Many important practical problems require a control system to be able to auto-matically, efficiently, and accurately detect changes in dynamical systems that the controlsystem is monitoring. In some instances, public safely is involved. Well-known examplesinclude analysis of seismic data to detect earthquakes, analysis of radar data in aircraftnavigation, and monitoring of activities in chemical plants.

The SIGEST paper in this issue, “A Nonlinear Filtering Approach to ChangepointDetection Problems: Direct and Differential-Geometric Methods” by M. H. Vellekoopand J. M. C. Clark, from the SIAM Journal on Control and Optimization, significantly ad-vances the state of the art in this area. In particular, it considers the problem of onlinedetection of parameter changes in dynamical systems, when the data are noisy, andwhen both the time of the change and the size of the change are unknown a priori. Theproblem of changepoint detection in dynamical systems on the basis of noisy observa-tions has been well studied in cases when only one of these two factors is unknown. Itcan be solved by the Shiryayev–Wonham equation if the value after the change is knowna priori, or by a Kalman filter if the time of the change is known a priori. But whenboth are unknown, the problem turns out to be much more difficult.

Vellekoop and Clark use differential-geometric methods to derive an approxi-mate, suboptimal filter for solving this challenging changepoint detection problem. Themethod they derive draws upon both of the approaches mentioned above. In theirwords, their new nonlinear filter can be interpreted as an adaptive version of theShiryayev–Wonham equation for the detection of a priori known changes, combinedwith a modified Kalman filer structure to generate estimates of the unknown size ofthe change.

The paper includes excellent mathematics, as well as nicely presented and readilyunderstandable simulation results that compare the performance of the proposed newfilters to more exact but computationally expensive approaches. These results indicatethat the proposed new filters may be quite useful in practice. We hope that SIAM Reviewreaders enjoy this fascinating glimpse into state-of-the-art research in optimal control.

The Editors

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