6 papers
On the Second-Order Positive Burgers' Equation: Integrability, Lax Pair, Darboux Transformations, and Lie Symmetry Reduction
Suman Pal, Prasanta chatterjee
This paper derives the second-order positive Burgers' equation from the standard Burgers' hierarchy to explore its complete integrability and exact analytical solutions. We constru…
Exact Moment Estimation of Stochastic Differential Dynamics
Shenghua Feng, Jie An, Naijun Zhan +1
Moment estimation for stochastic differential equations (SDEs) is fundamental to the formal reasoning and verification of stochastic dynamical systems, yet remains challenging and…
Piecewise Analysis of Probabilistic Programs via -Induction
Tengshun Yang, Shenghua Feng, Hongfei Fu +3
In probabilistic program analysis, quantitative analysis aims at deriving tight numerical bounds for probabilistic properties such as expectation and assertion probability. Most pr…
On Completeness of SDP-Based Barrier Certificate Synthesis over Unbounded Domains
Hao Wu, Shenghua Feng, Ting Gan +3
Barrier certificates, serving as differential invariants that witness system safety, play a crucial role in the verification of cyber-physical systems (CPS). Prevailing computation…
Switching Controller Synthesis for Hybrid Systems Against STL Formulas
Han Su, Shenghua Feng, Sinong Zhan +1
Switching controllers play a pivotal role in directing hybrid systems (HSs) towards the desired objective, embodying a ``correct-by-construction'' approach to HS design. Identifyin…
Reset Controller Synthesis by Reach-avoid Analysis for Delay Hybrid Systems
Han Su, Jiyu Zhu, Shenghua Feng +5
A reset controller plays a crucial role in designing hybrid systems. It restricts the initial set and redefines the reset map associated with discrete transitions, in order to guar…