Probabilistic Faults Research Articles

Resilient sampled-data control for fractional-order PMVG-based WTS with actuator saturation and probabilistic faults using fuzzy Lyapunov function method

The goal of this study is to present a new fuzzy Lyapunov function-based resilient sampled-data control method for a fractional-order permanent magnet vernier generator (PMVG)-based wind turbine system (WTS) that addresses actuator saturation and probabilistic faults. To achieve this, we first model the dynamical fractional model of the PMVG-based WTS as a T-S fuzzy model. Next, we introduce a fuzzy Lyapunov function within a unified framework that incorporates actuator saturation, probabilistic faults, and uncertainty information from control gain matrices. We then present an actuator fault model that represents actuator faults as stochastic variables with a specific probability distribution. Subsequently, we formulate a robust asymptotic stability criterion for closed-loop systems using linear matrix inequality (LMI), which integrates the fuzzy Lyapunov function and membership function information with fractional integral inequality techniques based on sampling time. We also propose an LMI approach to identify the domain of attraction that meets the necessary actuator saturation criteria. Finally, we apply the proposed method to a PMVG-based WTS, demonstrating its superiority and practical applicability through a comparison with existing methods using a numerical example of a nonlinear truck trailer system.

Overcoming probabilistic faults in disoriented linear search

We consider search by mobile agents for a hidden, idle target, placed on the infinite line. Feasible solutions are agent trajectories in which all agents reach the target sooner or later. A special feature of our problem is that the agents are p-faulty, meaning that every attempt to change direction is an independent Bernoulli trial with known probability p, where p is the probability that a turn fails. We are looking for agent trajectories that minimize the worst-case expected termination time, relative to the distance of the hidden target to the origin (competitive analysis). Hence, searching with one 0-faulty agent is the celebrated linear search (cow-path) problem that admits optimal 9 and 4.59112 competitive ratios, with deterministic and randomized algorithms, respectively.First, we study linear search with one deterministic p-faulty agent, i.e., with no access to random oracles, p∈(0,1/2). For this problem, we provide trajectories that leverage the probabilistic faults into an algorithmic advantage. Our strongest result pertains to a search algorithm (deterministic, aside from the adversarial probabilistic faults) which, as p→0, has optimal performance 4.59112+ϵ, up to the additive term ϵ that can be arbitrarily small. Additionally, it has performance less than 9 for p≤0.390388. When p→1/2, our algorithm has performance Θ(1/(1−2p)), which we also show is optimal up to a constant factor.Second, we consider linear search with two p-faulty agents, p∈(0,1/2), for which we provide three algorithms of different advantages, all with a bounded competitive ratio even as p→1/2. Indeed, for this problem, we show how the agents can simulate the trajectory of any 0-faulty agent (deterministic or randomized), independently of the underlying communication model. As a result, searching with two agents allows for a solution with a competitive ratio of 9+ϵ (which we show can be achieved with arbitrarily high concentration) or a competitive ratio of 4.59112+ϵ. Our final contribution is a novel algorithm for searching with two p-faulty agents that achieves a competitive ratio 3+4p(1−p), in expectation and with arbitrarily high concentration.

Dynamic output-feedback H<SUB align="right">∞ control for TS fuzzy systems with probabilistic faults and time-varying input delay

Dynamic output-feedback H<SUB align="right">∞ control for TS fuzzy systems with probabilistic faults and time-varying input delay

On event‐triggered guaranteed cost control for discrete‐time semi‐Markovian neural networks having communication delays and dual‐terminal probabilistic faults

AbstractThis article aims to address the guaranteed cost control synthesis problem for discrete‐time semi‐Markovian neural networks (D‐SMNNs) considering communication delays along with probabilistic faulty sensors and actuators (dual‐terminal probabilistic faults) by adopting a modified event‐triggered mechanism. Our primary target of this research is to implement a suitable feedback controller such that the resulting D‐SMNNs achieve stochastically stable. To be more concrete, the structural and coefficient switchings of the NNs are characterized by a semi‐Markovian process (SMP) along with the lower and upper bounds of the transition probabilities (TPs), which can reflect the reality more accurately and has a wider application scope. For optimize the resource utilization of the band‐limited communication networks, a modified event‐triggered transmission strategy is put forward to lessen the unnecessary data transmission over network. Additionally, according to different failure rates and the measurement distributions of intelligent modules, a more practical probabilistic sensors and actuators faulty model for networked D‐SMNNs is synthesized, which including additivity and multiplicity. The anamorphic probability of sensors and actuators are governed by a battery of mutually independent stochastic variables that obeys certain probabilistic distribution over the preknown interval . Therein, the distortion degree and failure rate for each sensor and actuator can be separately quantized and characterized with the aid of mathematical variance and expectation. Briefly, in comparison to the existing faulty models, the novelty of this extended fault model lies in it can characterize more features in practical industrial applications. Afterwards, by resorting to the Lyapunov functional method and combining with both the stochastic analysis technique and matrix inequality decoupling manipulation, several sufficient conditions on ensuring stabilization for solving both the guaranteed cost controller gains and event‐triggered coefficients are formulated in the shape of a group of linear matrix inequalities (LMIs), which can be verified by exploiting standard compute software. After that, the controller design is reformulated as an optimization problem with LMI constraints immediately. Eventually, three simulation examples are carried out to substantiate the potency and accuracy of the proposed control synthesis methodology.

H-infinity bipartite consensus of multi-agent systems with external disturbance and probabilistic actuator faults in signed networks

<abstract><p>The H-infinity bipartite consensus problem is addressed for a class of linear multi-agent systems with external disturbance, where the positive and negative links are allowed in communication topology. A novel event-triggered communication scheme is presented to save limited network resources, which dependents on information from neighboring agents at event-triggered instants, the given event-triggered condition is detected only at discrete sampling times, thus Zeno behavior can be excluded, two types of event-triggered matrices have been introduced in our event-triggered communication scheme, which can further reduce the sampled-data transmission compared with some existed results. Considering the probabilistic actuator faults, the reliable controller is designed based on sampled-data, then a new distribution-based fault model is constructed by using coordinate transform. Some H-infinity bipartite consensus criteria can be derived by the Lyapunov stability theory and algebraic graph theory, at the same time, the feedback matrices and event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, a numerical example is employed to show the validity and advantage of the proposed transmission scheme.</p></abstract>

Dissipativity-based synthesis for semi-Markovian systems with simultaneous probabilistic sensors and actuators faults: A modified event-triggered strategy

Aided by a modified event-triggered communication policy (ETCP), this article addresses the dissipativity-based control synthesis problem for semi-Markovian switching systems (SMSSs) with simultaneous multiplicative probabilistic faults on sensors and actuators modules. The resulting model under consideration is more extensive, which covers semi-Markovian switching coefficients, transmission delays, and randomly occurring sensors and actuators faults in a unified systematic analytical framework instead of investigating separately in some existing works. More specifically, the probabilistic faults are assumed to happen on both the sensors and actuators modules simultaneously, and the distortion probability for each sensor and actuator is irrelevant, which can be characterized by multiplicate mutually independent stochastic variables that obeys certain statistical features and probabilistic distribution delineate on the interval [0,✠](✠≥1). To reduce the bandwidth usage, a novel event-triggered strategy is designed. Additionally, in the light of this newly developed ETCP, and considering the effects of the signal transmission delays and multitudinous probabilistic failures, a generalized and more realistic faulty pattern for SMSSs is presented, which is more fit for real applications. Hereby, the principal superiority of the established new type faulty pattern lies in its practicality and generality, which contains some previous faulty models as special scenarios. By constructing an appropriate semi-Markovian Lyapunov functional (SMLF) together with mathematical analysis technique and matrix inequality decoupling operation, sojourn-time-dependent sufficient conditions for determining both the control gain matrices and triggered configuration coefficients are developed and formulated in terms of a group of feasible linear matrix inequalities (LMIs). Eventually, several practical examples are exploited to substantiate the validity and practicability of the developed control design methodology.

Memory-event-triggering H ∞ reliable control for networked jacket platforms against earthquakes and stochastic actuator faults

This paper deals with the problems of networked modelling and memory-event-triggering reliable control for steel jacket-type platforms in network environments. First, a networked model of the jacket platform against earthquakes and probabilistic actuator faults is established. Based on this model, a memory-based event-triggering communication scheme is introduced to account for the constrained communication resources. A distinct feature of the proposed triggering scheme is that it has great potential to identify and trigger the significantly changed data than the existing ones without ‘memory’. Then, by formulating the network-based closed-loop platform system as a stochastic delay system, some sufficient conditions are derived for co-designing the desired controller and the triggering scheme. Finally, comparative simulation results are provided to demonstrate the effectiveness and merits of the proposed triggering and control co-design method. It is shown that compared with some existing event-triggering control methods, the proposed memory-event-triggering reliable controller is effective to mitigate vibrations of the jacket platform and is potentially advantageous to save more network bandwidth and control cost.

Resilient controller synthesis for Markovian jump systems with probabilistic faults and gain fluctuations under stochastic sampling operational mechanism

In this article, by exploiting the sampling communication mechanism (SCM) with probabilistically switching signals, the dissipativity-based resilient reliable control design problem is addressed for Markovian jump systems (MJSs), which simultaneous against the multiplicate stochastic intermittent actuator faults (MSIAFs) and randomly occurring controller gain fluctuations (ROCGFs). The primary objective of this work is to synthesis a resilient controller such that the underlying MJSs is stochastically stable while meeting an expected (Q,S,R)−ϑ dissipative performance index in the presence of ROCGFs. First and foremost, the randomly occurring actuator faults (ROAFs) and their failures rates are characterized by a series of mutually independent stochastic variables that satisfy prescribed probabilistic distributions for each actuator. The distortion degree and failure rate of each actuator can be quantized and calculated with the help of mathematical variance and expectation respectively. Secondly, the sampling controller with stochastically variable operation periods is considered and just assumed to switch between two different values in stochastic circumstances with certain probability. Thirdly, the nonfragile controller gain fluctuations also happens in a random framework which are obedient to Bernoulli distribution sequence (BDS). Fourthly, by resorting to an appropriately Lyapunov–Krasovskii functional (LKF) and adopting matrix inequality decoupling technique, several sufficient conditions for the solvability of the addressed problem are eventually formulated in the shape of linear matrix inequalities (LMIs). Ultimately, three real-life numerical examples are exploited to illustrate the effectiveness and applicability of the presented theoretical findings.

Stabilization of Flexible Spacecraft with Probabilistic Faults via Reliable Memory Sampled-data Control

This paper investigates the problem of stability analysis for a flexible spacecraft model via the reliable memory sampled-data control technique. Unlike the previous studies, the actuator fault under the stochastic environment and signal transmission delay are considered to tackle the stabilization problem of flexible spacecraft model. In this regard, the random variable is introduced to characterize the probabilistic actuator fault, which satisfies the Bernoulli distribution. The delay-dependent looped Lyapunov-Krasovskii functional (LKF) is constructed with full information about the whole sampling interval to derive the stability and stabilization analysis of the proposed results. Thus, the designed memory sampled-data control for the given spacecraft model guarantees the asymptotic stability performance in the formation of linear matrix inequalities (LMIs). The numerical section illustrates the effectiveness of the proposed theoretical results.

New reliable nonuniform sampling control for uncertain chaotic neural networks under Markov switching topologies

This paper studies the stochastic exponential synchronization problem for uncertain chaotic neural networks (UCNNs) with probabilistic faults (PFs) and randomly occurring time-varying parameters uncertainties(ROTVPUs). To reflect more realistic control behaviors, a new stochastic reliable nonuniform sampling controller with Markov switching topologies is designed for the first time. First, by taking into full account more information on sawtooth structural sampling pattern, time delay and its variation, a novel loose-looped Lyapunov–Krasovskii functional (LLLKF) is developed via introducing matrices-refined-function and adjustable parameters. Second, with the aid of novel LLLKF and relaxed Wirtinger-based integral inequality (RWBII), new synchronization algorithms are established to guarantee that UCNNs are synchronous exponentially under probabilistic actuator and sensor faults. Third, based on the proposed optimization algorithm, the desired reliable sampled-data controller can be achieved under more larger exponential decay rate. Finally, two numerical examples are given to illustrate the effectiveness and advantages of the designed algorithms.

Event-triggered platoon control of vehicles with time-varying delay and probabilistic faults

This paper investigates event-triggered platoon control of vehicles with probabilistic faults (i.e., sensor and actuator) and time-varying communication delay. A novel platoon model is established, in which the effect of time-varying delay, event-triggered scheme and probabilistic faults are involved. Based on the new model, criteria for the exponential stability and criteria for co-designing both the output feedback and the trigger parameters are derived by using Lyapunov functional. The obtained controller is complemented by additional conditions established for guaranteeing string stability and zero steady state velocity errors, yielding a useful string stable platoon control method. The effectiveness and advantage of the presented methodology are demonstrated by both numerical simulations and experiments with laboratory scale Arduino cars.

Reliable control for nonlinear systems with stochastic actuators fault and random delays through a T-S fuzzy model approach

This paper considers the reliable control design for T-S fuzzy systems with probabilistic actuators faults and random time-varying delays. The faults of each actuator occurs randomly and its failure rates are governed by a set of unrelated random variables satisfying certain probabilistic distribution. In terms of the probabilistic failures of each actuator and time-varying random delays, new fault model is proposed. Based on the new fuzzy model, reliable controller is designed and sufficient conditions for the exponentially mean square stability (EMSS) of T-S fuzzy systems are derived by using Lyapunov functional method and linear matrix inequality (LMI) technique. It should be noted that the obtained criteria depend on not only the size of the delay, but also the probability distribution of it. Finally, a numerical example is given to show the effectiveness of the proposed method.

A study of risk-aware program transformation

In the trend towards tolerating hardware unreliability, accuracy is exchanged for cost savings. Running on less reliable machines, functionally correct code becomes risky and one needs to know how risk propagates so as to mitigate it. Risk estimation, however, seems to live outside the average programmer's technical competence and core practice.In this paper we propose that program design by source-to-source transformation be risk-aware in the sense of making probabilistic faults visible and supporting equational reasoning on the probabilistic behaviour of programs caused by faults. à la Bird-Moor algebra of programming.This paper studies, in particular, the propagation of faults across standard program transformation techniques known as tupling and fusion, enabling the fault of the whole to be expressed in terms of the faults of its parts.

Event-Triggered Reliable Control in Networked Control Systems with Probabilistic Actuator Faults

This paper introduces a novel event-triggered scheme into networked control systems which is used to determine when to transmit the newly sampled state information to the controller. Considering the effect of the network transmission delay and probabilistic actuator fault with different failure rates, a new actuator fault model is proposed under this event-triggered scheme. Then, criteria for the exponential mean square stability (EMSS) and criteria for codesigning both the feedback and the trigger parameters are derived by using Lyapunov functional method. These criteria are obtained in the form of linear matrix inequalities. A simulation example is employed to show that our event-triggered scheme can lead to a larger release period than some existing ones.

多自由度遥操作机器人可靠性控制研究

In this paper, the reliable controller design is considered for multi-degree of freedom-based telerobotics. Time-delay estimation is employed to obtain the unknown dynamics and the external disturbances of robots online and to perform a compensation during the control. The faults of each actuator occur randomly and their failure rates are governed by a set of unrelated stochastic variables satisfying some certain probabilistic distribution. A new unified tele-robotics model is built by assuming the probabilistic distribution-based actuator fault and the input time varying delay. By considering the input time varying delay and the probabilistic actuator faults, we study the problem of the reliable control. By using Lyapunov functional method and stochastic systems theory, actuator distributed-dependent sufficient conditions for the exponentially mean square stability of telerobotics system are obtained in the form of linear matrix inequalities, which can be solved easily by the application of convex optimization algorithms. A simulation example is given to show that: firstly, using the distribution information of the actuator, the maximum effective delay bound can be easily obtained for the tele-robotics system; secondly, the proposed design procedures can also be used when the tele-robotics is without actuator faults; lastly, the proposed reliable controller can stabilize the tele-robotics system with probabilistic actuator faults, which may be unstable under the designed controller without considering the faults of actuator.

Toward robust network based complex systems: from evolutionary cellular automata to biological models

Abstract Sitting between your past and your future doesn't mean you are in the present. Dakota Skye Complex systems science is an interdisciplinary field grouping under the same umbrella dynamical phenomena from social, natural or mathematical sciences. The emergence of a higher order organization or behavior, transcending that expected of the linear addition of the parts, is a key factor shared by all these systems. Most complex systems can be modeled as networks that represent the interactions amongst the system's components. In addition to the actual nature of the part's interactions, the intrinsic topological structure of underlying network is believed to play a crucial role in the remarkable emergent behaviors exhibited by the systems. Moreover, the topology is also a key a factor to explain the extraordinary flexibility and resilience to perturbations when applied to transmission and diffusion phenomena. In this work, we study the effect of different network structures on the performance and on the fault tolerance of systems in two different contexts. In the first part, we study cellular automata, which are a simple paradigm for distributed computation. Cellular automata are made of basic Boolean computational units, the cells; relying on simple rules and information from- the surrounding cells to perform a global task. The limited visibility of the cells can be modeled as a network, where interactions amongst cells are governed by an underlying structure, usually a regular one. In order to increase the performance of cellular automata, we chose to change its topology. We applied computational principles inspired by Darwinian evolution, called evolutionary algorithms, to alter the system's topological structure starting from either a regular or a random one. The outcome is remarkable, as the resulting topologies find themselves sharing properties of both regular and random network, and display similitudes Watts-Strogtz's small-world network found in social systems. Moreover, the performance and tolerance to probabilistic faults of our small-world like cellular automata surpasses that of regular ones. In the second part, we use the context of biological genetic regulatory networks and, in particular, Kauffman's random Boolean networks model. In some ways, this model is close to cellular automata, although is not expected to perform any task. Instead, it simulates the time-evolution of genetic regulation within living organisms under strict conditions. The original model, though very attractive by it's simplicity, suffered from important shortcomings unveiled by the recent advances in genetics and biology. We propose to use these new discoveries to improve the original model. Firstly, we have used artificial topologies believed to be closer to that of gene regulatory networks. We have also studied actual biological organisms, and used parts of their genetic regulatory networks in our models. Secondly, we have addressed the improbable full synchronicity of the event taking place on. Boolean networks and proposed a more biologically plausible cascading scheme. Finally, we tackled the actual Boolean functions of the model, i.e. the specifics of how genes activate according to the activity of upstream genes, and presented a new update function that takes into account the actual promoting and repressing effects of one gene on another. Our improved models demonstrate the expected, biologically sound, behavior of previous GRN model, yet with superior resistance to perturbations. We believe they are one step closer to the biological reality.

Reliable control for networked control systems with probabilistic sensors and actuators faults

This study is concerned with the reliable controller design for networked control systems (NCS) against both probabilistic sensors faults and actuators faults. The faults of each sensor or actuator occur randomly and their failure rates are governed by two sets of unrelated random variables satisfying certain probabilistic distribution. In terms of the probabilistic failures of every sensor or actuator, new type of distribution-based NCS fault model is proposed. Based on the new built model, reliable controller is designed and sufficient conditions for the exponentially mean square stability (EMSS) of NCS are obtained by using Lyapunov functional method. The main contribution of the proposed fault model and methods lies with its practicality and generalisation, which contains many realistic problems in the NCS, such as probabilistic sensors or actuators failures, partial degradation, data distortion, packet dropout, network-induced delay and so on. Moreover, some existing models in the open literatures are deemed as special cases of the proposed fault model. To illustrate the implementation procedure, a vertical take-off and landing (VTOL) aircraft system is given to show the effectiveness and application of the proposed method.

Safety, Dependability and Performance Analysis of Extended AADL Models

This paper presents a component-based modelling approach to system-software co-engineering of real-time embedded systems, in particular aerospace systems. Our method is centred around the standardized Architecture Analysis and Design Language (AADL) modelling framework. We formalize a significant subset of AADL, incorporating its recent Error Model Annex for modelling faults and repairs. The major distinguishing aspects of this component-based approach are the possibility to describe nominal hardware and software operations, hybrid (and timing) aspects, as well as probabilistic faults and their propagation and recovery. Moreover, it supports dynamic (i.e. on-the-fly) reconfiguration of components and inter-component connections. The operational semantics gives a precise interpretation of specifications by providing a mapping onto networks of event-data automata. These networks are then subject to different kinds of formal analysis such as model checking, safety and dependability analysis and performance evaluation. Mature tool support realizes these analyses. The activities reported in this paper are carried out in the context of the correctness, modelling, and performance of aerospace systems, project which is funded by the European Space Agency.