Fractional Order Fault Tolerant Control - A Survey

In this paper, a comprehensive review of recent advances and trends regarding Fractional Order Fault Tolerant Control (FOFTC) design is presented. This novel robust control approach has been emerging in the last decade and is still gathering great research efforts mainly because of its promising results and outcomes. The purpose of this study is to provide a useful overview for researchers interested in developing this interesting solution for plants that are subject to faults and disturbances with an obligation for a maintained performance level. Throughout the paper, the various works related to FOFTC in literature are categorized first by considering their research objective between fault detection with diagnosis and fault tolerance with accommodation, and second by considering the nature of the studied plants depending on whether they are modelized by integer order or fractional order models. One of the main drawbacks of these approaches lies in the increase in complexity associated with introducing the fractional operators, their approximation and especially during the stability analysis. A discussion on the main disadvantages and challenges that face this novel fractional order robust control research field is given in conjunction with motivations for its future development. This study provides a simulation example for the application of a FOFTC against actuator faults in a Boeing 747 civil transport aircraft is provided to illustrate the efficiency of such robust control strategies

Synchronization of two fractional-order chaotic systems via nonsingular terminal Fuzzy Sliding Mode Control

La sincronización de dos sistemas caóticos complejos de orden fraccional se discute en este documento. El parámetro incertidumbre y la perturbación externa se incluyen en el modelo del sistema, y la sincronización de los sistemas considerados caóticos se implementa en base al concepto de tiempo finito. Primero, se propone una nueva superficie deslizante terminal no singular de orden fraccional que es adecuada para los sistemas de orden fraccional considerados. Se ha demostrado que una vez que las trayectorias del estado del sistema alcancen la superficie de deslizamiento propuesta, convergerán al origen dentro de un tiempo finito dado. En segundo lugar, en términos de la superficie deslizante terminal no singular establecida, que combina el control difuso y los esquemas de control de modo deslizante, se introduce una ley de control de modo deslizante difusa única novedosa y robusta que puede forzar las trayectorias del sistema de error dinámico de circuito cerrado para alcanzar el deslizamiento superficie durante un tiempo finito. Finalmente, utilizando el teorema de estabilidad fraccional de Lyapunov, se demuestra la estabilidad del método propuesto. El método propuesto se implementa para la sincronización de dos sistemas caóticos Genesio-Tesi de orden fraccional con parámetros inciertos y perturbaciones externas para verificar la efectividad del controlador de modo de deslizamiento difuso terminal no-singular de orden fraccional propuesto.The synchronization of two fractional-order complex chaotic systems is discussed in this paper. The parameter uncertainty and external disturbance are included in the system model, and the synchronization of the considered chaotic systems is implemented based on the finite-time concept. First, a novel fractional-order nonsingular terminal sliding surface which is suitable for the considered fractional-order systems is proposed. It is proven that once the state trajectories of the system reach the proposed sliding surface they will converge to the origin within a given finite time. Second, in terms of the established nonsingular terminal sliding surface, combining the fuzzy control and the sliding mode control schemes, a novel robust single fuzzy sliding mode control law is introduced, which can force the closed-loop dynamic error system trajectories to reach the sliding surface over a finite time. Finally, using the fractional Lyapunov stability theorem, the stability of the proposed method is proven. The proposed method is implemented for synchronization of two fractional-order Genesio-Tesi chaotic systems with uncertain parameters and external disturbances to verify the effectiveness of the proposed fractional-order nonsingular terminal fuzzy sliding mode controller.• National Natural Science Foundation of China. Becas U1604146, U1404610, 61473115, 61203047 • Science and Technology Research Project in Henan Province. 152102210273, 162102410024 • Foundation for the University Technological Innovative Talents of Henan Province. Beca 18HASTIT019peerReviewe

Fixed-time sliding mode based observer for nonlinear systems with unknown parameters and unknown inputs

International audienceIt is of importance to design observers for multi-variable nonlinear systems with unknown parameters and partially driven by unknown inputs. Such a problem arises in systems subject to disturbances or with inaccessible inputs and in many applications such as parameter identification, fault detection and isolation or cryptography. In this paper, the problem of fixed-time observation for nonlinear dynamical systems with unknown parameter and inputs is studied. Conditions on full/partial state and parameters identification are provided by the the way of an observation algorithm based on differential geometry theory. Then, an uniform differentiator for estimating simultaneously the states and unknown parameters in fixed-time while avoiding observability singularities is designed. An example on topology identification of network systems is described to show the effectiveness of the proposed method

Risk Control for Synchronizing a New Economic Model

Risk analysis in control problems is a critical but often overlooked issue in this research area. The main goal of this analysis is to assess the reliability of designed controllers and their impact on applied systems. The chaotic behavior of fractional-order economical systems has been extensively investigated in previous studies, leading to advancements in such systems. However, this chaotic behavior poses unpredictable risks to the economic system. This paper specifically investigates the reliability and risk analysis of chaotic fractional-order systems synchronization. Furthermore, we present a technique as a new mechanism to evaluate controller performance in the presence of obvious effects. Through a series of simulation studies, the reliability and risk associated with the proposed controllers are illustrated. Ultimately, we show that the suggested technique effectively reduces the risks associated with designed controllers

Resilience-oriented control and communication framework for cyber-physical microgrids

Climate change drives the energy supply transition from traditional fossil fuel-based power generation to renewable energy resources. This transition has been widely recognised as one of the most significant developing pathways promoting the decarbonisation process toward a zero-carbon and sustainable society. Rapidly developing renewables gradually dominate energy systems and promote the current energy supply system towards decentralisation and digitisation. The manifestation of decentralisation is at massive dispatchable energy resources, while the digitisation features strong cohesion and coherence between electrical power technologies and information and communication technologies (ICT). Massive dispatchable physical devices and cyber components are interdependent and coupled tightly as a cyber-physical energy supply system, while this cyber-physical energy supply system currently faces an increase of extreme weather (e.g., earthquake, flooding) and cyber-contingencies (e.g., cyberattacks) in the frequency, intensity, and duration. Hence, one major challenge is to find an appropriate cyber-physical solution to accommodate increasing renewables while enhancing power supply resilience. The main focus of this thesis is to blend centralised and decentralised frameworks to propose a collaboratively centralised-and-decentralised resilient control framework for energy systems i.e., networked microgrids (MGs) that can operate optimally in the normal condition while can mitigate simultaneous cyber-physical contingencies in the extreme condition. To achieve this, we investigate the concept of "cyber-physical resilience" including four phases, namely prevention/upgrade, resistance, adaption/mitigation, and recovery. Throughout these stages, we tackle different cyber-physical challenges under the concept of microgrid ranging from a centralised-to-decentralised transitional control framework coping with cyber-physical out of service, a cyber-resilient distributed control methodology for networked MGs, a UAV assisted post-contingency cyber-physical service restoration, to a fast-convergent distributed dynamic state estimation algorithm for a class of interconnected systems.Open Acces

Fixed-Time Synchronization for Hybrid Coupled Dynamical Networks with Multilinks and Time-Varying Delays

This paper concerns the problem of fixed/finite-time synchronization of hybrid coupled dynamical networks. The considered dynamical networks with multilinks contain only one transmittal time-varying delay for each subnetwork, which makes us get hold of more interesting and practical points. Two kinds of delay-dependent feedback controllers with multilinks as well as appropriate Lyapunov functions are defined to achieve the goal of fixed-time synchronization and finite-time synchronization for the networks. Some novel and effective criteria of hybrid coupled networks are derived based on fixed-time and finite-time stability analysis. Finally, two numerical simulation examples are given to show the effectiveness of the results proposed in our paper

Sliding Mode Control

The main objective of this monograph is to present a broad range of well worked out, recent application studies as well as theoretical contributions in the field of sliding mode control system analysis and design. The contributions presented here include new theoretical developments as well as successful applications of variable structure controllers primarily in the field of power electronics, electric drives and motion steering systems. They enrich the current state of the art, and motivate and encourage new ideas and solutions in the sliding mode control area

Fast synchronization of complex dynamical networks with time-varying delay via periodically intermittent control

The fast synchronization problem for a class of complex dynamical networks with time varying delay by means of periodically intermittent control is studied. Based on the finite-time stability theory and periodically intermittent control technique, some sufficient synchronization criteria are obtained to guarantee the fast synchronization. Furthermore, the essential condition for guaranteeing periodically intermittent control realized in finite time is given in this paper. Finally, two examples are illustrated to verify the proposed theoretical results.http://www.elsevier.com/locate/neucom2017-09-30hb2016Electrical, Electronic and Computer Engineerin

Nonlinear Systems

Open Mathematics is a challenging notion for theoretical modeling, technical analysis, and numerical simulation in physics and mathematics, as well as in many other fields, as highly correlated nonlinear phenomena, evolving over a large range of time scales and length scales, control the underlying systems and processes in their spatiotemporal evolution. Indeed, available data, be they physical, biological, or financial, and technologically complex systems and stochastic systems, such as mechanical or electronic devices, can be managed from the same conceptual approach, both analytically and through computer simulation, using effective nonlinear dynamics methods. The aim of this Special Issue is to highlight papers that show the dynamics, control, optimization and applications of nonlinear systems. This has recently become an increasingly popular subject, with impressive growth concerning applications in engineering, economics, biology, and medicine, and can be considered a veritable contribution to the literature. Original papers relating to the objective presented above are especially welcome subjects. Potential topics include, but are not limited to: Stability analysis of discrete and continuous dynamical systems; Nonlinear dynamics in biological complex systems; Stability and stabilization of stochastic systems; Mathematical models in statistics and probability; Synchronization of oscillators and chaotic systems; Optimization methods of complex systems; Reliability modeling and system optimization; Computation and control over networked systems

Synchronization of complex dynamical networks with fractional order

Complex dynamical networks (CDN) can be applied to many areas in real world, from medicine, biology, Internet to sociology. Study on CDNs has drawn great attention in recent years. Nodes in a CDN can be modelled as systems represented by differential equations. Study has shown that fractional order differential equations (DF) can better represent some real world systems than integer-order DFs. This research work focuses on synchronization in fractional CDNs.  A literature review on CDNs with fractional order has summarized the latest works in this area.  Fractional chaotic systems are studied in our initial investigation.  Fractional calculus is introduced and the relevant fundamentals to model, describe and analyse dynamical networks are presented. It is shown that the structure and topological characteristics of a network can have a big impact on its synchronizability. Synchronizability and its various interpretations in dynamical networks are studied. To synchronize a CDN efficiently, controllers are generally needed. Controller design is one of the main tasks in this research. Our first design is a new sliding mode control to synchronize a dynamical network with two nodes. Its stability has been proven and verified by simulations.  Its convergence speed outperforms Vaidyanathan's scheme, a well-recognized scheme in this area. The design can be generalized to CDNs with more nodes.  As many applications can be modelled as CDNs with node clustering, a different sliding mode control is designed for cluster synchronization of a CDN with fractional order. Its stability is proven by using Lyapunov method. Its convergence and efficiency is shown in a simulation. Besides these nonlinear methods mentioned, linear control is also studied intensively for the synchronization.  A novel linear method for synchronization of fractional CDNs using a new fractional Proportional-Integral (PI) pinning control is proposed.  Its stability is proven and the synchronization criteria are obtained. The criteria have been simplified using two corollaries so the right value for the variables can be easily assigned. The proposed method is compared with the conventional linear method which uses Proportional (P) controller. In the comparison, the mean squared error function is used. The function measures the average of the squared errors and it is an instant indicator of the synchronization efficiency. A numerical simulation is repeated 100 times to obtain the averages over these runs. Each simulation has different random initial values for both controllers. The average of the errors in all the 100 simulations is obtained and the area under the function curve is defined as an overall performance index (OPI), which indicates the controller's overall performance. In control, small overshoot is always desired. In our work, the error variation is also used as a measure.  The maximum variation from the average of 100 simulations is calculated and compared for both methods. With all the statistical comparisons, it is clear that with the same power consumption, the proposed method outperforms the conventional one and achieves faster and smoother synchronization. Communication constraints exist in most real world CDNs. Communication constraints and their impact on control and synchronization of CDNs with fractional order are investigated in our study. A new adaptive method for synchronizing fractional CDN with disturbance and uncertainty is designed. Its stability is proven and its synchronization criteria are obtained for both fractional CDN with known and unknown parameters. Random disturbance is also included in both cases. Our results show that the new method is efficient in synchronizing CDNs with presence of both disturbance and uncertainty