Control of a class of patterned systems

Abstract

ABSTRACTEngineering systems are often architected to consist of a number of interconnected parts that interact in distinct patterns. Because most control design methods only provide general, unpatterned control laws, a compelling open question is how to synthesise distributed control laws that adhere to a system's interconnection pattern. This paper addresses patterned control synthesis for systems with interconnection patterns. The pattern is encoded algebraically through commuting relationships of the system's state space matrices. We show that several classic control problems are amenable to a patterned synthesis. Moreover, we show that these patterned control problems have the same solvability conditions as their unpatterned counterparts. That is, a patterned control law can be found whenever any control law can be found. Our findings suggest that patterned systems naturally admit patterned controllers.