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Kai Cai

Publications and source records attributed to Kai Cai.

At least 37 records · Page 2Linked to original sources
arXiv2021

Local Opacity Verification for Distributed Discrete Event Systems

This paper studies current-state opacity and initial-state opacity verification of distributed discrete event systems. The distributed system's global model is the parallel composition of multiple local systems: each of which represents a component. We propose sufficient conditions for verifying opacity of the global system model based only on the opacity of the local systems. We also present efficient approaches for the opacity verification problem that only rely on the intruder's observer automata of the local systems.

eess.SY↗
arXiv2021

$ω-$nonblocking supervisory control of discrete-event systems with infinite behavior

In the supervisory control framework of discrete-event systems (DES) with infinite behavior initiated by Thistle and Wonham, a supervisor satisfying the minimal acceptable specification and the maximal legal specification is synthesized. However, this supervisor may incur livelocks as it cannot ensure that the infinite behavior under supervision will always visit some marker states. To tackle this problem, we propose the definition of markability by requiring that all infinite cycles include at least one marker state. Then we formulate the problem of $ω-$nonblocking supervisory control of DES with infinite behavior to synthesize an $ω-$nonblocking (i.e. nonblocking, deadlock-free and livelock-free) supervisor. An algorithm is proposed to achieve $ω-$nonblockingness by computing the supremal $*-$controllable, $*-$closed, $ω-$controllable and markable sublanguage. We utilize the example of a robot as a running example.

eess.SY↗
arXiv2021

Usability Aware Secret Protection with Minimum Cost

In this paper we study a cybersecurity problem of protecting system's secrets with multiple protections and a required security level, while minimizing the associated cost due to implementation/maintenance of these protections as well as the affected system usability. The target system is modeled as a discrete-event system (DES) in which there are a subset of marker states denoting the services/functions provided to regular users, a subset of secret states, and multiple subsets of protectable events with different security levels. We first introduce usability-aware cost levels for the protectable events, and then formulate the security problem as to ensure that every system trajectory that reaches a secret state contains a specified number of protectable events with at least a certain security level, and the highest usability-aware cost level of these events is minimum. We first provide a necessary and sufficient condition under which this security problem is solvable, and when this condition holds we propose an algorithm to solve the problem based on the supervisory control theory of DES. Moreover, we extend the problem to the case of heterogeneous secrets with different levels of importance, and develop an algorithm to solve this extended problem. Finally, we demonstrate the effectiveness of our solutions with a network security example.

eess.SY↗
arXiv2020

Distributed Dual Gradient Tracking for Resource Allocation in Unbalanced Networks

This paper proposes a distributed dual gradient tracking algorithm (DDGT) to solve resource allocation problems over an unbalanced network, where each node in the network holds a private cost function and computes the optimal resource by interacting only with its neighboring nodes. Our key idea is the novel use of the distributed push-pull gradient algorithm (PPG) to solve the dual problem of the resource allocation problem. To study the convergence of the DDGT, we first establish the sublinear convergence rate of PPG for non-convex objective functions, which advances the existing results on PPG as they require the strong-convexity of objective functions. Then we show that the DDGT converges linearly for strongly convex and Lipschitz smooth cost functions, and sublinearly without the Lipschitz smoothness. Finally, experimental results suggest that DDGT outperforms existing algorithms.

eess.SP↗
arXiv2020

Real-time estimation of the optically detected magnetic resonance shift in diamond quantum thermometry

We investigate the real-time estimation protocols for the frequency shift of optically detected magnetic resonance (ODMR) of nitrogen-vacancy (NV) centers in nanodiamonds (NDs). Efficiently integrating multipoint ODMR measurements and ND particle tracking into fluorescence microscopy has recently demonstrated stable monitoring of the temperature inside living animals. We analyze the multipoint ODMR measurement techniques (3-, 4-, and 6-point methods) in detail and quantify the amount of measurement artifact owing to several systematic errors derived from instrumental errors of experimental hardware and ODMR spectral shape. We propose a practical approach to minimize the effect of these factors, which allows for measuring accurate temperatures of single NDs during dynamic thermal events. We also discuss integration of noise filters, data estimation protocols, and possible artifacts for further developments in real-time temperature estimation. The present study provides technical details of quantum diamond thermometry and discusses factors that may affect the temperature estimation in biological applications.

physics.app-ph↗
arXiv2019

Distributed Robust Output Regulation of Heterogeneous Uncertain Linear Agents by Adaptive Internal Model Principle

We study a multi-agent output regulation problem, where not all agents have access to the exosystem's dynamics. We propose a fully distributed controller that solves the problem for linear, heterogeneous, and uncertain agent dynamics as well as time-varying directed networks. The distributed controller consists of two parts: (1) an exosystem generator that locally estimates the exosystem dynamics, and (2) a dynamic compensator that, by locally approaching the internal model of the exosystem, achieves perfect output regulation. Moreover, we extend this distributed controller to solve an output synchronization problem where not all agents initially have the same internal model dynamics. Our approach leverages methods from internal model based controller synthesis and multi-agent consensus over time-varying directed networks; the derived result is a generalization of the (centralized) internal model principle to the distributed, networked setting.

eess.SY↗
arXiv2019

Secret Securing with Multiple Protections and Minimum Costs

In this paper we study a security problem of protecting secrets with multiple protections and minimum costs. The target system is modeled as a discrete-event system (DES) in which a few states are secrets, and there are multiple subsets of protectable events with different cost levels. We formulate the problem as to ensure that every string that reaches a secret state (from the initial state) contains a specified number of protectable events and the highest cost level of these events is minimum. We first provide a necessary and sufficient condition under which this security problem is solvable, and then propose an algorithm to solve the problem based on the supervisory control theory of DES. The resulting solution is a protection policy which specifies at each state which events to protect and the highest cost level of protecting these events is minimum. Finally, we demonstrate the effectiveness of our solution with a network security example.

eess.SY↗
arXiv2019

Supervisor Localization of Timed Discrete-Event Systems under Partial Observation and Communication Delay

We study supervisor localization for timed discrete-event systems under partial observation and communication delay in the Brandin-Wonham framework. First, we employ timed relative observability to synthesize a partial-observation monolithic supervisor; the control actions of this supervisor include not only disabling action of prohibitible events (as that of controllable events in the untimed case) but also "clock-preempting" action of forcible events. Accordingly we decompose the supervisor into a set of partial-observation local controllers one for each prohibitible event, as well as a set of partial-observation local preemptors one for each forcible event. We prove that these local controllers and preemptors collectively achieve the same controlled behavior as the partial-observation monolithic supervisor does. Moreover, we propose channel models for inter-agent event communication and impose bounded and unbounded delay as temporal specifications. In this formulation, there exist multiple distinct observable event sets; thus we employ timed relative coobservability to synthesize partial-observation decentralized supervisors, and then localize these supervisors into local controllers and preemptors. The above results are illustrated by a timed workcell example.

eess.SY↗
arXiv2018

On Scalable Supervisory Control of Multi-Agent Discrete-Event Systems

In this paper we study multi-agent discrete-event systems where the agents can be divided into several groups, and within each group the agents have similar or identical state transition structures. We employ a relabeling map to generate a "template structure" for each group, and synthesize a scalable supervisor whose state size and computational process are independent of the number of agents. This scalability allows the supervisor to remain invariant (no recomputation or reconfiguration needed) if and when there are agents removed due to failure or added for increasing productivity. The constant computational effort for synthesizing the scalable supervisor also makes our method promising for handling large-scale multi-agent systems. Moreover, based on the scalable supervisor we design scalable local controllers, one for each component agent, to establish a purely distributed control architecture. Three examples are provided to illustrate our proposed scalable supervisory synthesis and the resulting scalable supervisors as well as local controllers.

eess.SY↗
arXiv2018

A 3D Hydrodynamics Study of Gravitational Instabilities in a Young Circumbinary Disc

We present a 3D hydrodynamics study of gravitational instabilities (GIs) in a 0.14 M$_{\odot}$ circumbinary protoplanetary disc orbiting a 1 M$_{\odot}$ star and a 0.02 M$_{\odot}$ brown dwarf companion. We examine the thermodynamical state of the disc and determine the strengths of GI-induced density waves, nonaxisymmetric density structures, mass inflow and outflow, and gravitational torques. Results are compared with a parallel simulation of a protoplanetary disc without the brown dwarf binary companion. Simulations are performed using CHYMERA, a radiative 3D hydrodynamics code. The onset of GIs in the circumbinary disc is much more violent due to the stimulation of a strong one-armed density wave by the brown dwarf. Despite this early difference, detailed analyses show that both discs relax to a very similar quasi-steady phase by 2,500 years after the beginning of the simulations. Similarities include the thermodynamics of the quasi-steady phase, the final surface density distribution, radial mass influx, and nonaxisymmetric power and torques for spiral arm multiplicities of two or more. Effects of binarity in the disc are evident in gravitational torque profiles, temperature profiles in the inner discs, and radial mass transport. After 3,800 years, the semimajor axis of the binary decreases by about one percentage and the eccentricity roughly doubles. The mass transport in the outer circumbinary disc associated with the one-armed wave may influence planet formation.

astro-ph.SR↗
arXiv2018

Supervisor Localization of Discrete-Event Systems under Partial Observation

Recently we developed supervisor localization, a top-down approach to distributed control of discrete-event systems. Its essence is the allocation of monolithic (global) control action among the local control strategies of individual agents. In this paper, we extend supervisor localization by considering partial observation; namely not all events are observable. Specifically, we employ the recently proposed concept of relative observability to compute a partial-observation monolithic supervisor, and then design a suitable localization procedure to decompose the supervisor into a set of local controllers. In the resulting local controllers, only observable events can cause state change. Further, to deal with large-scale systems, we combine the partial-observation supervisor localization with an efficient architectural synthesis approach: first compute a heterarchical array of partial-observation decentralized supervisors and coordinators, and then localize each of these supervisors/coordinators into local controllers.

eess.SY↗
arXiv2018

An Optimization Approach to the Langberg-Médard Multiple Unicast Conjecture

The Langberg-Médard multiple unicast conjecture claims that for any strongly reachable $k$-pair network, there exists a multi-flow with rate $(1,1,\dots,1)$. In a previous work, through combining and concatenating the so-called elementary flows, we have constructed a multi-flow with rate at least $(\frac{8}{9}, \frac{8}{9}, \dots, \frac{8}{9})$ for any $k$. In this paper, we examine an optimization problem arising from this construction framework. We first show that our previous construction yields a sequence of asymptotically optimal solutions to the aforementioned optimization problem. And furthermore, based on this solution sequence, we propose a perturbation framework, which not only promises a better solution for any $k \mod 4 \neq 2$ but also solves the optimization problem for the cases $k=3, 4, \dots, 10$, accordingly yielding multi-flows with the largest rate to date.

cs.IT↗
arXiv2017

Supervisor Localization of Discrete-Event Systems with Infinite Behavior

Recently we developed supervisor localization, a top-down approach to distributed control of discrete-event systems (DES) with finite behavior. Its essence is the allocation of monolithic (global) control action among the local control strategies of individual agents. In this report, we extend supervisor localization to study the distributed control of DES with infinite behavior. Specifically, we first employ Thistle and Wonham's supervisory control theory for DES with infinite behavior to compute a safety supervisor (for safety specifications) and a liveness supervisor (for liveness specifications), and then design a suitable localization procedure to decompose the safety supervisor into a set of safety local controllers, one for each controllable event, and decompose the liveness supervisor into a set of liveness local controllers, two for each controllable event. The localization procedure for decomposing the liveness supervisor is novel; in particular, a local controller is responsible for disabling the corresponding controllable event on only part of the states of the liveness supervisor, and consequently, the derived local controller in general has states number no more than that computed by considering the disablement on all the states. Moreover, we prove that the derived local controllers achieve the same controlled behavior with the safety and liveness supervisors. We finally illustrate the result by a Small Factory example.

eess.SY↗
arXiv2017

Supervisor Localization for Large-Scale Discrete-Event Systems under Partial Observation

Recently we developed partial-observation supervisor localization, a top-down approach to distributed control of discrete-event systems (DES) under partial observation. Its essence is the decomposition of the partial-observation monolithic supervisor into partial-observation local controllers for individual controllable events. In this paper we extend the partial-observation supervisor localization to large-scale DES, for which the monolithic supervisor may be incomputable. Specifically, we first employ an efficient heterarchical supervisor synthesis procedure to compute a heterarchical array of partial-observation decentralized supervisors and partial-observation coordinators. Then we localize each of these supervisors/coordinators into partial-observation local controllers. This procedure suggests a systematic approach to the distributed control of large-scale DES under partial observation. The results are illustrated by a system of automatic guided vehicles (AGV) serving a manufacturing workcell.

eess.SY↗
arXiv2017

Top-Down Synthesis of Multi-Agent Formation Control: An Eigenstructure Assignment based Approach

We propose a top-down approach for formation control of heterogeneous multi-agent systems, based on the method of eigenstructure assignment. Given the problem of achieving scalable formations on the plane, our approach globally computes a state feedback control that assigns desired closed-loop eigenvalues/eigenvectors. We characterize the relation between the eigenvalues/eigenvectors and the resulting inter-agent communication topology, and design special (sparse) topologies such that the synthesized control may be implemented locally by the individual agents. Moreover, we present a hierarchical synthesis procedure that significantly improves computational efficiency. Finally, we extend the proposed approach to achieve rigid formation and circular motion, and illustrate these results by simulation examples.

eess.SY↗
arXiv2016

On Sequential Locally Repairable Codes

We consider the locally repairable codes (LRC), aiming at sequential recovering multiple erasures. We define the (n,k,r,t)-SLRC (Sequential Locally Repairable Codes) as an [n,k] linear code where any t'(>= t) erasures can be sequentially recovered, each one by r (2<=r =3 erasures and bounds to evaluate the performance of such codes. We first derive a tight upper bound on the code rate of (n, k, r, t)-SLRC for t=3 and r>=2. We then propose two constructions of binary (n, k, r, t)-SLRCs for general r,t>=2 (Existing constructions are dealing with t<=7 erasures. The first construction generalizes the method of direct product construction. The second construction is based on the resolvable configurations and yields SLRCs for any r>=2 and odd t>=3. For both constructions, the rates are optimal for t in {2,3} and are higher than most of the existing LRC families for arbitrary t>=4.

cs.IT↗
arXiv2016

Characterizations and Effective Computation of Supremal Relatively Observable Sublanguages

Recently we proposed relative observability for supervisory control of discrete-event systems under partial observation. Relative observability is closed under set unions and hence there exists the supremal relatively observable sublanguage of a given language. In this paper we present a new characterization of relative observability, based on which an operator on languages is proposed whose largest fixpoint is the supremal relatively observable sublanguage. Iteratively applying this operator yields a monotone sequence of languages; exploiting the linguistic concept of support based on Nerode equivalence, we prove for regular languages that the sequence converges finitely to the supremal relatively observable sublanguage, and the operator is effectively computable. Moreover, for the purpose of control, we propose a second operator that in the regular case computes the supremal relatively observable and controllable sublanguage. The computational effectiveness of the operator is demonstrated on a case study.

eess.SY↗