Robust Decentralized Control of Systems of Random Structure

摘要

Complex control systems represented by a family of stochastic differential equations with state dependent noises are considered. Each equation of the family describes the dynamics of the control object in a certain mode. In this case, the object itself consists of a set of interconnected subsystems. The mode change proceeds in accordance with the evolution of a homogeneous Markovian chain. At the instant of the mode change, the state vector of the object can vary in a jumplike way. The robust decentralized control is found as a family of local feedbacks that are switched simultaneously with jumps in the Markovian chain. This control ensures the exponentially mean-square stability (EMSS) of a closed-loop system for fixed noise levels and for any transition probabilities of the Markovian chain (mode changes) from a specified domain. Moreover, the complete robust control in such a switching decentralized form providing the exponentially mean-square stability regardless of the probability of the mode changes is found. In a particular case, when the state vector of the object varies without jumps, such control has a simpler switchless form.