Department of Electrical and Computer Engineering
University of Minnesota
In this talk, we investigate the properties of systems on lattices with spatially distributed sensors and actuators. These systems arise in a variety of applications ranging from the macroscopic (e.g., cross directional paper machine processes, automated highway systems, unmanned aerial vehicle formations, and satellite constellations), to the microscopic (e.g., arrays of micro-cantilevers for massively parallel data storage). The key design issues in the control of such systems are architectural, such as the choice of localized versus centralized control.
In the first part of the talk, we describe how backstepping can be utilized as a tool for distributed control of nonlinear systems on lattices. We demonstrate that distributed backstepping design yields controllers that are intrinsically decentralized, with a strong similarity between plant and controller architectures, and quantify the number of control induced interactions necessary to guarantee desired dynamical behavior.
In the second part of the talk, we investigate some fundamental limitations and tradeoffs in the control of vehicular platoons. We reveal ill-posedness inherent in several widely cited results in this area and show how to formulate well-posed control problems. By considering infinite platoons as limits of large-but-finite platoons, we establish analytically how these formulations lack stabilizability or detectability. Our results indicate that the infinite dimensional systems with dynamical symmetries represent a useful abstraction of the large scale systems that is more amenable to analysis.