INFORMATION AND COMPLEXITY IN CONTROL SYSTEMS: A TUTORIAL

1 IntroductionPhysical systems differ greatly in their sizes, structtires, compositions and operations. Consequently, quatiflcation and comparison of system complexities at physical levels are far beyondthe domain of control systems and information science. Systems theory studies physical systems from a generic and information poillt of view: Systems are regarded as plats that processsignals and information, regardless the underlying physical realizations. This paper will explore complealty i…

INFORMATION AND COMPLEXITY IN CONTROL SYSTEMS: A TUTORIAL

This is a tutorial paper which presents schematically the concepts of information, uncertainty, and complexity, and their relationships in their applications to control systems. By focusing on exact or lower bounds on achievable performance in the presence of uncertainties, studies of complexity in a control system can potentially reveal fundamentally limiting factors of the system, suggest beneficial modifications to system structures and hardware configurations to remove these limitations, provide benchmark values for evaluating a design and for quantifying rooms for performance improvement, and demonstrate intrinsic tradeoffs. Compared to its counterparts in communications (Shannon's information theory), computations (computational complexity and information-based complexity), and approxima- tions (n-widths and Kolmogorov entropy), studies of information and complexity in control systems encounter further challenges, such as characterization of feedback robustness, interaction between identification and control, and co-existence of deterministic and stochastic uncertainties. Some of these issues are outlined and discussed.