This paper addresses the problem of estimating upper bounds on the probability that a dynamical system will enter an undesirable region at some point within a finite time horizon. The primary source of uncertainty lies in the system's initial state, for which only a finite set of moments is known or within a prescribed interval. To tackle this problem, we formulate a measure-based program and propose its relaxation using the moment-sum-of-squares (moment-SOS) framework. The corresponding dual problem is introduced as a functional program, which is subsequently strengthened into a sum-of-squares (SOS) program. Notably, this dual formulation bears a structural resemblance to classical barrier function techniques for certifying system safety, with the key distinction that it yields a probabilistic certificate. The effectiveness of the proposed approach is demonstrated through multiple case studies, including a case involving an object in orbit.
Signal Temporal Logic control synthesis frequently encounters physical infeasibility due to actuator limits or flawed task deadlines. Standard optimization methods model time by discretizing the horizon, which leads to exponential computational growth and prevents the extraction of continuous temporal adjustments. This...
Robust optimization under interval uncertainty aims to compute solutions that perform well on a range of scenarios that are described by interval-constrained costs. In this paper, we revisit a framework introduced by Ganesh, Maggs and Panigrahi in 2020 to study the robust optimization of NP-hard problems under interval...
This paper focuses on the joint non-fragile state and fault estimation issue for a class of stochastic nonlinear systems under the dynamic event-triggered transmission scheme (DETS). To better conform to practical engineering scenarios, we consider an additive fault whose second-order difference is piecewise zero. A ze...
Xue-Gang Tian, Shao-Ying Wang, Kai-Fu Jiang et al.· International Journal of Net...· 0 citations
Constrained optimization is central to many engineering systems in which decisions must satisfy strict safety and operational requirements, especially in real-time settings with limited computational budgets. In such scenarios, optimization algorithms are often terminated before full convergence, making *anytime feasib...
Sina Sharifi, Jiarui Wang, Mahyar Fazlyab· 0 citations
Data-driven techniques have shown promising potential for checking behavior of complex systems operating in safety-critical domains against safety and other temporal requirements. This paper studies a class of data-driven techniques that are based on learning a representation of the system from data using non-parametri...
This work addresses the computation of extreme values of observables along trajectories of dynamical systems over an \ks{infinite time horizon}. The setting is intrinsically global: trajectories may exhibit large transient excursions, approach their largest values only asymptotically as time tends to infinity, or escap...
Karolína Sehnalová, Milan Korda· 0 citations
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