A computational method for boundary estimation and control via the sequentially semi separable approach

Recent work has shown that many types of distributed system with distributed actuators and sensors have state space realizations with “Sequentially Semi Separable” (SSS) structure. The special properties of the SSS arithmetic allow the analysis and synthesis of controllers with similarly distributed architecture, with arbitrarily small loss of optimality, in linear computational complexity (in the number of subsystems) for systems interconnected on a line. However, in spite of the current popularity in research on distributed actuators and sensors, and consensus algorithms, many estimation and control problems for distributed systems in practice are limited by the high cost of sensors and actuators, and hence are limited to boundary sensing, boundary actuation, or both. In this paper, we show how to fit boundary actuation and sensing problems into the SSS structure, allowing the use of the aforementioned powerful and fast analysis and synthesis methods. We then demonstrate on a few examples the results of this approach, and discuss characteristics of other examples on which it will work well.