Lyapunov-based output-feedback distributed control of systems on lattices

We study output-feedback control of systems on lattices with spatially distributed sensing and actuating capabilities. These systems are encountered in a wide range of modern applications such as: platoons of vehicles, arrays of microcantilevers, unmanned aerial vehicles in formation, and satellites in synchronous orbit. We use a Lyapunov-based framework as a tool for stabilization/regulation of systems in which nonlinearities depend only on the distributed output variable. We first present results for nominal design and then describe the design of adaptive output-feedback controllers in the presence of parametric uncertainties. These uncertainties are assumed to be temporally constant, but are allowed to be spatially varying. We show that our design yields the distributed controllers that inherit the information passing structure from the original plant. We also provide several examples of systems on lattices and validate derived results using computer simulations of systems containing a large number of units.