SIGEST

Abstract

Many important practical problems require a control system to be able to automatically, efficiently, and accurately detect changes in dynamical systems that the control system is monitoring. In some instances, public safely is involved. Well-known examples include analysis of seismic data to detect earthquakes, analysis of radar data in aircraft navigation, and monitoring of activities in chemical plants. The SIGEST paper in this issue, “A Nonlinear Filtering Approach to Changepoint Detection Problems: Direct and Differential-Geometric Methods” by M. H. Vellekoop and J. M. C. Clark, from the SIAM Journal on Control and Optimization, significantly advances the state of the art in this area. In particular, it considers the problem of online detection of parameter changes in dynamical systems, when the data are noisy, and when both the time of the change and the size of the change are unknown a priori. The problem of changepoint detection in dynamical systems on the basis of noisy observations has been well studied in cases when only one of these two factors is unknown. It can be solved by the Shiryayev–Wonham equation if the value after the change is known a priori, or by a Kalman filter if the time of the change is known a priori. But when both are unknown, the problem turns out to be much more difficult. Vellekoop and Clark use differential-geometric methods to derive an approximate, suboptimal filter for solving this challenging changepoint detection problem. The method they derive draws upon both of the approaches mentioned above. In their words, their new nonlinear filter can be interpreted as an adaptive version of the Shiryayev–Wonham equation for the detection of a priori known changes, combined with a modified Kalman filer structure to generate estimates of the unknown size of the change. The paper includes excellent mathematics, as well as nicely presented and readily understandable simulation results that compare the performance of the proposed new filters to more exact but computationally expensive approaches. These results indicate that the proposed new filters may be quite useful in practice. We hope that SIAM Review readers enjoy this fascinating glimpse into state-of-the-art research in optimal control.