajectories. [ABSTRACT FROM AUTHOR]

In this article, we develop a data-based controller design framework for diffusively coupled systems with guaranteed convergence to an $\epsilon$ -neighborhood of the desired formation. The controller is composed of a fixed controller with an adjustable gain on each edge. Via passivity theory and network optimization, we not only prove that there exists a gain attaining the desired formation control goal, but we present a data-based method to find an upper bound on this gain. Furthermore, by allowing for additional experiments, the conservatism of the upper bound can be reduced via iterative sampling schemes. The introduced scheme is based on the assumption of passive systems, which we relax by discussing different methods for estimating the systems’ passivity shortage, as well as applying transformations passivizing them. Finally, we illustrate the developed model-free cooperative control scheme with a case study. [ABSTRACT FROM AUTHOR]

Due to their relevance in controller design, we consider the problem of determining the L2-gain, passivity properties, and conic relations of an input–output system. While, in practice, the input–output relation is often undisclosed, input–output data tuples can be sampled by performing (numerical) experiments. Hence, we present sampling strategies for discrete time and continuous time linear time-invariant systems to iteratively determine the L2-gain, the shortage of passivity and the cone with minimal radius that the input–output relation is confined to. These sampling strategies are based on gradient dynamical systems and saddle point flows to solve the reformulated optimization problems, where the gradients can be evaluated from only input–output data samples. This leads us to evolution equations, whose convergence properties are then discussed in continuous time and discrete time. [ABSTRACT FROM AUTHOR]