Related papers: Tropical Abstractions of Max-Plus-Linear Systems
Designing controllers to satisfy temporal requirements has proven to be challenging for dynamical systems that are affected by uncertainty. This is mainly due to the states evolving in a continuous uncountable space, the stochastic…
Abstraction is a desirable capability for deep learning models, which means to induce abstract concepts from concrete instances and flexibly apply them beyond the learning context. At the same time, there is a lack of clear understanding…
In this paper, we propose a compositional approach for the construction of finite abstractions (a.k.a. finite Markov decision processes (MDPs)) for networks of discrete-time stochastic control subsystems that are not necessarily…
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be…
Finite-state abstractions (a.k.a. symbolic models) present a promising avenue for the formal verification and synthesis of controllers in continuous-space control systems. These abstractions provide simplified models that capture the…
We propose a compositional approach for constructing abstractions of general Markov decision processes using approximate probabilistic relations. The abstraction framework is based on the notion of $\delta$-lifted relations, using which one…
Linear Time Invariant (LTI) systems are ubiquitous in control applications. Unbounded-time reachability analysis that can cope with industrial-scale models with thousands of variables is needed. To tackle this problem, we use abstract…
Scheduling communication traffic in networks of event-triggered control (ETC) systems is challenging, as their sampling times are unknown, hindering application of ETC in networks. In previous work, finite-state abstractions were created,…
This paper is concerned with a compositional approach for constructing both infinite (reduced-order models) and finite abstractions (a.k.a. finite Markov decision processes (MDPs)) of large-scale interconnected discrete-time stochastic…
In this note, we propose a novel technique to reduce the algorithmic complexity of neural network training by using matrices of tropical real numbers instead of matrices of real numbers. Since the tropical arithmetics replaces…
In this paper we study the convergence of the max-consensus protocol. Tropical algebra is used to formulate the problem. Necessary and sufficient conditions for convergence of the max-consensus protocol over fixed as well as switching…
This paper investigates one-step backward reachability for uncertain max-plus linear systems with additive disturbances. Given a target set, the problem is to compute the set of states from which there exists an admissible control input…
Abstraction of Markov Decision Processes is a useful tool for solving complex problems, as it can ignore unimportant aspects of an environment, simplifying the process of learning an optimal policy. In this paper, we propose a new algorithm…
A class of queueing networks which may have an arbitrary topology, and consist of single-server fork-join nodes with both infinite and finite buffers is examined to derive a representation of the network dynamics in terms of max-plus…
This paper introduces a compositional framework for constructing finite abstractions of nonlinear interconnected impulsive systems using dissipativity-based conditions. Central to our approach is the concept of "alternating simulation…
In this paper, we provide a compositional approach for constructing finite abstractions (a.k.a. finite Markov decision processes (MDPs)) of interconnected discrete-time stochastic switched systems. The proposed framework is based on a…
Max-plus equations are derived from tropically discretized Sel'kov model via ultradiscretization. These max-plus equations possess common dynamical structures with the discretized model: Neimark-Sacker bifurcation and limit cycles. The…
Recent analysis of classical algorithms resulted in their axiomatization as transition systems satisfying some simple postulates, and in the formulation of the Abstract State Machine Theorem, which assures us that any classical algorithm…
Abstraction is essential for reducing the complexity of systems across diverse fields, yet designing effective abstraction methodology for probabilistic models is inherently challenging due to stochastic behaviors and uncertainties. Current…
We consider abstraction-based design of output-feedback controllers for non-linear dynamical systems against specifications over state-based predicates in linear-time temporal logic (LTL). In this context, our contribution is two-fold: (I)…