Tejaswi K. C.

Tejaswi K. C., Srikant Sukumar, Ravi Banavar

The notion of feedback integrators permits Euclidean integration schemes for dynamical systems evolving on manifolds. Here, a constructive Lyapunov function for the attitude dynamics embedded in an ambient Euclidean space has been proposed. We then combine the notion of feedback integrators with the proposed Lyapunov function to obtain a feedback law for the attitude control system. The combination of the two techniques yields a domain of attraction for the closed loop dynamics, where earlier contributions were based on linearization ideas. Further, the analysis and synthesis of the feedback scheme is carried out entirely in Euclidean space. The proposed scheme is also shown to be robust to numerical errors.

Kaito Iwasaki, Tejaswi K. C., Anthony Bloch et al.

Stochastic hybrid systems combine continuous-time stochastic dynamics with discrete reset events, producing intrinsically non-Gaussian and often multimodal uncertainty. A consistent propagation law must also account for boundary-induced probability flux across guard sets, making direct density propagation through hybrid Fokker-Planck equations expensive. We develop a hybrid extension of the Max-Entropy Moment Kalman Filter (MEM-KF) that performs filtering from partial statistical information by propagating a finite collection of moments through stochastic hybrid dynamics and reconstructing beliefs using moment-constrained maximum-entropy distributions. The key step is a moment propagation rule derived from Dynkin's formula with a jump-sum, in which reset effects appear as a boundary-flux correction over the guard set. This yields tractable moment dynamics without solving the underlying hybrid PDE. In a stochastic bouncing-ball example, the proposed method captures reset-induced non-Gaussianity through corrected moment equations while retaining the MEM-KF's optimization-based maximum-entropy representation.

Tejaswi K. C., Taeyoung Lee

This paper studies probability density evolution for stochastic hybrid systems with reset maps that change the dimension of the continuous state across modes. Existing Frobenius--Perron formulations typically represent reset-induced probability transfer through boundary conditions, which is insufficient when resets map guard sets into the interior or onto lower-dimensional subsets of another mode. We develop a weak-form formulation in which reset-induced transfer is represented by the pushforward of probability flux across the guard, yielding a unified description for such systems. The proposed framework naturally captures both cases: when the reset decreases dimension, the transferred probability appears as an interior source density, whereas when the reset increases dimension, it generally appears as a singular source supported on a lower-dimensional subset. The approach is illustrated using a stochastic hybrid model in which two particles merge into one and later split back into two, demonstrating how dimension-changing resets lead to source terms beyond classical boundary-condition-based formulations.