Control Capacity
| Autor: | Anant Sahai, Gireeja Ranade |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
FOS: Computer and information sciences
Information Theory (cs.IT) Computer Science - Information Theory Linear system Scalar (physics) Systems and Control (eess.SY) Library and Information Sciences Information theory 01 natural sciences 010305 fluids & plasmas Computer Science Applications Moment (mathematics) 010104 statistics & probability Control theory Control system 0103 physical sciences FOS: Electrical engineering electronic engineering information engineering Computer Science - Systems and Control Limit (mathematics) 0101 mathematics Eigenvalues and eigenvectors Computer Science::Information Theory Communication channel Mathematics Information Systems |
| Zdroj: | IEEE Transactions on Information Theory. 65:235-254 |
| ISSN: | 1557-9654 0018-9448 |
| Popis: | Feedback control actively dissipates uncertainty from a dynamical system by means of actuation. We develop a notion of "control capacity" that gives a fundamental limit (in bits) on the rate at which a controller can dissipate the uncertainty from a system, i.e. stabilize to a known fixed point. We give a computable single-letter characterization of control capacity for memoryless stationary scalar multiplicative actuation channels. Control capacity allows us to answer questions of stabilizability for scalar linear systems: a system with actuation uncertainty is stabilizable if and only if the control capacity is larger than the log of the unstable open-loop eigenvalue. For second-moment senses of stability, we recover the classic uncertainty threshold principle result. However, our definition of control capacity can quantify the stabilizability limits for any moment of stability. Our formulation parallels the notion of Shannon's communication capacity, and thus yields both a strong converse and a way to compute the value of side-information in control. The results in our paper are motivated by bit-level models for control that build on the deterministic models that are widely used to understand information flows in wireless network information theory. 52 pages |
| Databáze: | OpenAIRE |
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