Anomaly detection is critical for ensuring the reliability of industrial cyber-physical systems. Identifying anomalies based on data distribution is regarded as a promising approach. However, inherent noise in data collection and complex dependencies within the underlying structure can lead to class ambiguity. This ambiguity obscures the boundary between normal data and anomalies, thereby degrading the accuracy of distribution modeling. To address this issue, we shift the distribution modeling from the data space to a latent space to mitigate ambiguity and then propose a label free anomaly detection network, named ALDM. In ALDM, a contrastive-based methods is designed to facilitate the construction of a latent space, where the margin between normal data and anomalies has been expanded. Anomalies are then discerned through embeddings using a flow-based process. Recognizing the importance of distance metrics in contrastive-based methods, we propose an adaptive approach to obtain the optimal distance metric during network training instead of presetting a fixed formula. Furthermore, to accommodate anomalies of varying durations, we propose another event-wise performance index for evaluation. Extensive evaluations on three widely used benchmarks and a newly constructed dataset demonstrate that ALDM achieves state-of-the-art detection performance across both conventional metrics and our proposed index.

This paper investigates the problem of information control in networked multi-user systems, where agents such as robots, sensors, and software entities interact via a communication network to achieve individual or shared goals. Information control involves deciding which state estimates to share or broadcast, balancing cooperation among friends and privacy from adversaries. Since each user has only partial knowledge of the system, efficient protocols for sharing relevant data to balance privacy, security, and transparency is needed. This study models multi-user systems as discrete-event systems where agents need to distinguish certain state pairs in order to perform their tasks. We systematically study and solve critical problems to address the key aspects of information control: determining the necessity of shared information, minimizing communication for security, and maximizing public information release when required. A framework that addresses private communications, public broadcasting, and adversarial dynamics, offering strategies to meet both security and transparency requirements is introduced. Solutions and algorithms are proposed to solve these problems.

This paper presents a multipath wide-bandwidth magnetic current sensor based on Hall effect. To simultaneously achieve wide bandwidth, minimal ripple and small area, the system incorporates a non-spun filter-free main path with offset elimination through a continuous-time compact auxiliary path. The auxiliary path cancels the main path offset via feedforward, alleviating the need for area-consuming blocking capacitor or DC servo loop. Therefore, the chip occupies only 1.52 mm2. To suppress ripple in the auxiliary path induced by spinning current, a ping-pong switch-capacitor (PPSC) filter is proposed which mitigates ripple by sampling and averaging in the forward path, with the system achieving a residual ripple of$4.1~{\mu }$T. Compared with the state-of-the-art Hall sensor, it achieves$5{\times }$bandwidth improvement,$2{\times }$ripple reduction while occupying$5{\times }$less area.

In a recent article, we mathematically extended conventional discrete-time finite Markov chains, characterized by an $N \times N$ transition probability matrix, to discrete-time finite fuzzy Markov chains capable of modeling fuzzy states and fuzzy events, which frequently arise in fields such as biomedicine. This advancement is built upon the theory of stochastic fuzzy discrete event systems (SFDESs) and the supervised learning algorithm for FDESs, previously published by the authors. The fuzzy Markov chain is represented by a single-event SFDES comprising $N^{2}$ FDES, each with its own occurrence probability and an associated $N \times N$ event transition matrix, which is automatically learned using the aforementioned learning algorithm. Additionally, each FDES is associated with a set of fuzzy sets that fuzzify the random variable values and are required to satisfy specific constraints. Manually designing these fuzzy sets can be challenging, especially for modelers with little or no prior knowledge of fuzzy set theory. To overcome this challenge, we develop stochastic gradient descent-based algorithms that simultaneously learn constrained Gaussian fuzzy sets and the event transition matrices. To reduce the complexity of parameter learning, the Gaussian fuzzy sets are designed such that their means are computed directly from the terminal points of the subintervals that divide the ranges of the random variables, rather than being learned. Furthermore, dependencies between the Gaussian fuzzy sets for each random variable are introduced, reducing the number of standard deviations to be learned to $N$ for all Gaussian fuzzy sets in an FDES, while the remaining standard deviations are computed based on these dependencies. In addition, we establish that these new algorithms are fully applicable to continuous-time finite fuzzy Markov chains, extending their utility to a broader range of applications. An illustrative example is provided to demonstrate the effectiveness of the learning algorithms. These new algorithms make fuzzy Markov chains more accessible to modelers, regardless of their familiarity with fuzzy sets, while enhancing the overall practicality of the approach.

Fuzzy Discrete Event Systems (FDES) extend traditional Discrete Event Systems (DES) by incorporating fuzzy logic to handle uncertainties and vagueness in system states and events. While supervisory control of FDES has been studied before, existing approaches often assume crisp distinctions between safe and unsafe states and do not consider target states. In this paper, we substantially extend the existing results in the literature by developing three new frameworks of supervisory control. First, we introduce a threshold-based safe-state supervisory control framework where fuzzy states are classified as partially safe or unsafe based on a user-defined threshold. Second, we propose a target-seeking supervisory control framework. The framework allows supervisors to select control actions that ensure the supervised system can always reach some target fuzzy states. Third, we propose a threshold-based target-seeking supervisory control framework, where target fuzzy states are subject to user-specified thresholds. For all these frameworks, we derive necessary and sufficient conditions for existence of the supervisors and develop algorithms for calculating them online. The proposed methods enhance the flexibility and applicability of FDES supervisory control, allowing complete or partial fulfillment of control targets while ensuring threshold-based safety and target seeking. This is particularly important in real-world scenarios such as medical treatment planning, where the goal is to maximize treatment effectiveness while minimizing adverse side effects.

In this paper, an RC relaxation oscillator exhibiting robust performance over an extended temperature and supply range is proposed. By incorporating a digitally-assisted calibration loop, the design eliminates the errors from switch on-resistance, comparator offset and propagation delay. Fabricated using a 180 nm bipolar-CMOS-DMOS (BCD) process technology, the oscillator operates at a frequency of 7MHz with the supply sensitivity of 870 ppm/V across a voltage range of 1.7 to 4.2 V. The evaluation of 40 untrimmed samples achieved an average temperature coefficient (TC) of 52 ppm/$^{\circ}$C from$-$40$^{\circ}$C to 165$^{\circ}$C, with the worst observed TC being 81 ppm/$^{\circ}$C. The aging test results indicate small deviations of 0.3% and 11% in the oscillation frequency and its TC, respectively. Furthermore, the direct power injection test confirms its reliability and robustness with a maximum error of oscillation frequency of 6.4%.

This paper presents a RC relaxation oscillator with wide temperature range for automotive application. By using a digitally assisted calibration loop, the comparator offset and the loop delay are efficiently cancelled. With both reference voltage and current derived from the same ΔVBE-based bias circuit, the proposed design cancels leakage currents and makes the design insensitive to high-temperature. The oscillator was fabricated in a 180 nm BCD process, the oscillator operates at 7MHz and achieves a supply sensitivity of 870 ppm/V from 1.7 to 4.2 V at room temperature. Measurements on 40 samples without trimming show that it has an average temperature coefficient of 52 ppm/°C over a wide temperature range (-40°C to 165°C), with the worst case temperature coefficient of 65 ppm/°C.

Most of existing category-level object pose estimation methods devote to learning the object category information from point cloud modality. However, the scale of 3D datasets is limited due to the high cost of 3D data collection and annotation. Consequently, the category features extracted from these limited point cloud samples may not be comprehensive. This motivates us to investigate whether we can draw on knowledge of other modalities to obtain category information. Inspired by this motivation, we propose CLIPose, a novel 6D pose framework that employs the pre-trained vision-language model to develop better learning of object category information, which can fully leverage abundant semantic knowledge in image and text modalities. To make the 3D encoder learn category-specific features more efficiently, we align representations of three modalities in feature space via multi-modal contrastive learning. In addition to exploiting the pre-trained knowledge of the CLIP’s model, we also expect it to be more sensitive with pose parameters. Therefore, we introduce a prompt tuning approach to fine-tune image encoder while we incorporate rotations and translations information in the text descriptions. CLIPose achieves state-of-the-art performance on two mainstream benchmark datasets, REAL275 and CAMERA25, and runs in real-time during inference (40FPS).

We introduce a new class of fuzzy discrete event systems (FDESs) called stochastic FDESs (SFDESs), which is significantly different from the probabilistic FDESs (PFDESs) in the literature. It offers an effective modeling framework for applications that are unsuitable for the PFDES framework. An SFDES is comprised of multiple fuzzy automata that occur randomly one at time with different occurrence probabilities. It uses either the max-product fuzzy inference or the max–min fuzzy inference. This article focuses on single-event SFDES—each of the fuzzy automata of such an SFDES has one event. Assuming nothing is known about an SFDES, we develop an innovative technique capable of determining number of fuzzy automata and their event transition matrices as well as estimating their occurrence probabilities. The technique, called prerequired-pre-event-state-based technique, creates and uses merely$N$particular pre-event state vectors of dimension$N$to identify event transition matrices of$M$fuzzy automata, involving a total of$MN^{2}$unknown parameters. One necessary and sufficient condition and three sufficient conditions are established for the identification of SFDES with different settings. The technique does not have any adjustable parameter or hyperparameter to set. A numerical example is provided to concretely illustrate the technique.

We recently introduced a novel category of fuzzy discrete event systems (FDESs) termed stochastic FDESs (SFDESs), wherein multiple fuzzy automata occur randomly with different probabilities. We also developed two techniques for identifying event transition matrices in single-event SFDES employing the max-product fuzzy inference. One of them, named the equation-systems-based technique, focuses on the single-event SFDES identification, where the fuzzy automaton of each FDES has only one event. Expanding on our research, this article delves into multievent SFDES identification, allowing each FDES to encompass a sequence of events. This is a new research direction that has not been mentioned in the literature before. Upon activation of an FDES, all its events occur sequentially. Our mathematical proof first establishes the associativity of the max-product inference operation, leading to the introduction of a pivotal and novel concept called an equivalent overall event transition matrix for a consecutive event sequence. This concept establishes a theoretical framework for utilizing the equation-systems-based technique in a novel three-step method for identifying multievent SFDESs. The technique is employed in the first two steps to: 1) determine the number of fuzzy automata in an SFDES and 2) calculate their occurrence frequencies. In the third step, multievent transition matrices of the SFDES are learned by using the stochastic-gradient-descent-based algorithms that we previously developed for multievent FDESs, provided the numbers of consecutive events for each fuzzy automaton within the SFDES are known. Theoretical analysis reveals, for the first time, the interconnections between the event transition matrices learned by the algorithms, the equivalent overall event transition matrices derived from these matrices, and the target event transition matrices. To illustrate our findings, we present an informative example.

In a distributed system, the plant and its controlling entity, the supervisor, are situated in separate locations, communicating remotely. This setup introduces delays and the potential for information loss during communication. This study delves into the supervisory control of networked fuzzy discrete event systems, an area relatively unexplored in existing literature. The plant is conceptualized as a fuzzy discrete event system with inherent constraints. Events within this system are both observed and managed from a distance by the supervisor, encountering two types of delays and losses. One type occurs during observation, where the plant transmits information to the supervisor, whereas the other arises during control, stemming from communication between the supervisor and the plant. The article first addresses the challenge of estimating states in the presence of observation delays and losses. An online methodology is devised to compute these state estimates. Leveraging these estimates, a supervisor is then designed to selectively enable or disable events, ensuring that the plant never transitions into undesirable or unsafe fuzzy states. A necessary and sufficient condition is established to guarantee the existence of such a supervisor. In addition, online techniques are developed to implement the computation of the supervisor's control actions.

We recently proposed a new class of fuzzy discrete event systems called the stochastic fuzzy discrete event systems (SFDES), which has the potential to be useful in a variety of applications, including those in healthcare. An SFDES is comprised of multiple fuzzy automata with different occurrence probabilities. Assuming the number of states is known, goals of SFDES identification are: 1) determining number of fuzzy automata and their event transition matrices, and 2) estimating the occurrence probabilities of the fuzzy automata. In this article, we develop an innovative technique, named the equation-systems-based technique, which uses whatever pre- and post-event state vector pairs available to establish and solve equation systems to achieve the identification goals. The ability of using arbitrary state vector pairs is a crucial and practical advantage over another SFDES identification technique that we previously published. That technique, called the prerequired-pre-event-state-based technique, requires the system of interest to be subject to some special pre-event states during the identification process, which may not be feasible for many real-world systems. The new equation-systems-based technique has no adjustable parameter to set or hyperparameter to experiment with. Theoretical analysis is conducted on the Technique, resulting in necessary or sufficient conditions as well as formulas for computing the minimal (or near minimal) number of state vector pairs needed for various SFDES settings. Computer simulation results are provided to demonstrate the effectiveness of the Technique.

The binary nature of the states and transitions in discrete-time finite Markov chains makes this modeling methodology unsuitable for many practical systems, such as those found in biomedicine. To address this fundamental limitation, we have extended in this article Markov chains to fuzzy Markov chains capable of handling fuzzy states and fuzzy events. This innovative and significant advancement is founded on the theory of stochastic fuzzy discrete event systems (SFDES) and the supervised learning algorithm for fuzzy discrete event systems (FDES), recently published by the authors. We mathematically generalize a traditional Markov chain with$N$states to a fuzzy Markov chain with$N$fuzzy states, which is represented by an SFDES consisting of$N^{2}$FDES. Each FDES has its own$N \times N$event transition matrix that is automatically learned by the aforementioned learning algorithm. Crucially, the fuzzy Markov chain fully preserves the stochastic characteristics defined by the transition probability matrix of the binary Markov chain, ensuring identical stochastic behaviors. A defuzzifier is used to yield crisp model output. The structurally more complex fuzzy Markov chain encompasses its binary counterpart as a special case and degenerates into it when fuzzy states degenerate into binary states. A simulation example is provided to illustrate the systematic design procedure and demonstrate the higher prediction accuracy of the fuzzy Markov chain over its binary counterpart. Due to their advantages, fuzzy Markov chains have the potential to address real-world stochastic problems beyond the reach of conventional Markov chains, especially in biomedicine.

In this article, supervised learning of fuzzy discrete-event systems (FDES) is investigated. A learning algorithm that performs supervised learning for multievent transition matrices of a sequence of fuzzy discrete events is derived. FDES can be used to describe a large class of practical systems that consist of fuzzy discrete states, fuzzy discrete events, and transitions among fuzzy discrete states via fuzzy discrete events. Because fuzzy discrete states, fuzzy discrete events, and fuzzy transitions are well defined in FDES, the FDES model is highly explainable, which is important in many applications, especially in biomedical applications. Based on this explainable model, the proposed learning algorithm can be used to learn events and event sequences in the model. Hence, it allows system developers to build an explainable model for a complex system based on the data available. Simulations using MATLAB are conducted to verify the effectiveness of the proposed algorithm.

Supervisory control of fuzzy discrete event systems (FDES) under partial observation is investigated in this article. Without loss of generality, we consider FDES with constraints where a FDES is modeled by a fuzzy automaton. Sequences of events that can be generated by the system are regarded as constraints and are modeled by a crisp automaton. A supervisor is designed to control the FDES so that the supervised system is prevented from entering a prespecified set of illegal/unsafe fuzzy states. A necessary and sufficient condition for the existence of a supervisor is obtained. When the condition is satisfied, an online supervisor can be designed. Fuzzy state estimation problem is first solved, as the supervisor is fuzzy-state-estimate-based. A method is developed to estimate fuzzy state iteratively after observation of each new event. We show that the supervisor so developed ensures the safety of the system and is least restrictive among all possible safe supervisors. Potential of the theoretical results for real-world applications is illustrated through an example of HIV/AIDS treatment decision-making.

Compared to other system modeling techniques, the fuzzy discrete event systems (FDESs) methodology has the unique capability of modeling a class of event-driven systems as fuzzy automata with ambiguous state and event-invoked state transition. In two recent papers, we developed algorithms for online-supervised learning of the fuzzy automaton's event transition matrix using fuzzy states before and after the occurrence of fuzzy events. The post-event state was assumed to be readily available while the pre-event state was either directly available or estimatable through learning. This article is focused on algorithm development for learning the transition matrix in a different setting-when the pre-event state is available but the post-event state is not. We suppose the post-event state is described by a fuzzy set that is linked to a (physical) variable whose value is available. Stochastic-gradient-descent-based algorithms are developed that can learn the transition matrix plus the parameters of the fuzzy sets when the fuzzy sets are of the Gaussian type. Computer simulation results are presented to confirm the theoretical development.

Many biomedical systems and some engineering systems can be modeled as fuzzy discrete event systems. In this article, fuzzy discrete event systems with constraints (FDESwC) are introduced and detectabilities of FDESwC are investigated. While detectabilities of conventional crisp discrete event systems (DES) have been investigated before, detectabilities of FDESwC are much more complex because the state space of FDESwC is infinite, unlike that of crisp DES. To overcome this difficulty, trajectories of FDESwC bounded by$N$observations are considered and$N$-detectabilities are introduced.$N$-detectabilities of crisp DES are first defined and proved to be equivalent to detectabilities if$N$is sufficiently large. Fuzzy$N$-detectabilities of FDESwC are then defined. An algorithm is derived to check fuzzy$N$-detectabilities. While fuzzy detectabilities require to determine which state the system is in, this requirement can be relaxed in some applications. To do so, fuzzy$D$-detectabilities are introduced and investigated, where the requirement is to distinguish certain pairs of states.

The well-known backpropagation learning algorithm is probably the most popular learning algorithm in artificial neural networks. It has been widely used in various applications of deep learning. The backpropagation algorithm requires a separate feedback network to back propagate errors. This feedback network must have the same topology and connection strengths (weights) as the feed-forward network. In this article, we propose a new learning algorithm that is mathematically equivalent to the backpropagation algorithm but does not require a feedback network. The elimination of the feedback network makes the implementation of the new algorithm much simpler. The elimination of the feedback network also significantly increases biological plausibility for biological neural networks to learn using the new algorithm by means of some retrograde regulatory mechanisms that may exist in neurons. This new algorithm also eliminates the need for two-phase adaptation (feed-forward phase and feedback phase). Hence, neurons can adapt asynchronously and concurrently in a way analogous to that of biological neurons.

In practical systems, due to reasons such as sensor limitations, sensor faults, and packet losses in networks, the observation of events becomes nondeterministic. In this article, we extend strong detectability and weak detectability to the case of nondeterministic observations and denote them as A-($k_{1}$,$k_{2}$)-detectability and O-($k_{1}$,$k_{2}$)-detectability, respectively. A-($k_{1}$,$k_{2}$)-detectability says that, for any string, we can distinguish state pairs in the specification for all possible observations of the string. O-($k_{1}$,$k_{2}$)-detectability says that, for at least one string, we can distinguish state pairs in the specification for all possible observations of the string. For A-($k_{1}$,$k_{2}$)-detectability, we construct a transformed automaton and then translate the A-($k_{1}$,$k_{2}$)-detectability problem into the traditional detectability problem that has been solved. We show that A-($k_{1}$,$k_{2}$)-detectability can be used to solve the deterministic supervisory control problem. For O-($k_{1}$,$k_{2}$)-detectability, we construct an augmented automaton that includes all the information of the given automaton and its state estimates. Based on the augmented automaton, we propose a depth-first search (DFS)-based algorithm to check O-($k_{1}$,$k_{2}$)-detectability.Note to Practitioners—Nowadays, practical engineering systems become more and more complex. In these systems, the observation of events often becomes nondeterministic due to reasons such as sensor limitations, sensor faults, and packet losses in networks. Consider a mobile robot as an example. The availability of a sensor output may depend on the current location of the mobile robot. If the mobile robot is in an area where the wireless network is unreliable, the sensor output may not be received by the supervisor. In this article, we investigate the state estimation problem for practical engineering systems under nondeterministic observations within a discrete-event system framework. The results in this article provide not only insights for engineers in the automatic control field to understand nondeterministic observations in practical systems but also the methodology to estimate the current discrete state that is always an important issue. Therefore, we believe that the engineers in the automatic control field should be interested in this article and can benefit from it.

The fuzzy discrete event system theory is unique in that it is capable of modeling a class of event-driven systems as fuzzy automata with states and event-invoked state transitions being ambiguous. At present, the theory lacks a self-learning component, an important topic that has hardly been touched in the literature. In this article, we use stochastic gradient descent to develop online learning algorithms for the fuzzy automata. We uncover an inherent obstacle in the initial derived algorithms that fundamentally restricts their learning capability owing to dependences of the model parameters to be learned. We develop a novel mechanism to not only overcome the obstacle but also make the learning adaptive. Our final algorithms can learn an event transition matrix based on automaton's states before and after the occurrence of a fuzzy event, and learn the transition matrix and multidimensional Gaussian fuzzy sets yielding initial automaton states from relevant input variables and target states. Computer simulation results are presented to show learning performance of the final algorithms.

To make the fuzzy discrete event system theory more useful in a wide range of applications, it is crucial to equip it with learning capability, an issue that has hardly been touched upon in the literature. In this paper, we develop stochastic-gradient-decent-based algorithms for online learning of the event transition matrices and parameters of the fuzzy sets fuzzifying input variables of a fuzzy discrete event system modeled as a fuzzy automaton. We uncover an intrinsic obstacle in the algorithms that significantly impedes the learning owing to dependences of the fuzzy set parameters on the matrix. As a remedy, we modify the algorithms using the exponential penalty function. Preliminary computer simulation results are presented to illustrate learning performance of our final algorithms.

Opacity is a property of a system that captures whether certain event sequences (or certain states) are indistinguishable from other event sequences (or states) in the system. Opacity is used in analyzing privacy, secrecy, and other aspects of systems modeled by discrete-event systems. In this paper, we introduce the concept of minimal information release policies for non-opacity and the concept of mixed opacity. Mixed opacity policies are introduced as a holistic approach for solving problems that involve a combination of releasing information to make some objectives of the system opaque while making some other objectives non-opaque. We present a set of algorithms for information release under a mixed opacity policy. These algorithms compute policies in a system such that two given sublanguages are opaque, and at the same time, two other sublanguages in the same system are non-opaque. The application of mixed opacity is demonstrated on the Dining Cryptographers Problem.

Fuzzy discrete event systems are useful models for solving complex practical problems in biomedical and other fields. The theory of detectabilities in conventional crisp discrete event systems investigates state determination or estimation based on event observation. The theory is also important to fuzzy discrete event systems (e.g., disease diagnosis and treatment effectiveness evaluation). In this paper, we investigate fuzzy detectabilities for fuzzy discrete event systems. We first introduce fuzzy discrete event systems with constraints, which provide a new and more realistic model for complex systems. We also extend detectabilities of crisp discrete event systems to N-detectabilities and prove the relation between detectabilities and N-detectabilities. We then define fuzzy N-detectabilities and develop an algorithm to check fuzzy N-detectabilities of a fuzzy discrete event system. The computational complexity of the algorithm is analyzed.

Predictable link reliability is required for wireless networked control, yet co-channel interference remains a major source of uncertainty in wireless link reliability. Formulated specifically for distributed predictable control of co-channel interference, the physical-ratio-K (PRK) interference model integrates the protocol model's locality and the physical model's high fidelity while addressing their weaknesses, and it transforms interference control in arbitrary networks to a problem involving coordination between close-by nodes only. To apply the PRK model in real-world settings, we design protocol PRKS that addresses the challenges of model instantiation and protocol signaling in PRK-based scheduling. In particular, PRKS uses a control-theoretic approach to instantiate the PRK model in dynamic uncertain networks, uses local signal maps to address the challenges of large interference range and anisotropic asymmetric wireless communication, and leverages the different timescales of PRK model adaptation and data transmission to decouple protocol signaling from data transmission. Through testbed-based measurement study, we show that, unlike existing scheduling protocols where link reliability is unpredictable and the ratio of links whose reliability meets application requirements can be as low as 0%, PRKS enables predictably high link reliability (e.g., 95%) for all the links in different network and environmental conditions without a priori knowledge of these conditions. Through local distributed coordination, PRKS also achieves a channel spatial reuse very close to what is enabled by the state-of-the-art centralized scheduler while ensuring the required link reliability. By ensuring the required link reliability in scheduling, PRKS also enables a lower communication delay and a higher network throughput than existing scheduling protocols.

In this paper, we investigate the robust control problem of discrete event systems in a networked environment. In other words, we use a supervisor to control several possible plants (discrete event systems) to achieve given specifications when there are communication delays and losses in communication networks linking the supervisor and the plants. We translate the robust networked control problem into a conventional networked control problem by constructing an augmented automaton for all possible plants and an augmented specification automaton for the corresponding specification automata. We then solve the robust networked control problem. We consider two cases. The first case is when all the specifications are the same. For this case, we derive a necessary and sufficient condition for the existence of a robust networked supervisor. The second case is when the specifications are different, which is more general compared with the first case. In the second case, we can only obtain a sufficient condition for the existence of a networked supervisor. The results are illustrated by an example of customized products filling line.

Predictable link reliability is required for wireless networked control, yet co-channel interference remains a major source of uncertainty in wireless link reliability. Integrating the protocol model's locality and the physical model's high fidelity, the physical-ratio-K (PRK) interference model has the potential to enable distributed, predictable control of co-channel interference and thus predictable link reliability. To realize the potential of the PRK model, we design protocol PRKS that addresses the challenge of instantiating the PRK model in the presence of network and environmental uncertainties. Formulating the PRK-model-instantiation problem as a minimum-variance regulation control problem, in particular, PRKS uses a control-theoretic approach to instantiating the PRK model on the fly. Through testbed-based measurement study, we show that, unlike existing scheduling protocols where link reliability is unpredictable and the ratio of links whose reliability meets application requirements can be as low as 0%, PRKS enables predictably high link reliability (e.g., 95%) for all the links in different network and environmental conditions without a priori knowledge of these conditions. Through local, distributed coordination, PRKS also achieves a channel spatial reuse very close to what is enabled by the state-of-the-art centralized scheduler while ensuring the required link reliability. By ensuring the required link reliability in scheduling, PRKS also enables a lower communication delay and a higher network throughput than existing scheduling protocols.

Opacity is important in investigating secrecy, privacy, and other properties in general systems that can be modeled as discrete event systems. To ensure opacity, a controller may be used to control information released to the public. For transparency and other reasons, it is often desired that the information released to the public be maximum, as long as opacity is not violated. In this paper, we investigate how to release the maximum information while ensuring opacity. We find a necessary and sufficient condition for an information release policy to ensure opacity. We also develop methods and algorithms to design a controller that releases maximum information. We consider both strong opacity and weak opacity. We apply the results to the dining cryptographers problem. Note to Practitioners-Nowadays, networks and computers make the collection, storage and dissemination of information much easier. This brings us a lot of convenience, but at the same time, also brings us the worry that some private information may be released to the public undesirably. The problem of how to control the release of information thus becomes very important. In this paper, we propose a discrete-event-system approach to investigate the information release problem. The solution can ensure the opacity of private information while releasing the maximum information to the public. We believe that the practitioners both in the field of system and control and in the field of information science will benefit from the results.

Opacity is important in investigating secrecy, privacy, and other important properties in general systems that can be modeled as discrete event systems. To ensure opacity, a controller may be used to control information released to the public. For transparency and other reasons, it is often desired the information released to the public be maximum, as long as opacity is not violated. In this paper, we investigate how to release the maximum information while ensuring opacity. We find a necessary and sufficient condition for a control policy to ensure opacity. We also develop methods and algorithms to design a controller that releases maximum information. We consider both strong opacity and weak opacity.

This paper considers fault-tolerant control that ensures the safety of a discrete-event system. We consider multiple faulty modes. Each faulty mode is modeled by an automaton. These automata, together with the automaton modeling normal mode, describe a discrete-event system with faults. Each faulty mode has some illegal states that must be avoided by control so that the fault can be tolerated. We assume that fault-tolerant control takes actions (disablements) only when the occurrence of a fault is certain. We consider cases of both full event observation and partial event observation. We derive necessary and sufficient conditions for the existence of fault-tolerant control. We also provide formulas and algorithms to calculate control actions if the necessary and sufficient conditions are satisfied. Both offline control synthesis (for full event observation) and online control synthesis (for partial event observation) are investigated. We allow multiple faults as well as single faults.

In this paper, we investigate online sensor activation to ensure detectability of discrete event systems. Detectability requires that states of a system can be determined or certain pairs of states can be distinguished by an external observer eventually or periodically. Since minimal sensor activation policies for detectability may not exist, two new concepts are introduced: 1)k-step distinguishability is introduced for strong detectability and 2) information-preserving is introduced for strong periodic detectability. The online sensor activation is then proposed and is based on the best state estimate available at the time of decision making. Three algorithms are developed for online sensor activation. The first two algorithms are for strong detectability. They minimize sensor activation while preservingk-step distinguishability. The third algorithm deals with strong periodic detectability. It minimizes sensor activation while preserving state information.

State estimation has always been important in discrete-event systems. There are two types of state estimation problems in discrete-event systems: one is to determine the initial state of the system and the other is to determine the current state of the system. In this paper, we investigate the initial state estimation problem. We formulate initial state estimation problem as I-detectability. A discrete-event system is strongly I-detectable if we can determine the initial state of the system after a finite number of event observations for all trajectories of the system. It is weakly I-detectable if we can determine the initial state of the system for some trajectories of the system. We construct I-observer to analyze strong and weak I-detectability and construct I-detector to check strong I-detectability. For some applications, strong I-detectability is required but not satisfied; hence we investigated how to control a system to achieve strong I-detectability if needed. If there exists a controllable, observable, and strongly I-detectable sublanguage, then we say the system is closed-loop strongly I-detectable. We derive an effective algorithm to check whether a system is closed-loop strongly I-detectable. The algorithm can also calculate a controllable, observable, and strongly I-detectable sublanguage if the system is closed-loop strongly I-detectable.

This paper considers fault-tolerant control that ensures the safety of a discrete event system. We consider multiple faulty modes. Each faulty mode is modeled by an automaton. These automata, together with the automaton modeling the normal mode, describe a discrete event system with faults. Each faulty mode has some illegal states that must be avoided by control so that the fault can be tolerated. We assume that fault-tolerant control will take action (disablements) only when the occurrence of a fault is certain. We consider both full event observation and partial event observation. We derive necessary and sufficient conditions for the existence of fault-tolerant control. We also provide formula and algorithm to calculate control actions if the necessary and sufficient conditions are satisfied. Both offline control synthesis (for full event observation) and online control synthesis (for partial event observation) are investigated.

In a 2002 paper, we combined fuzzy logic with discrete-event systems (DESs) and established an automaton model of fuzzy DESs (FDESs). The model can effectively represent deterministic uncertainties and vagueness, as well as human subjective observation and judgment inherent to many real-world problems, particularly those in biomedicine. We also investigated optimal control of FDESs and applied the results to optimize HIV/AIDS treatments for individual patients. Since then, other researchers have investigated supervisory control problems in FDESs, and several results have been obtained. These results are mostly derived by extending the traditional supervisory control of (crisp) DESs, which are string based. In this paper, we develop state-feedback control of FDESs that is different from the supervisory control extensions. We use state space to describe the system behaviors and use state feedback in control. Both disablement and enforcement are allowed. Furthermore, we study controllability based on the state space and prove that a controller exists if and only if the controlled system behavior is (state-based) controllable. We discuss various properties of the state-based controllability. Aside from novelty, the proposed new framework has the advantages of being able to address a wide range of practical problems that cannot be effectively dealt with by existing approaches. We use the diabetes treatment as an example to illustrate some key aspects of our theoretical results.

In 2001, we originated a theory of fuzzy discrete-event systems (FDESs) that generalized the conventional/crisp discrete-event systems (DESs). Vagueness and imprecision concerning states and event transitions of DESs were represented by membership grades and computed via fuzzy logic. Our application of the FDES theory to computerized human immunodeficiency virus/acquired immune deficiency syndrome treatment regimen selection, although preliminarily successful, suggests that a more comprehensive FDES theory is needed to address two general issues critically important not only to biomedical applications, but also to real-world problems in other industries. First, domain experts should have means other than point estimates and type-1 fuzzy sets mandated in the current framework to describe uncertainties, subjectivity, and imprecision in their (complex) knowledge and experience. Second, when a group of experts with distinct opinions is involved, they should not be forced to reach consensus for the sake of system development. This is because collective consensus may not be achievable, which is often the case in medicine, where individual expertspsila opinions should be equally respected since the underlying ground truth is unknown most of the time. The theory of extended FDES presented in this paper addresses both the problems and contains the FDES theory as a special case. Experts are now allowed to use interval numbers and type-1 and type-2 fuzzy sets to intuitively and quantitatively express their diverse knowledge and experience, which will then be processed by the new theory to form fuzzy state vectors and fuzzy event transition matrices. Accordingly, we have established mathematical operations that cover the computations of fuzzy states, fuzzy event transitions, and parallel composition. Numerical examples are provided.

As a very effective method for universal purpose pattern recognition, support vector machine (SVM) was proposed for dichotomic classification problem, which exhibits a remarkable resistance to overfitting, a feature explained by the fact that it directly implements the principle of structural risk minimization. However, in real world, most of classification problems consist of multiple categories. In an attempt to extend the binary SVM classifier for multiclass classification, decision-tree-based multiclass SVM was proposed recently, in which the structure of decision tree plays an important role in minimizing the classification error. The present study aims at developing a systematic way for the design of decision tree for multiclass SVM. Kernel-induced distance function between datasets was discussed and then kernelized hierarchical clustering was developed and used in determining the structure of decision tree. Further, simulation results on satellite image interpretation show the superiority of the proposed classification strategy over the conventional multiclass SVM algorithms.

The U.S. Department of Health and Human Services Human Immunodeficiency Virus (HIV)/Acquired Immune Deficiency Syndrome (AIDS) treatment guidelines are modified several times per year to reflect the rapid evolution of the field (e.g., emergence of new antiretroviral drugs). As such, a treatment-decision support system that is capable of self-learning is highly desirable. Based on the fuzzy discrete event system (FDES) theory that we recently created, we have developed a self-learning HIV/AIDS regimen selection system for the initial round of combination antiretroviral therapy, one of the most complex therapies in medicine. The system consisted of a treatment objectives classifier, fuzzy finite state machine models for treatment regimens, and a genetic-algorithm-based optimizer. Supervised learning was achieved through automatically adjusting the parameters of the models by the optimizer. We focused on the four historically popular regimens with 32 associated treatment objectives involving the four most important clinical variables (potency, adherence, adverse effects, and future drug options). The learning targets for the objectives were produced by two expert AIDS physicians on the project, and their averaged overall agreement rate was 70.6%. The system's learning ability and new regimen suitability prediction capability were tested under various conditions of clinical importance. The prediction accuracy was found between 84.4% and 100%. Finally, we retrospectively evaluated the system using 23 patients treated by 11 experienced nonexpert faculty physicians and 12 patients treated by the two experts at our AIDS Clinical Center in 2001. The overall exact agreement between the 13 physicians' selections and the system's choices was 82.9% with the agreement for the two experts being both 100%. For the seven mismatched cases, the system actually chose more appropriate regimens in four cases and equivalent regimens in another two cases. It made a mistake in one case. These (preliminary) results show that 1) the System outperformed the nonexpert physicians and 2) it performed as well as the expert physicians did. This learning and prediction approach, as well as our original FDESs theory, is general purpose and can be applied to other medical or nonmedical problems.

An optimal control problem for hybrid systems is formulated based on hybrid machine models. A practical approach to solving the problem, suitable for a class of hybrid systems, is presented. This approach consists of transforming the hybrid machine model into a dynamic programming model. Transition costs, in this latter model, are computed using mixed integer programs formulated based on the structure of the original hybrid machine. It is shown that the optimal solution for this dynamic program corresponds to the optimal control decision sequence in the hybrid system. Practical examples, inspired from process-oriented industry applications, are provided to illustrate the solution approach.

Treatment decision-making is complex and involves many factors. A systematic decision-making and optimization technology capable of handling variations and uncertainties of patient characteristics and physician's subjectivity is currently unavailable. We recently developed a novel general-purpose fuzzy discrete event systems theory for optimal decision-making. We now apply it to develop an innovative system for medical treatment, specifically for the first round of highly active antiretroviral therapy of human immunodeficiency virus/acquired immunodeficiency syndrome (HIV/AIDS) patients involving three historically widely used regimens. The objective is to develop such a system whose regimen choice for any given patient will exactly match expert AIDS physician's selection to produce the (anticipated) optimal treatment outcome. Our regimen selection system consists of a treatment objectives classifier, fuzzy finite state machine models for treatment regimens, and a genetic-algorithm-based optimizer. The optimizer enables the system to either emulate an individual doctor's decision-making or generate a regimen that simultaneously satisfies diverse treatment preferences of multiple physicians to the maximum extent. We used the optimizer to automatically learn the values of 26 parameters of the models. The learning was based on the consensus of AIDS specialists A and B on this project, whose exact agreement was only 35%. The performance of the resulting models was first assessed. We then carried out a retrospective study of the entire system using all the qualifying patients treated in our institution's AIDS Clinical Center in 2001. A total of 35 patients were treated by 13 specialists using the regimens (four and eight patients were treated by specialists A and B, respectively). We compared the actually prescribed regimens with those selected by the system using the same available information. The overall exact agreement was 82.9% (29 out of 35), with the exact agreement with specialists A and B both at 100%. The exact agreement for the remaining 11 physicians not involved in the system training was 73.9% (17 out of 23), an impressive result given the fact that expert opinion can be quite divergent for treatment decisions of such complexity. Our specialists also carefully examined the six mismatched cases and deemed that the system actually chose a more appropriate regimen for four of them. In the other two cases, either would be reasonable choices. Our approach has the capabilities of generalizing, learning, and representing knowledge even in the face of weak consensus, and being readily upgradeable to new medical knowledge. These are practically important features to medical applications in general, and HIV/AIDS treatment in particular, as national HIV/AIDS treatment guidelines are modified several times per year.

The United Nations estimates that 38 million people worldwide are infected with HIV/AIDS, and that more than 22 million have died. Like most diseases, treatment decision-making for this disease is currently more an art than science. This is partially because every patient is unique, with his/her own history, set of genetic traits, predisposition to side effects, and prognosis. We reported previously how we had developed a theoretical framework of novel fuzzy discrete event systems, which are knowledge-based (Lin and Ying, 2002). We showed how to apply it to develop a part of HIV/AIDS regimen selection system for treating antiretroviral-naive patients (Lin et al., 2004). In the present paper, we describe our recent development - we have furthered the system design by adding a Genetic-Algorithm-Based Regimen Selection Optimizer and a Treatment Objectives Classifier to the system. The full system is capable of prescribing a regimen for any given patient. The Optimizer enables the system to either emulate an individual doctor's decision-making or generate a regimen that simultaneously satisfies diverse treatment preferences of multiple physicians to the maximum extent. We show the promising preliminary results of retrospective evaluation of the system using 48 treatment-naive patients who started antiretroviral treatment in our AIDS Clinic in 2001. Our fuzzy DES approach possesses a number of unique features and advantages that are especially important to medical applications: (1) higher flexibility and scalability, and (2) easier knowledge upgrade for accommodating fast treatment strategy evolution with minimal system modification. These are particularly important to HIV/AIDS treatment as the U.S. Public Health Service updates its treatment guidelines at least once a year

As the only effective treatment strategy against HIV/AIDS, highly active antiretroviral therapy (HAART) is an extremely promising development in the treatment of HIV/AIDS. The success of HAART highly depends on patient's adherence to this complex treatment. Recent studies found that poor adherence was a major cause of treatment failure and emerging drug resistance, and thus it is important to understand the factors that contribute to good and poor adherence. However, the discovery of factors salient to adherence is constrained by the well known fact that medical data gathering is expensive and thus usually only a limited amount of information is available. Our study of HIV/AIDS treatment adherence is no exception - we only have data on 33 patients. For this reason, we apply the support vector machine (SVM) to model the relationship of nine patient factors to the level of medication adherence. To establish the baseline performance, we first randomly generated test data sets of comparable sample size and data dimension to the patient pool. A SVM was evaluated using the test data. The SVM was then applied to the real patient data. Finally, a three-layer neural network with back propagation learning was applied to the patient data as well as the test data. The results show that the SVM performed reasonably well and significantly outperformed the neural networks. Our work demonstrates that SVM techniques can be effective in quantitatively modeling complex relationships important in clinical medicine even when the data set size is very small by industrial standards. To our knowledge, this is the first application of a SVM to HIV/AIDS.

It is well-known that the multiple sliding surface control was developed to eliminate the problem of “explosion of complexity” inherent in the celebrated backstepping method. In this paper, we extend the multiple sliding surface control method further for systems in nonlinear block controllable form. As an application of the proposed control scheme, the robust attitude control law was synthesized for highly maneuverable missiles. Contrary to the classical SISO methods, all nonlinearities of missile attitude dynamics as well as coupling effects between roll, yaw and pitch channels due to roll rate are fully accommodated in the designed nonlinear control law.

We propose an algorithmic approach to the problem of verification of the property of intransitive noninterference (INI), using tools and concepts of discrete event systems (DES). INI can be used to characterize and solve several important security problems in multilevel security systems. In a previous work, we have established the notion of iP-observability, which precisely captures the property of INI. We have also developed an algorithm for checking iP-observability by indirectly checking P-observability for systems with at most three security levels. In this paper, we generalize the results for systems with any finite number of security levels by developing a direct method for checking iP-observability, based on an insightful observation that the iP function is a left congruence in terms of relations on formal languages. To demonstrate the applicability of our approach, we propose a formal method to detect denial of service vulnerabilities in security protocols based on INI. This method is illustrated using the TCP/IP protocol. The work extends the theory of supervisory control of DES to a new application domain.

Treatment decision-making for most diseases is currently partial art and partial science. To a large extent, this is due to the fact that every patient is unique, and many symptoms and diagnoses are inherently imprecise and difficult to measure. A systematic decision-making and optimization technology capable of handling all the clinical difficulties is still unavailable despite significant efforts documented in the literature, including the use of artificial intelligence and statistical methods. One promising approach is the novel fuzzy discrete event systems whose theoretical framework was recently developed by us. We apply it to treatment planning for HIV/AIDS patients who have never received antiretroviral therapy. We show how to design such a system. We have also statistically evaluated the preliminary results produced by the system in comparison with two AIDS specialists on our team. The results indicate strong agreement between the physicians and the fuzzy discrete event system. This is the first application of fuzzy discrete event systems in the literature.

In order to make it possible to effectively represent deterministic uncertainties and vagueness as well as the human subjective observation and judgement inherent to many real-world problems, especially those in biomedicine, we introduce, in this paper, fuzzy states and fuzzy events and generalize (crisp) discrete event systems (DES) to fuzzy DES. The largely graph-based current framework of the crisp DES is unsuitable for the expansion, and we have thus reformulated it using state vectors and event transition matrices which can be extended to fuzzy vectors and matrices by allowing their elements to take values between 0 and 1. To measure information related to fuzzy DES, we generalize the crisp DES observability. The new observability allows one to determine whether or not the system output observed is sufficient for decision making. Finally, we extend the optimal control of DES to fuzzy DES. The new fuzzy DES theory is consistent with the existing theory, both at the conceptual and the computation levels, in that the former contains the latter as a special case when the memberships must be either 0 or 1. Numerical examples are provided to illustrate the theoretical development.