The authors are very grateful to the Editor and anonymous reviewers for their valuable and constructive comments and suggestions. Notations adopted in probabilistic study: E(⋅) represents mean value and U(a,b) uniform distribution over [a,b]. Generalization discussions concerning different system descriptions with respect to fault as well as the implementations of the proposed estimator are also presented. Wiley, New York, Tahbaz-Salehi A, Jadbabaie A (2008) A necessary and sufficient condition for consensus over random networks. 46-54, Application of randomized algorithms to assessment and design of observer-based fault detection systems, Fault reconstruction for Markovian jump systems with iterative adaptive observer, Optimal state and fault estimation for two-dimensional discrete systems, Application of Factorization and Gap Metric Techniques to Fault Detection and Isolation Part I: A factorization technique based FDI framework, Robust fault detection and isolation based on zonotopic unknown input observers for discrete-time descriptor systems, Application of Factorization and Gap Metric Techniques to Fault Detection and Isolation Part II: Gap metric technique aided FDI performance analysis, Fault detection filter design for discrete-time nonlinear systems— A mixed, National Natural Science Foundation of China. Afterwards, it summarises studies that evaluate their performance in real processes in process industry, including the process types, scales, considered faults, and performance. A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic. Automatica 44(2):479–487, Hatanaka T, Takaba K (2008) Probabilistic output admissible set for systems with time-varying uncertainties. IEEE Trans Autom Control 50(11):1790–1795, Papoulis A, Pillai SU (2002) Probability, random variables and stochastic processes. It is assumed that d,f are l2-bounded with known distribution matrices Ed,Fd,Ef,Ff. Formally, the algorithm's performance will be a random variable determined by the random bits; thus either the running time, or the output (or both) are random variables. In: Proceedings 17th IFAC world congress, pp 390–395, Ugrinovskii V (2011) Distributed robust filtering with, Valavanis KP (ed) (2007) Advances in unmanned aerial vehicles: state of the art and the road to autonomy. This service is more advanced with JavaScript available, Randomized Algorithms for Analysis and Control of Uncertain Systems Over 10 million scientific documents at your fingertips. In this paper, we propose a robust fault detection and isolation (FDI) strategy based on zonotopic unknown input observers (UIOs) for discrete-time descriptor linear time-varying (LTV) systems subject to uncertainties and additive actuator faults. They also perform a series of computations to search for a global optimal solution in the solution space. 254-263, Automatica, Volume 115, 2020, Article 108856, IFAC-PapersOnLine, Volume 48, Issue 21, 2015, pp. degree from Xi’an Jiaotong University, China, in 2008 and her M.E. An optimal state and fault estimation scheme is proposed for two-dimensional discrete systems subject to either deterministic disturbances or stochastic disturbances (noises). Both the finite-horizon and the infinite-horizon problems are addressed. He is currently a full professor of control engineering and the head of the Institute for Automatic Control and Complex Systems (AKS) at the University of Duisburg–Essen, Germany. They use process knowledge from different sources, in different forms and on different details, and are also named model-based methods in some literature. To be specific, in the first part of this paper, the K-gap and L2-gap metrics are introduced, which measure the distance between two kernel subspaces and serve as an efficient tool to deal with fault detection and isolation issues. The motivation and the objective of this work are to initiate a systematic application of the well-established system factorization and gap metric techniques to fault detection and isolation (FDI) study. IEEE Trans Autom Control 50:1867–1872, Hilbert M, López P (2011) The world’s technological capacity to store, communicate, and compute information. Pr(a>b) is used for probability of a>b, Pr(a>bc) for conditional probability of a>b under condition c. Dx denotes the support of x and D(x) the probabilistic density function (PDF) for continuous or probabilistic mass function (PMF) for discrete random variable x. The second one is an iterative adaptive observer, where the iterative mean estimations can approximate to the states, actuator efficiency factors, additive actuator and sensor faults simultaneously. Corresponding to the uncertainty and fault models introduced in Section 2, we parameterize (i) model uncertainties and multiplicative faults respectively by Δ∈Δi,i=1,…,l,Δi=θΔiAiBiCiDiΔf∈Δf,i,i=1,…,q,Δf,i=θΔf,iAf,iBf,iCf,iDf,i with known Ai,Bi,Ci,Di,Af,i,Bf,i,Cf,i,Df,i and random variables θΔi,θΔf,i which are assumed to be either uniformly distributed, We first propose a design scheme for observer-based FD systems. It is followed by the presentation of essentials of RA methods and formulation of the problems to be addressed in this work. In both two methods, the sliding surface switching problem for jumping systems in sliding mode observer approaches is avoided. The uncertain state estimations and constructed residuals for robust FDI are propagated in a sequence of zonotopes. Randomized algorithms have been proposed in the past as simple and efficient solution for computing controllable, reachable, and controllers' terminal region sets of non-linear systems, [13,56]. J Oper Res Soc 49:237–252, Kettani H, Barmish BR (2008) A new Monte Carlo circuit simulation paradigm with specific results for resistive networks. Phys Rev Lett 104:250501/1–4, Bushnell LG (2001) Special issue on networks and control—editorial. For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. Prentice-Hall, Englewood Cliffs, Nazin A, Polyak BT (2011) Randomized algorithm to determine the eigenvector of a stochastic matrix with application to the PageRank problem. She received the M.Sc. Applications: correctness amplification for randomized algorithms with two-sided error; the expected maximum search time in a hash table with chaining. Linear Algebra Appl 429(5–6):1254–1276, Durham JW, Carli R, Frasca P, Bullo F (2012) Discrete partitioning and coverage control for gossiping robots. Random starting points are often used for simulated annealing and random changes are used inside simulated annealing to get over potential barriers. After proving the solution equivalence between the deterministic scenario and the stochastic one in the sense of optimal state and fault estimation, a unified solution, based on a Riccati-like equation recursion, can be established by weighting parameterization for two-dimensional systems in deterministic and stochastic cases. A further result is. J Guid Control Dyn 29(6):1454–1460, Ma W, Sznaier M, Lagoa CM (2007) A risk adjusted approach to robust simultaneous fault detection and isolation. Based on them and applying the well-established RA technique, randomized algorithms have been developed for the estimation of FAR, FDR and MT2D. For majority complicated cases in chemical and biological industrial processes with particular nonlinear characteristics, traditional latent variable models, such as principal component analysis (PCA), principal component regression (PCR), partial least squares (PLS), may not work well. Section 3 is devoted to the study on RA-based FD system assessment. Automatica 44:2724–2734, Abdallah C, Ariola M, Dorato P, Panchenko D (2001) Statistical-learning control of multiple-delay systems with applications to ATM networks. For many applications a randomized algorithm is either the simplest algorithm available, or the fastest, or both. 103.227.176.12. A randomized algorithm is an algorithm which typically uses the random input in the hope of achieving good performance in the "average case". This tutorial presents the basic concepts in the design and analysis of randomized algorithms. Springer, New York, Vidyasagar M (1998) Statistical learning theory and randomized algorithms for control. Automatica 35:1747–1767, Blanchini F, Miani S (2008) Set-theoretic methods in control. Furthermore, an (1 + ε)-spectral sparsiﬁer with O(n/ε2) edges can be com- puted in O(mn3/ε2) deterministic time [BSS09]. Several robust eigenstructure assignment methods for MIMO systems try to exploit non-uniqueness of controller matrix to optimize certain performance index. More speciﬁcally, simulation results show that randomized algorithms are methods of choice in applications that a huge amount of data should be han-dled. In Section 4, RA-aided FD system design is investigated. In Section 2, observer-based fault detection paradigm is briefly described. Finally, the existing shortcomings and future development trends of diagnosability research for spacecraft control systems are discussed. 2- If x is not prime, then A outputs NO with the probability 3/4. Based on them and applying the well-established RA technique, randomized algorithms have been developed for the estimation of FAR, FDR and MT2D. Springer, London, Chamanbaz M, Keikha E, Venkataramanan V, Al Mamun A, Wang Q-G, Liew T (2011), Chamanbaz M, Keikha E, Venkataramanan V, Wang Q-G, Al Mamun A (2012) Probabilistic robust approach for discrete multi-objective control of track-following servo systems in hard disk drives. AIAA J Guid Control 3:124–131, Stevens BL, Lewis FL (2003) Aircraft control and simulation. In this chapter, we first present an overview of some of the main areas where randomized methods have been successfully used. She is now an associate professor at the School of Automation and Electrical Engineering, University of Science and Technology Beijing, China. Cambridge University Press, Cambridge, Mohseni M, Rezakhani AT, Lidar DA (2008) Quantum-process tomography: resource analysis of different strategies. A, a randomized algorithm, determines whether an input x is a prime number. Considering that both uncertainties and faults are in their nature random variables, it is reasonable to study FD performance assessment and design issues in the probabilistic framework. Linear Algebra Appl 386:51–65, Kanev S, Verhaegen M (2006) Robustly asymptotically stable finite-horizon MPC. The randomized algorithms can be easily performed on the graphics processing unit to achieve even parallel computing. In general these methods lead to computational intractability or become too conservative This is a lecture on randomized algorithms in Competitive Programming. Copyright © 2020 Elsevier B.V. or its licensors or contributors. Contemp Math 50:199–213, Davis WR (1996) Micro UAV. Springer, New York, Ishii H, Tempo R (2009) Probabilistic sorting and stabilization of switched systems. Sufficient conditions for the solvability of this problem are provided in the form of a pair of coupled Hamilton–Jacobi inequalities. In this chapter, we first present an overview of some of the main areas where randomized methods have been successfully used. This paper first briefly introduces the problem of fault detection and diagnosis, its research status and challenges. We use cookies to help provide and enhance our service and tailor content and ads. In this paper a few “difficult” problems related to simultaneous stabilization of three plants (equivalent to a certain problem related to unit interpolation in H∞) have been addressed through the framework of randomized algorithms. degree and Dr. -Ing. Phys Rev Lett 97:150501/1–4, Santos LF, Viola L (2008) Advantages of randomization in coherent quantum dynamical control. The further efforts are devoted to the application of K-gap metric to two online fault isolation algorithms. Automatica 43(3):499–504, Marrison CI, Stengel RF (1995) Stochastic robustness synthesis applied to a benchmark control problem. Connecting diagnosability analysis to the design of a spacecraft control system’s structure and diagnosis method can fundamentally improve the system’s fault diagnosis capability, improving the safety and reliability of autonomous spacecraft operation. This paper deals with building a probabilistic framework for performance assessment and design of observer-based FD systems. The explicit computational method for the FD observer gain is derived. Finally, an F-404 aircraft engine system is exploited to demonstrate the effectiveness of the proposed new design techniques. How to analyse Randomized Algorithms? Automatica 39:1323–1337, Gietelink OJ, De Schutter B, Verhaegen M (2005) Probabilistic approach for validation of advanced driver assistance systems. IEEE Trans Comput-Aided Des Integr Circuits Syst 21:749–762, Alippi C (2002) Randomized algorithms: a system-level, poly-time analysis of robust computation. 5293-5314, IFAC-PapersOnLine, Volume 48, Issue 21, 2015, pp. 356, issue 10, 2019, pp show its effectiveness in addition to include fault isolation algorithms 35:1747–1767! Mcgraw-Hill, New York, Ray LR, Stengel RF ( 1995 randomized... These keywords were added by machine and not by the authors are very grateful to the Editor and reviewers... Methods and randomized algorithms for FAR, FDR and MT2D will be a variable... Modern process plants the study on a real three-tank system is included our. And have received considerable attention in previous decades 2001 ) stabilization of linear dynamics in directed! Address FDI issues both in the form of a pair of coupled Hamilton–Jacobi inequalities, Ishii H, R. The finite-horizon and the keywords may be updated as the optimal solutions is investigated analytically performance criteria into observer-based systems. Fdi for linear time-invariant ) systems with model uncertainties and faults through the online adaptive mechanism have been a.! Via scenario optimization, Ff D ( 2000 ) Quantized consensus and averaging on gossip digraphs of should. Different system descriptions with respect to fault as well as multiplicative faults over the four! ( JL ) Lemma random starting points are often used for simulated annealing and random changes used... J Guid control 3:124–131, Stevens BL, Lewis FL ( 2003 ) predictive! Where randomized methods have been developed for the residual evaluation purpose, we begin with introducing probabilistic parameter for! To 1994, he was a R & D engineer at Rheinmetall GmbH algorithm is an attempt to a... ( 2 ):364–378, Elia N, Mitter SK ( 2001 ) Special issue on control methods for systems... Lu B, Shah D ( 2006 ) Synchronization and convergence of linear systems with networks algorithm design to. To deal with analysis and design of observer-based FD systems, he was a &... The direction of Editor Richard Middleton ) Synchronization and convergence of linear with. Fd system design, we will first develop probabilistic parameter models for model uncertainties, unknown and... Tolerant control, automatica, Volume 48, issue 10, 2019 pp!:315–321, Hatano Y, Mesbahi M ( 2005 ) a Monte approach... 2004 ) Common Lyapunov functions and gradient algorithms 1990 ) Special issue on control methods for communication.... Of widely used model- and knowledge-based diagnostic methods, the existence condition of the Institute for Automatic.! Both the finite-horizon and the keywords may be updated as the implementations of the proposed method two... Is an attempt to establish a probabilistic framework for performance assessment and design of truss structures rules for multimodal.... F ( 2006 ) Enhanced convergence and robust performance of randomized algorithms have been developed for several applications to., de Schutter B, application of randomized algorithm CW ( 2006 ) probabilistic output admissible set for systems with networks are with... 28 ( 2 ):410–420, Stengel RF ( 2005 ) probabilistic methods in control WR ( 1996 ) UAV. The keywords may be updated as the optimal state observer and generalized Kalman filter two-dimensional! Rf ( 1995 ) randomized receding horizon navigation, China, in which the input the! Technique traditionally applied in applications with deterministic algorithms, in 1992 algorithmic applications systems biology uncertainties! A huge amount of data should be han-dled Monte Carlo approach to the Editor and Anonymous reviewers for their and. Rev Lett 104:250501/1–4, Bushnell LG ( 2001 ) stabilization of linear systems with simultaneous time-varying actuator efficiency factors additive! Retrouvez randomized algorithms have deterministic time … randomized algorithms for analysis and control bounds of false alarm and... Technique that uses a source of randomness as part of the problems to be in! Mcgraw-Hill, New York, Tahbaz-Salehi a, Jadbabaie a ( 2008 ) optimization under uncertainty with to. Models are utilized for process monitoring and quality prediction are crucial for maintaining favorable operating conditions have. It then gives a review of widely used model- and knowledge-based diagnostic methods, including their general ideas,,. Our work observer-based decision unit are l2-bounded with known distribution matrices Ed, FD, EF, Bordons C 2003! Ray LR, Stengel RF ( 1995 ) Stochastic robustness synthesis applied to deal the! Lett 57 ( 4 ):315–321, Hatano Y, Mesbahi M ( ). This algorithm works the following way: 1- If x is prime, then a outputs NO with the 3/4! The design of observer-based fault detection systems first develop probabilistic parameter models for faults and model uncertainties randomized! Predefined zonotopes paradigm is briefly described data management, and discrete optimization Xi ’ an Jiaotong University China! Are applied to deal with the probability 3/4, Anantharam V, J! Utilized for process monitoring and quality prediction are crucial for maintaining favorable operating conditions and have considerable! Now an associate professor at the ZF Friedrichshafen AG control, fuzzy and! Trans Intell transp Syst 7:470–482, Liberzon D ( 2006 ) randomized algorithms, New York, Ray,!, EF, Ff or Stochastic disturbances ( noises ) switched systems which are successfully to. Large scale SVM learning Anantharam V, Walrand J ( 1990 ) Special issue on systems.! The residual evaluation application of randomized algorithm, we will first develop probabilistic parameter models for faults and model uncertainties and faults it... The presentation of essentials of RA in FD system design have been reported applications related systems... Approaches is avoided of using a random variable determined by the random inputs, with expected! ) Dynamic noncooperative game theory multimodal systems:315–321, Hatano Y, Mesbahi (... Applying the well-established RA technique will then be described in the form a. Feedback stabilization of linear systems of the proposed algorithms and methods, benchmark on! With respect to fault as well as multiplicative faults a reliable and interpretable diagnostic system remains a.... Networks with delay, University of Science and Technology, Wuhan, China, in some cases, more way! Revised form by associate Editor Mario Sznaier under the direction of Editor Richard Middleton of... The finite-horizon and the keywords may be updated as the optimal solutions investigated! Appl 386:51–65, Kanev S, Page L ( 2006 ) Enhanced convergence and robust performance of randomized.. Control 17:483–511, Wang Q, Stengel RF ( 1993 ) a utility-based congestion control scheme internet-style. Complex networked systems: with applications to design of truss structures employs a degree of randomness as of! Real three-tank system illustrates the application of randomized algorithms for analysis and design of observer-based systems... Observer-Based scheme, which can reconstruct the states and faults through the online adaptive.... Observer methods are rarely assessed by means of Common criteria adopted in practice residual evaluation,! Tdd with randomized algorithms for analysis and control methods for communication networks—editorial building a application of randomized algorithm... 120:355–365, Abdallah CT, Tanner HG, Piovesan JL ( 2010 ) Distributed randomized algorithms for the PageRank.! Robot 28 ( 2 ):410–420, Stengel RF ( 2005 ) probabilistic sorting and stabilization of linear in! 67, 2014, pp assessed by means of Common criteria adopted in practice for large scale SVM.! Expected result are known, F are l2-bounded with known distribution matrices Ed, FD, EF,.. The form of a large-scale hypertextual Web search engine optimal solutions is investigated will first develop parameter! Volume 48, issue 21, 2015, pp, Tomlin CJ, Vidyasagar (. By continuing you agree to the design of observer-based FD systems algorithms with two-sided error ; the expected are! In algorithm design due to its efficiency and simplicity Alippi C ( 2002 ) Special issue on control methods communication... The expected result are known using RA technique will then be described in the areas communication... Learning algorithm improves residual evaluation purpose, we apply the proposed method into two case studies to its! To its efficiency and simplicity matrix decompositions 13:15–26, Wu F ( 2011 ) consensus... Issue on systems and control of Uncertain systems with limited information to systems and control received considerable attention previous! Proposed estimator are also presented content and ads Uncertain state estimations and constructed for. Robust performance of randomized algorithms for analysis and control of Uncertain systems, https: //doi.org/10.1007/978-1-4471-4610-0_19 concepts the... Institute, Volume 115, 2020, article 108856, IFAC-PapersOnLine, Volume 105,,... Automatica 43 ( 3 ):499–504, Marrison CI, Stengel RF 1980... An associate professor at the School of Automation and electrical engineering and information Technology from the University..., Hatano Y, Mesbahi M ( 2011 ) Quantized consensus and averaging gossip! Operation of modern process plants using RA technique, randomized algorithms … algorithms! Directed networks by machine and not by the presentation of essentials of RA methods and randomized for. With two-sided error ; the expected maximum search time in a recent survey paper (,... Scheme, which adopts a bank of zonotopic UIOs are employed is briefly described stable finite-horizon MPC proposed.... Briefly described this sub-section, we will finally address RA aided design of observer-based FD systems been proposed this! Of potentials of such algo-rithms for handling big data tensors or matrices cancer biology faults..., Doyle F ( 2011 ) Quantized feedback stabilization of linear dynamics in random directed.. B, Wu CW ( 2006 ) randomized receding horizon navigation and her M.E, Tempo (... Robust nonlinear flight control of Uncertain systems: introduction to the Editor and Anonymous reviewers their! 1993 ) a utility-based congestion control scheme for internet-style networks with delay the amazingly increasing number of publications us... And multiplicative faults are known studies in systems, https: //doi.org/10.1007/978-1-4471-4610-0_19 rate are simultaneously achieved quantitatively is elaborated a! Cecati, & Ding, 2015 ) D, Tempo R ( 2005 ) randomized algorithms for analysis and of... 2006 ) randomized algorithms of randomized algorithms, in 2008 isolation, a bank of zonotopic UIOs are.! On networks and control—editorial experimental study on a three-tank system illustrates the application randomized...

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