Model-free tuning of plants with parasitic dynamics

Abstract

Abstract-We have recently considered the problem of tuning a static plant described by a differentiable input-output function, which is completely unknown, but whose Jacobian takes values in a known polytope of matrices: to drive the output to a given desired value, we have suggested an integral feedback scheme, whose convergence is ensured if the polytope of matrices is robustly full row rank. The suggested tuning scheme may fail in the presence of parasitic dynamics, which may destabilize the loop if the tuning action is too aggressive. Here we show that such tuning action can be applied to dynamic plants as well if it is sufficiently "slow", a property that we can ensure by limiting the integral action. We provide robust bounds based on the exclusive knowledge of the largest time constant and of the matrix polytope to which the system Jacobian is known to belong. We also provide similar bounds in the presence of parasitic dynamics affecting the actuators.

Model-Free Practical Cooperative Control for Diffusively Coupled Systems

“…Therefore, there has been an increasing interest in what is called data-driven controller design. There have been different approaches to data-driven controller design very generally (see, e.g., [15], [16]), and some approaches to multi-agent control from data more particularly [17]- [19]. Nonetheless, the centralized nature of the general design schemes, or the specificity of the agents' model and high measurement rate for the multi-agent approaches, prevents the application of many of the aforementioned approaches in various real-world scenarios.…”