Modular Sign Compensation Solves MIMO Control Direction Uncertainty

Controlling multiple-input multiple-output (MIMO) systems is notoriously difficult when the direction of each control input is unknown or time-varying—a common issue in robotics, aerospace, and industrial automation. Existing methods like Nussbaum gains or monitoring functions often introduce unbounded signals or require complex adaptive mechanisms. In a new arXiv preprint, Gutiérrez-Oribio and Stefanou from the University of [implied] propose a modular sign-compensation layer that acts as an outer wrapper around any nominal controller. The key insight: by only toggling the sign of each control input (plus or minus) using bounded switches, the wrapper can recover the exact nominal closed-loop behavior once the correct sign configuration is found. This means the original control magnitude and stability properties are preserved throughout the search process.

The authors develop two scheduling strategies for exploring sign configurations. The vector scheduler assigns each input channel its own adaptive variable—built from nominal Lyapunov quantities—and provides an online trapping certificate that ensures the system stays bounded while searching. The scalar pattern scheduler uses a single variable to sequentially visit all possible diagonal sign matrices, offering a design-time recovery guarantee provided that sign-constant intervals are sufficiently long. Once the correct signs are locked in, the real system behaves identically to the nominal one. The approach is validated on three diverse benchmarks: an aircraft roll-reversal problem (aerospace), a visual-servoing task (robotics), and an underground reservoir control example aimed at mitigating human-induced seismicity (geotechnical engineering), demonstrating its broad applicability.