Practical stability of approximating discrete-time filters with respect to model mismatch using relative entropy concepts

This paper establishes practical stability results for an important range of approximate discrete-time filtering problems involving mismatch between the true system and the approximating filter model. Using local consistency assumption, the practical stability established is in the sense of an asymptotic bound on the amount of bias introduced by the model approximation. Significantly, these practical stability results do not require the approximating model to be of the same model type as the true system. Our analysis applies to a wide range of estimation problems and justifies the common practice of approximating intractable infinite dimensional nonlinear filters by simpler computationally tractable filters.

Removal of toxic arsenic and antimony from groundwater Spiro Tunnel Bulkhead in Park City Utah using colloidal iron hydroxide : comparison with reverse ssmosis

Verification testing of two model technologies in pilot scale to remove arsenic and antimony based on reverse osmosis and chemical coagulation/filtration systems was conducted in Spiro Tunnel Water Filtration Plant located in Park City, Utah, US. The source water was groundwater in abandoned silver mine, naturally contaminated by 60-80 ppb of arsenic and antimony below 10 ppb. This water represents one of the sources of drinking water for Park City and constitutes about 44% of the water supply. The failure to remove antimony efficiently by coagulation/filtration (only 4.4% removal rate) under design conditions is discussed in terms of the chemistry differences between Sb (III, V) and As (III, V). Removal of Sb(V) at pH > 7, using coagulation/filtration technology, requires much higher (50 to 80 times) concentration of iron (III) than As. The stronger adsorption of arsenate over a wider pH range can be explained by the fact that arsenic acid is tri-protic, whereas antimonic acid is monoprotic. This difference in properties of As(V) and Sb(V) makes antimony (V) more difficult to be efficiently removed in low concentrations of iron hydroxide and alkaline pH waters, especially in concentration of Sb < 10 ppb.

Practical stability with respect to model mismatch of approximate discrete-time output feedback control

This paper establishes a practical stability result for discrete-time output feedback control involving mismatch between the exact system to be stabilised and the approximating system used to design the controller. The practical stability is in the sense of an asymptotic bound on the amount of error bias introduced by the model approximation, and is established using local consistency properties of the systems. Importantly, the practical stability established here does not require the approximating system to be of the same model type as the exact system. Examples are presented to illustrate the nature of our practical stability result.