arXiv subjects

Jan Komenda

Publications and source records attributed to Jan Komenda.

At least 19 recordsLinked to original sources

arXiv2025

Active prognosis and diagnosis of modular discrete-event systems

This paper addresses the verification and enforcement of prognosability and diagnosability for discreteevent systems (DESs) modeled by deterministic finite automata. We establish the equivalence between prognosability (respectively, diagnosability) and pre-normality over a subset of the non-faulty language (respectively, a suffix of the faulty language). We then demonstrate the existence of supremal prognosable (respectively, diagnosable) and normal sublanguages. Furthermore, an algorithm is then designed to compute the supremal controllable, normal, and prognosable (respectively, diagnosable) sublanguages. Since DESs are typically composed of multiple components operating in parallel, pure local supervisors are generally insufficient, as prognosability and diagnosability are global properties of a system. Given the limited work on enforcing prognosability or diagnosability in modular DESs, where these properties are enforced through local supervisors, this paper leverages a refined version of pre-normality to compute modular supervisors for local subsystems. The resulting closed-loop system is shown to be globally controllable, normal, and prognosable/ diagnosable. Examples are provided to illustrate the proposed method.

eess.SY↗

arXiv2023

Coordination Control of Discrete Event Systems under Cyber Attacks

In this paper, coordination control of discrete event systems under joint sensor and actuator attacks is investigated. Sensor attacks are described by a set of attack languages using a proposed ALTER model. Several local supervisors are used to control the system. The goal is to design local supervisors to ensure safety of the system even under cyber attacks (CA). The necessary and sufficient conditions for the existence of such supervisors are derived in terms of conditional decomposability, CA-controllability and CA-observability. A method is developed to calculate local state estimates under sensor attacks. Two methods are also developed to design local supervisors, one for discrete event systems satisfying conditional decomposability, CA-controllability and CA-observability, and one for discrete event systems satisfying conditional decomposability only. The approach works for both stealthy and non-stealthy attacks. A practical example is given to illustrate the results.

eess.SY↗

arXiv2023

Switched max-plus linear-dual inequalities: cycle time analysis and applications

P-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows. Their dynamics can be represented by max-plus linear-dual inequalities (LDIs), i.e., systems of linear dynamical inequalities in the primal and dual operations of the max-plus algebra. We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operation, each corresponding to a set of LDIs, according to a sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the considered schedule is fixed and either periodic or intermittently periodic. We show that SLDIs can model a wide range of applications including single-robot multi-product processing networks, in which every product has different processing requirements and corresponds to a specific mode of operation. Based on the analysis of SLDIs, we propose algorithms to compute: i. minimum and maximum cycle times for these processes, improving the time complexity of other existing approaches; ii. a complete trajectory of the robot including start-up and shut-down transients.

eess.SY↗

arXiv2023

Conditions for Hierarchical Supervisory Control under Partial Observation

The fundamental problem in hierarchical supervisory control under partial observation is to find conditions preserving observability between the original (low-level) and the abstracted (high-level) plants. Two conditions for observable specifications were identified in the literature -- observation consistency (OC) and local observation consistency (LOC). However, the decidability of OC and LOC were left open. We show that both OC and LOC are decidable for regular systems. We further show that these conditions do not guarantee that supremal (normal or relatively observable) sublanguages computed on the low level and on the high level always coincide. To solve the issue, we suggest a new condition -- modified observation consistency -- and show that under this condition, the supremal normal sublanguages are preserved between the levels, while the supremal relatively observable high-level sublanguage is at least as good as the supremal relatively observable low-level sublanguage, i.e., the high-level solution may be even better than the low-level solution.

eess.SY↗

arXiv2023

Hierarchical Supervisory Control under Partial Observation: Normality

Conditions preserving observability of specifications between the plant and its abstraction are essential for hierarchical supervisory control of discrete-event systems under partial observation. Observation consistency and local observation consistency were identified as such conditions. To preserve normality, only observation consistency is required. Although observation consistency preserves normality between the levels for normal specifications, for specifications that are not normal, observation consistency is insufficient to guarantee that the supremal normal sublanguage computed on the low level and on the high level coincide. We define modified observation consistency, under which the supremal normal sublanguages of different levels coincide. We show that the verification of (modified) observation consistency is PSPACE-hard for finite automata and undecidable for slightly more expressive models than finite automata. Decidability of (modified) observation consistency is an open problem. Hence we further discuss two stronger conditions that are easy to verify. Finally, we illustrate the conditions on an example of a railroad controller and on a case study of a part of an MRI scanner.

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arXiv2023

Supervisory Control of Modular Discrete-Event Systems under Partial Observation: Normality

Complex systems are often composed of many small communicating components called modules. We investigate the synthesis of supervisory controllers for modular systems under partial observation that, as the closed-loop system, realize the supremal normal sublanguage of the specification. We call such controllers maximally permissive normal supervisors. The challenge in modular systems is to find conditions under which the global nonblocking and maximally permissive normal supervisor can be achieved locally as the parallel composition of local normal supervisors. We show that a structural concept of hierarchical supervisory control called modified observation consistency (MOC) is such a condition. However, the algorithmic verification of MOC is an open problem, and therefore it is necessary to find easily-verifiable conditions that ensure MOC. We show that the condition that all shared events are observable is such a condition. Considering specifications, we examine both local specifications, where each module has its own specification, and global specifications. We combine our results for normality with the existing results for controllability to locally synthesize the nonblocking and maximally permissive controllable and normal supervisor. Finally, we illustrate the results on an industrial case study of the patient table of an MRI scanner.

cs.FL↗

arXiv2022

Switched Max-Plus Linear-Dual Inequalities: Application in Scheduling of Multi-Product Processing Networks

P-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows. Their dynamics can be represented by systems of linear dynamical inequalities in the max-plus algebra and its dual, the min-plus algebra, referred to as max-plus linear-dual inequalities (LDIs). We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operations, each corresponding to an LDI, according to an infinite sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the schedule is fixed and periodic. We show that SLDIs can model single-robot multi-product processing networks, in which every product has different processing requirements and corresponds to a specific mode of operation. Based on the analysis of SLDIs, we propose an algorithm to compute minimum and maximum cycle times for these processes that improves the time complexity of other existing approaches.

eess.SY↗

arXiv2021

Supervisory Control of Multi-Agent Discrete-Event Systems with Partial Observation

In this paper we investigate multi-agent discrete-event systems with partial observation. The agents can be divided into several groups in each of which the agents have similar (isomorphic) state transition structures, and thus can be relabeled into the same template. Based on the template a scalable supervisor whose state size and computational cost are independent of the number of agents is designed for the case of partial observation. The scalable supervisor under partial observation does not need to be recomputed regardless of how many agents are added to or removed from the system. We generalize our earlier results to partial observation by proposing sufficient conditions for safety and maximal permissiveness of the scalable least restrictive supervisor on the template level. An example is provided to illustrate the proposed scalable supervisory synthesis.

eess.SY↗

arXiv2021

Periodic trajectories in P-time event graphs and the non-positive circuit weight problem

P-time event graphs (P-TEGs) are specific timed discrete-event systems, in which the timing of events is constrained by intervals. An important problem is to check, for all natural numbers $d$, the existence of consistent $d$-periodic trajectories for a given P-TEG. In graph theory, the Proportional-Inverse-Constant-Non-positive Circuit weight Problem (PIC-NCP) consists in finding all the values of a parameter such that a particular parametric weighted directed graph does not contain circuits with positive weight. In a related paper, we have proposed a strongly polynomial algorithm that solves the PIC-NCP in lower worst-case complexity compared to other algorithms reported in literature. In the present paper, we show that the first problem can be formulated as an instance of the second; consequently, we prove that the same algorithm can be used to find $d$-periodic trajectories in P-TEGs. Moreover, exploiting the connection between the PIC-NCP and max-plus algebra we prove that, given a P-TEG, the existence of a consistent 1-periodic trajectory of a certain period is a necessary and sufficient condition for the existence of a consistent $d$-periodic trajectory of the same period, for any value of $d$.

cs.DS↗

arXiv2021

The non-positive circuit weight problem in parametric graphs: a solution based on dioid theory

Let us consider a parametric weighted directed graph in which every arc $(j,i)$ has weight of the form $w((j,i))=\max(P_{ij}+\lambda,I_{ij}-\lambda,C_{ij})$, where $\lambda$ is a real parameter and $P$, $I$ and $C$ are arbitrary square matrices with elements in $\mathbb{R}\cup\{-\infty\}$. In this paper, we design an algorithm that solves the Non-positive Circuit weight Problem (NCP) on this class of parametric graphs, which consists in finding all values of $\lambda$ such that the graph does not contain circuits with positive weight. This problem, which generalizes other instances of the NCP previously investigated in the literature, has applications in the consistency analysis of a class of discrete-event systems called P-time event graphs. The proposed algorithm is based on max-plus algebra and formal languages, and improves the worst-case complexity of other existing approaches, achieving strongly polynomial time complexity $\mathcal{O}(n^4)$ (where $n$ is the number of nodes in the graph).

math.CO↗

arXiv2020

Analysis of P-time Event Graphs in (Max,+) and (Min,+) Algebras

In this work we investigate the behavior of P-time event graphs, a class of time Petri nets with nondeterministic timing of places. Our approach is based on combined linear descriptions in both (max,+) and (min,+) semirings, where lower bounds on the state vector are (max,+)-linear and upper bounds are (min,+)-linear. We present necessary and sufficient conditions for the existence of extremal (fastest and slowest) periodic trajectories that are derived from the new description. The results are illustrated by a realistic example of an electroplating process.

eess.SY↗

arXiv2019

A Uniform Approach to Maximal Permissiveness in Modular Control of Discrete-Event Systems

In this paper, a uniform approach to maximal permissiveness in modular control of discrete-event systems is proposed. It is based on three important concepts of modular closed-loops: monotonicity, distributivity, and exchangeability. Monotonicity of various closed-loops satisfying a given property considered in this paper holds whenever the underlying property is preserved under language unions. Distributivity holds if the inverse projections of local plants satisfy the given property with respect to each other. Among new results, sufficient conditions are proposed for distributed computation of supremal relatively observable sublanguages.

eess.SY↗

arXiv2017

Computation of Controllable and Coobservable Sublanguages in Decentralized Supervisory Control via Communication

In decentralized supervisory control, several local supervisors cooperate to accomplish a common goal (specification). Controllability and coobservability are the key conditions to achieve a specification in the controlled system. We construct a controllable and coobservable sublanguage of the specification by using additional communications between supervisors. Namely, we extend observable events of local supervisors via communication and apply a fully decentralized computation of local supervisors. Coobservability is then guaranteed by construction. Sufficient conditions to achieve the centralized optimal solution are discussed. Our approach can be used for both prefix-closed and non-prefix-closed specifications.

math.OC↗

arXiv2016

On a Distributed Computation of Supervisors in Modular Supervisory Control

In this paper, we discuss a supervisory control problem of modular discrete-event systems that allows for a distributed computation of supervisors. We provide a characterization and an algorithm to compute the supervisors. If the specification does not satisfy the properties, we make use of a relaxation of coordination control to compute a sublanguage of the specification for which the supervisors can be computed in a distributed way.

math.OC↗

arXiv2015

Combined Top-down and Bottom-up Approach to Multilevel Supervisory Control

Recently, we have proposed two complementary approaches, top-down and bottom-up, to multilevel supervisory control of discrete-event systems. In this paper, we compare and combine these approaches. The combined approach has strong features of both approaches, namely, a lower complexity of the top-down approach with the generality of the bottom-up approach. We show that, for prefix-closed languages, a posteriori supervisors computed in the bottom-up manner do not alter maximal permissiveness within the three-level coordination control architecture, that is, the supremal three-level conditionally-controllable and conditionally-normal language can always be computed in a distributed way using multilevel coordination. Moreover, a general polynomial-time procedure for non-prefix closed case is proposed based on coordinators for nonblockingness and a posteriori supervisors.

math.OC↗

arXiv2015

A Relaxed Framework for Coordination Control of Discrete-Event Systems

In this paper, we simplify the coordination control approach by removing the supervisor for the coordinator from the closed-loop system and relax the restrictions placed on a coordinator. This relaxation results in the simplification of the whole coordination control framework, including the notions of conditional controllability, conditional observability, and conditional normality. Compared to our previous work, the role of the supervisor on a coordinator alphabet is postponed until the final stage of the coordination control synthesis. This completes and clarifies our previous results, while all the fundamental theorems remain valid in the relaxed framework. Unlike previous approaches we can always compute a conditionally controllable sublanguage without any restricting conditions we have used before.

math.OC↗

arXiv2014

A Note on Relative Observability in Coordination Control

Relative observability has been introduced and studied in the framework of partially observed discrete-event systems as a condition stronger than observability, but weaker than normality. However, unlike observability, relative observability is closed under language unions, which makes it interesting for practical applications. In this paper, we investigate this notion in the framework of coordination control. We prove that conditional normality is a stronger condition than conditional (strong) relative observability, hence conditional strong relative observability can be used in coordination control instead of conditional normality, and present a distributive procedure for the computation of a conditionally controllable and conditionally observable sublanguage of the specification that contains the supremal conditionally strong relative observable sublanguage.

math.OC↗

arXiv2014

Decentralized Supervisory Control with Communicating Supervisors Based on Top-Down Coordination Control

In this paper we present a new approach to decentralized supervisory control of large automata with communicating supervisors. We first generalize the recently developed top-down architecture of multilevel coordination control with a hierarchical structure of groups of subsystems, their respective coordinators and supervisors. Namely, in the case where the equivalent conditions for achieving a specification language fail to be satisfied, we propose sufficient conditions for a distributed computation of the supremal achievable sublanguage. We then apply the obtained constructive results of multilevel coordination control to decentralized supervisory control with communication, where local supervisors of subsystems within a group communicate with each other via the coordinator of the group. Our approach is illustrated by an example.

math.OC↗