Related papers: Proofs for an Abstraction of Continuous Dynamical …
Model checking of temporal logics in a well established technique to verify and validate properties of multi-agent systems (MAS). However, practical model checking requires input models of manageable size. In this paper, we extend the model…
Timed automata have been introduced by Rajeev Alur and David Dill in the early 90's. In the last decades, timed automata have become the de facto model for the verification of real-time systems. Algorithms for timed automata are based on…
Abstract interpretation is a method to automatically find invariants of programs or pieces of code whose semantics is given via least fixed-points. Up-to techniques have been introduced as enhancements of coinduction, an abstract principle…
There is an apparent similarity between the descriptions of small-step operational semantics of imperative programs and the semantics of finite automata, so defining an abstraction mapping from semantics to automata and proving a simulation…
We prove that (local) input-to-state stability ((L)ISS) and integral input-to-state stability (iISS) of time-varying infinite-dimensional systems in abstract spaces follows from the existence of a {corresponding} Lyapunov function. In…
We address the stability problem for linear switching systems with mode-dependent restrictions on the switching intervals. Their lengths can be bounded as from below (the guaranteed dwell-time) as from above. The upper bounds make this…
Stability analysis plays a crucial role in studying the behavior of dynamical systems with theoretical and engineering applications. Among various kinds of stability, the stability of equilibrium points is of the greatest importance which…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
Finite-state models of control systems were proposed by several researchers as a convenient mechanism to synthesize controllers enforcing complex specifications. Most techniques for the construction of such symbolic models have two main…
Abstraction is one of the most important strategies for dealing with the state space explosion problem in model checking. In the abstract model, although the state space is largely reduced, however, a counterexample found in such a model…
We obtain sufficient conditions for the stability of the synchronized solutions for a class of coupled dynamical systems. This is accomplished by finding an analytical expression for the transverse Liapunov exponent through spectral…
While the utility of well-chosen abstractions for understanding and predicting the behaviour of complex systems is well appreciated, precisely what an abstraction $\textit{is}$ has so far has largely eluded mathematical formalization. In…
Structured recursion schemes such as folds and unfolds have been widely used for structuring both functional programs and program semantics. In this context, it has been customary to implement denotational semantics as folds over an…
We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in…
Generalized planning studies the computation of general solutions for a set of planning problems. Computing general solutions with correctness guarantee has long been a key issue in generalized planning. Abstractions are widely used to…
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…
Can simple algorithms with a good representation solve challenging reinforcement learning problems? In this work, we answer this question in the affirmative, where we take "simple learning algorithm" to be tabular Q-Learning, the "good…
Partially Observable Markov Decision Process (POMDP) is widely used to model probabilistic behavior for complex systems. Compared with MDPs, POMDP models a system more accurate but solving a POMDP generally takes exponential time in the…
For data-driven control of nonlinear systems, the basis functions characterizing the dynamics are usually essential. In existing works, the basis functions are often carefully chosen based on pre-knowledge of the dynamics so that the system…
The identification and modeling of time-varying systems is a fundamental challenge in signal processing and system identification. To address this challenge, we propose a class of time-varying state-space model (SSM) based neural networks…