An Excursion-Theoretic Approach to Stability of Discrete-Time Stochastic Hybrid Systems

An Excursion-Theoretic Approach to Regulator's Bank Reorganization Problem

The importance of the global financial system cannot be exaggerated. When a large financial institution becomes problematic and is bailed out, that bank is often claimed as "too big to fail". On the other hand, to prevent bank's failure, regulatory authorities adopt the Prompt Corrective Action (PCA) against a bank that violates certain criteria, often measured by its leverage ratio. In this article, we provide a framework where one can analyze the cost and effect of PCA's. We model a large bank with deteriorating asset and regulatory actions attempting to prevent a failure. The model uses the…

The Koopman Expectation: An Operator Theoretic Method for Efficient Analysis and Optimization of Uncertain Hybrid Dynamical Systems

For dynamical systems involving decision making, the success of the system greatly depends on its ability to make good decisions with incomplete and uncertain information. By leveraging the Koopman operator and its adjoint property, we introduce the Koopman Expectation, an efficient method for computing expectations as propagated through a dynamical system. Unlike other Koopman operator-based approaches in the literature, this is possible without an explicit representation of the Koopman operator. Furthermore, the efficiencies enabled by the Koopman Expectation are leveraged for optimization u…

Hybrid Angle Control and Almost Global Stability of Non-synchronous Hybrid AC/DC Power Grids

This paper explores the stability of nonsynchronous hybrid ac/dc power grids under the grid-forming hybrid angle control strategy. We formulate dynamical models for the ac grids and transmission lines, interlinking converters, and dc generations and interconnections. Next, we establish the existence and uniqueness of the closed-loop equilibria for the overall system. Subsequently, we demonstrate global attractivity of the equilibria, local asymptotic stability of the desired equilibrium point, and instability and zero-Lebesgue-measure region of attraction for other equilibria. The theoretic re…

通过张力到推力前馈实现被动容错：用于突发缆线断裂下分布式多无人机吊挂运输的混合输入到状态稳定性

Passive Fault Tolerance through Tension-to-Thrust Feed-Forward: Hybrid Input-to-State Stability for Decentralized Multi-UAV Slung-Load Transport under Abrupt Cable Severance

本文提出一种被动架构，通过将每个无人机测量的缆线张力直接输入到其高度推力指令中，以实现突发缆线断裂下的分布式多无人机吊挂运输的混合输入到状态稳定性。