The maximum clique problem is an NP hard combinatorial optimization problem, which is widely used in industrial and management processes. In order to approach the solution of the maximum clique problem, a deterministic annealing algorithm is proposed. When the barrier parameter is reduced from a large positive number to zero, the algorithm can track the minimum path of the obstacle problem to obtain a high-quality solution, which is a continuous method. The global convergence iteration of the Lagrange multiplier can be performed to obtain the minimum point of the obstacle problem in the feasible descent direction for any given positive value of the barrier parameter and has a desired property that it automatically satisfies the upper and lower bounds of variables if the steplength is a number that is between 0 and 1. Numerical results are provided to illustrate the efficiency of the proposed algorithm.
This paper establishes an adaptive synchronization problem for the master and slave structure of linear systems with nonlinear perturbations and mixed time-varying delays, where the mixed delays comprise different discrete and distributed time-delays. Using an appropriate Lyapunov-Krasovskii functional, some delay-dependent sufficient conditions and an adaption law which include the master-slave parameters are established for designing a delayed synchronization law in terms of linear matrix inequalities. The controller guarantees the H ∞ synchronization of the two coupled master and slave systems regardless of their initial states. Particularly, it is shown that the synchronization speed can be controlled by adjusting the update gain of the synchronization signal. A numerical example is given to show the effectiveness of the method.
This chapter intends to tackle the problem of finite-time projective synchronization of variable-order fractional (VOF) chaotic systems through the sliding mode control (SMC) method. First, for the VOF unperturbed chaotic systems, novel VOF integral- and derivative-type sliding surfaces are designed with the aid of VOF calculus. These surfaces play a crucial role in the control strategy by facilitating the management of system dynamics. Second, VOF control strategies are proposed, relying on the corresponding sliding surfaces to ensure that the projective error systems are asymptotically stable in finite time. Furthermore, by utilizing two transformations of VOF calculus, a novel finite-time stability criterion is also obtained, providing an upper bound of reaching time. This criterion is essential for predicting the system's behavior and ensuring timely synchronization. Finally, a numerical study is conducted to illustrate the superiority of the proposed method, demonstrating its effectiveness and practical applicability in achieving finite-time synchronization in VOF chaotic systems.
In this paper, robust H∞ control for a class of uncertain stochastic Markovian jump systems (SMJSs) with interval and distributed time-varying delays is investigated. The jumping parameters are modelled as a continuous-time, finite-state Markov chain. By employing the Lyapunov-Krasovskii functional and stochastic analysis theory, some novel sufficient conditions in terms of linear matrix inequalities are derived to guarantee the mean-square asymptotic stability of the equilibrium point. Numerical simulations are given to demonstrate the effectiveness and superiority of the proposed method comparing with some existing results.
No abstract is provided for this article.
This paper aims at providing new design approaches for positive observers of discrete-time positive linear systems based on a construction method of linear copositive Lyapunov function for positive systems. First, an efficient positive observer design approach is proposed by using linear programming such that the observer error system is exponentially stable. Furthermore, an interval observer design is proposed for uncertain positive systems. Then, the results are extended to positive time delay systems. In contrast with the previous design approaches, the new design method provides a general observer design with lower computational burden. Finally, three comparison examples are given to show the merit of the new design approach.
In this paper by using the quantized space and time theory we explain that why magnetic momentum of muons in Fermilab National Accelerator Laboratory (FNAL) has anomaly and doesn't compatible with the predicted amounts in the standard model. Also the speed of muons in cyclotron will be calculated precisely.
This article studies the decentralized event-triggered control problem for a class of constrained nonlinear interconnected systems. By assigning a specific cost function for each constrained auxiliary subsystem, the original control problem is equivalently transformed into finding a series of optimal control policies updating in an aperiodic manner, and these optimal event-triggered control laws together constitute the desired decentralized controller. It is strictly proven that the system under consideration is stable in the sense of uniformly ultimate boundedness provided by the solutions of event-triggered Hamilton-Jacobi-Bellman equations. Different from the traditional adaptive critic design methods, we present an identifier-critic network architecture to relax the restrictions posed on the system dynamics, and the actor network commonly used to approximate the optimal control law is circumvented. The weights in the critic network are tuned on the basis of the gradient descent approach as well as the historical data, such that the persistence of excitation condition is no longer needed. The validity of our control scheme is demonstrated through a simulation example.
This paper investigates the finite-time distributed<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mtext>–</mml:mtext><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math>consensus control problem of multiagent systems with parameter uncertainties. The relative states of neighboring agents are used to construct the control law and some agents know their own states. By substituting the control input into multiagent systems, an augmented closed-loop system is obtained. Then, we analyze its finite-time boundedness (FTB) and finite-time<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mtext>–</mml:mtext><mml:msub><mml:mrow><mml:mi>L</mml:mi></mml:mrow><mml:mrow><mml:mi>∞</mml:mi></mml:mrow></mml:msub></mml:math>performance. A sufficient condition for the existence of the designed controller is given with the form of linear matrix inequalities (LMIs). Finally, simulation results are described.
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No abstract is provided for this article.
Compared to the single-source domain adaptation fault diagnosis methods, the multi-source domain adaptation methods not only can take advantage of the rich and diverse diagnostic information of multiple source domains but also draw on the feature alignment of single-source setting to reduce the domain discrepancy. However, forcing the alignment of feature distributions is challenging and may lead to negative transfer. Meanwhile, labeled data are often scarce and difficult to collect in actual production, which can be mitigated by adequate multi-source information, but the diagnostic performance of the model is degraded by large domain differences. To tackle the above issues, a domain attribute and feature transfer network is proposed to model multi-source information domains in a unified deep network and achieve cross-domain fault diagnosis. In the attribute transfer section, we adopt an attention mechanism to extract transferable latent attributes from multi-source information. In the feature transfer section, we apply the local maximum mean discrepancy metric to adjust the category distribution of single-source information and target domains. Then, intra-class compactness learning and pseudo-labeling learning strategies are utilized to obtain richer feature representations. Finally, we propose the knowledge fusion module to fuse the results of multi-source information classifiers to yield a more reliable diagnosis result. Extensive experiments on three different multi-source information datasets show the superiority of our method compared to the state-of-the-art methods (SOTA) by comparing indicators from various aspects.
