Separation is Optimal for LQR under Intermittent Feedback

A team of researchers from Ohio State University and Bilkent University has solved a long-standing theoretical problem in control systems. Their paper, "Separation is Optimal for LQR under Intermittent Feedback," proves that the separation principle—a fundamental concept allowing controller and estimator design to be decoupled—remains valid for Linear Quadratic Regulator problems even when feedback arrives intermittently over unreliable communication channels. This addresses a 50-year-old question about whether optimal control could be separated from scheduling decisions in resource-constrained networked systems.

The researchers demonstrated that the optimal scheduling policy follows a symmetric threshold rule based on accumulated disturbance since the last update, while the optimal controller uses a discounted linear feedback law independent of the scheduling policy. Their proof applies to systems with independent, identically distributed zero-mean disturbances having symmetric distributions. This breakthrough provides mathematical certainty for engineers designing everything from autonomous vehicle networks to industrial IoT systems where communication bandwidth is limited and feedback signals may arrive sporadically.

The implications extend across robotics, multi-agent systems, and networked control applications where minimizing communication while maintaining stability is critical. By establishing that separation remains optimal, the work validates existing heuristic approaches and provides a rigorous foundation for future algorithm development. The dynamic programming solution they derived offers practical guidance for implementing efficient threshold-based update policies that balance control performance against communication costs in real-world systems.