An Informational Perspective on Uncertainty in Control
summary
Analyzes multiplicative uncertainty in actuation vs sensing, proving for scalar actuation noise BN IID that linear control is optimal for second-moment and that maximum stabilizable growth rate A equals a simple control capacity formula based on log(μB/σB); distribution shape only matters for moments beyond second. Shows erasure noise can give unbounded decay, contrasts with sensing-side multiplicative noise where linear strategies are provably suboptimal and a simple nonlinear hack strictly outperforms them, though a converse bound (via stability-in-probability and density arguments) leaves a large achievability gap. Vector cases and side-information gains (lookahead about drops) remain open and practically important.
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chapters (9)
- 0:00Introduction to control
- 1:21System parameters uncertainty
- 4:13Sources of uncertainty
- 7:53Actuation side uncertainty
- 16:52Stability in probability
- 22:38Information in control
- 28:11Sensing side uncertainty
- 33:17Side information impact
- 41:25Q&A and conclusion
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