Solomon Goldgraber Casspi

Solomon Goldgraber Casspi, Oliver Husser, Guy Revach et al. · eth-zurich

Stochastic control deals with finding an optimal control signal for a dynamical system in a setting with uncertainty, playing a key role in numerous applications. The linear quadratic Gaussian (LQG) is a widely-used setting, where the system dynamics is represented as a linear Gaussian statespace (SS) model, and the objective function is quadratic. For this setting, the optimal controller is obtained in closed form by the separation principle. However, in practice, the underlying system dynamics often cannot be faithfully captured by a fully known linear Gaussian SS model, limiting its performance. Here, we present LQGNet, a stochastic controller that leverages data to operate under partially known dynamics. LQGNet augments the state tracking module of separation-based control with a dedicated trainable algorithm. The resulting system preserves the operation of classic LQG control while learning to cope with partially known SS models without having to fully identify the dynamics. We empirically show that LQGNet outperforms classic stochastic control by overcoming mismatched SS models.

Solomon Goldgraber Casspi, Daniel Zelazo

This letter presents a geometric input-output analysis of distance-based formation control, focusing on the phenomenon of steady-state signal blocking between actuator and sensor pairs. We characterize steady-state multivariable transmission zeros, where fully excited rigid-body and deformational modes destructively interfere at the measured output. By analyzing the DC gain transfer matrix of the linearized closed-loop dynamics, we prove that for connected, flexible frameworks, structural transmission zeros are strictly non-generic; the configuration-dependent cross-coupling required to induce them occupies a proper algebraic set of measure zero. However, because extracting actionable sensor-placement rules from these complex algebraic varieties is analytically intractable, we restrict our focus to infinitesimally rigid formations. For these baselines, we prove that the absence of internal flexes forces the zero-transmission condition to collapse into an explicit affine hyperplane defined by the actuator and the global formation geometry, which we term the spatial locus of transmission zeros. Finally, we introduce the global transmission polygon--a convex polytope constructed from the intersection of these loci. This construct provides a direct geometric synthesis rule for robust sensor allocation, guaranteeing full-rank steady-state transmission against arbitrary single-node excitations.