Sensing Cost in Optimal Control: Engineers Can Now Optimize Sensor Use

A new paper by Tran, Ngo, and Das presents multiple formulations for integrating the cost of sensing into optimal control frameworks for Linear Time-Invariant (LTI) systems. The core idea is to treat sensing duration and sensor expenses as variables to be optimized alongside traditional control costs (like energy and stabilization). By applying Pontryagin's Minimum Principle, the authors derive optimal sensing intervals that minimize a combined cost function. The work extends to nonlinear systems and provides a reduced-form expression for infinite-horizon multi-dimensional systems with a single switching point. For the first-order infinite-horizon case, a closed-form solution is obtained.

The practical relevance is demonstrated through a real-world wastewater treatment plant case study. The Shrinking Horizon method is introduced to handle uncertainties and enable real-time implementation. This approach could significantly impact fields like autonomous systems, robotics, IoT, and industrial control—anywhere sensor usage has a non-negligible cost. By optimizing when to sense (rather than assuming continuous sensing), engineers can reduce power consumption, extend sensor lifespan, and lower operational costs without sacrificing control performance.