Filtering and control performance bounds with implications on asymptotic separation

✍ Scribed by Donald L. Snyder; Ian B. Rhodes

• Publisher: Elsevier Science
• Year: 1972
• Tongue: English
• Weight: 634 KB
• Volume: 8
• Category: Article
• ISSN: 0005-1098
• DOI: 10.1016/0005-1098(72)90085-4

✦ Synopsis

Lower bounds can be derived on the error covariance in causally filtering from various nonlinear observation formats, including doubly-stochastic Poisson processes. These lead to performance bounds and conditions for asymptotic separation in stochastic control problems.

Summary--A bound is derived on the accuracy in causally estimating a Gaussian process from nonlinear observations. Both additive Gaussian noise and Poisson observations are included. The bound is used to study the control of a stochastic linear dynamical system with nonlinear observations of either type and an average quadratic cost. An asymptotic Separation Theorem is established showing that a linear feedback control law, involving a state estimate, is asymptotically optimum as the accuracy of the state estimate approaches the bound.