Related papers: Computation of maximal reachability submodules
We consider non-monotone DR-submodular function maximization, where DR-submodularity (diminishing return submodularity) is an extension of submodularity for functions over the integer lattice based on the concept of the diminishing return…
We introduce a similarity relation between submodules of a module $M$ over a ring $R$, extending the classical notion of similarity for right ideals. Focusing on (faithfully) projective modules, we establish a sharp lower bound for the…
Reachability analysis, in general, is a fundamental method that supports formally-correct synthesis, robust model predictive control, set-based observers, fault detection, invariant computation, and conformance checking, to name but a few.…
This is a survey on the computational complexity of nonlinear mixed-integer optimization. It highlights a selection of important topics, ranging from incomputability results that arise from number theory and logic, to recently obtained…
The paper introduces a novel algorithm for computing the output admissible set of linear discrete-time systems subject to input saturation. The proposed method takes advantage of the piecewise-affine dynamics to propagate the output…
In this work, we consider the maximization of submodular functions constrained by independence systems. Because of the wide applicability of submodular functions, this problem has been extensively studied in the literature, on specialized…
We develop an algorithm for computing bounded reachability probability for hybrid systems, i.e., the probability that the system reaches an unsafe region within a finite number of discrete transitions. In particular, we focus on hybrid…
Reachable set computation is an important tool for analyzing control systems. Simulating a control system can show general trends, but a formal tool like reachability analysis can provide guarantees of correctness. Reachability analysis for…
Over-approximating the reachable sets of dynamical systems is a fundamental problem in safety verification and robust control synthesis. The representation of these sets is a key factor that affects the computational complexity and the…
In this paper a novel computational technique for finite discrete approximation of continuous dynamical systems suitable for a significant class of biochemical dynamical systems is introduced. The method is parameterized in order to affect…
The vulnerability of artificial intelligence (AI) and machine learning (ML) against adversarial disturbances and attacks significantly restricts their applicability in safety-critical systems including cyber-physical systems (CPS) equipped…
We present a practical and powerful new framework for both unconstrained and constrained submodular function optimization based on discrete semidifferentials (sub- and super-differentials). The resulting algorithms, which repeatedly compute…
In machine learning and big data, the optimization objectives based on set-cover, entropy, diversity, influence, feature selection, etc. are commonly modeled as submodular functions. Submodular (function) maximization is generally NP-hard,…
Computing tight over-approximation of reach sets of a controlled uncertain dynamical system is a common practice in verification of safety-critical cyber-physical systems (CPS). While several algorithms are available for this purpose, they…
We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the…
In this paper, we provide novel characterizations of the weakly unobservable and the strongly reachable subspaces corresponding to a given state-space system. These characterizations provide closed-form representations for the said…
Let $N$ be a submodule of a finitely generated module $M$ over a Noetherian ring. A method for the computation of the submodule generated by the envelope of $N$ is given. The relations between weakly prime submodules and their envelopes are…
We consider reachability in dynamical systems with discrete linear updates, but with fixed digital precision, i.e., such that values of the system are rounded at each step. Given a matrix $M \in \mathbb{Q}^{d \times d}$, an initial vector…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a difference between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
Control applications for cyber-physical systems must make reliably safe control decisions in the presence of continuous dynamics as well as stochastic uncertainty. Providing safety guarantees for such systems requires formal modeling and…