—In practice, most physical chaotic systems are inherently with unknown nonlinearities, and conventional adaptive control for such chaotic systems typically faces with formidable technical challenges. As a better alternative, we propose using the recurrent high-order neural networks to identify and control the unknown chaotic systems, in which the Lyapunov synthesis approach is utilized for tuning the neural network model parameters. The globally uniform boundedness of the parameters estimation errors and the asymptotical stability of the tracking errors are proved by Lyapunov stability theory and LaSalle-Yoshizawa theorem. This method, in a systematic way, enables stabilization of chaotic motion to a steady state as well as tracking of any desired trajectory. Computer simulation on a complex chaotic system illustrates the effectiveness of the proposed control method. Key Words : Chaotic systems; Adaptive control; Lyapunov function; LaSalle-Yoshizawa theorem 1. INTRODUCTION
This paper presents the design, tuning and performance analysis of a new predictive fuzzy controller structure for higher order plants with large time delays. The designed controller consists of a fuzzy proportional‐integral (PI) part and a fuzzy predictor. The fuzzy predictive PI controller combines the advantages of fuzzy control while maintaining the simplicity and robustness of a conventional PI controller. The dynamics of the prediction term are adaptive to the system’s time delay. The prediction term has two parts: a fuzzy predictor that uses the system time delay as an input for calculating the prediction horizon and an exponential term that uses the prediction horizon as its positive power. The prediction term also introduces phase lead into the system which compensates for the phase lag due to the time delay in the plant, thereby stabilizing the closed‐loop configuration. The performance of the proposed controller is compared with the responses of the conventional predictive PI controller, showing many advantages of the new design over its conventional counterpart.
This brief investigates the cooperative adaptive <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> output regulation problem for continuous-time heterogeneous multi-agent Markov jump systems. First, a distributed mode-dependent observer is designed to estimate the dynamics of the Markov jump linear exosystem over a communication digraph. Then, an adaptive mode-dependent control law is designed for each agent such that the mean-square <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> output synchronization of the whole network is achieved. Finally, simulation results are provided to verify the theoretical results and demonstrate the effective control performances.
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The dynamical behaviors of some general spreading phenomena in discrete small-world networks are investigated. A new discrete small-world spreading model is proposed, where typical spreading dynamics, including period-doubling bifurcations and chaos, are analyzed on the small-world probability and the nonlinear interaction gain constant.
In this letter, a simple nonlinear state feedback controller is designed for generating hyperchaos from a three-dimensional autonomous chaotic system. The hyperchaotic system is not only demonstrated by computer simulations but also verified with bifurcation analysis, and is implemented experimentally via an electronic circuit.
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In this paper, periodic discretization behaviors of a bang-bang type switching control system are studied. A unified framework is proposed for exploring the intriguing discretization behaviors of the control system. Simulations are presented to show the effectiveness of the analysis.
This paper presents a design and simulation study of a fuzzy PD+I controller optimized via a multi-objective genetic algorithm (MOGA). The fuzzy PD+I controller preserves the linear structure of the conventional PID controller but has self-tuned gains. The proportional, integral and derivative gains are nonlinear functions of their input signals, which have a certain adaptive capability in set-point tracking performance. The proposed design is then optimized by using the MOGA. It is tested with a couple of simulated nonlinear systems, which demonstrate that these optimized gains make the fuzzy PD+I controller robust, with a faster response time and less overshoot than its conventional and non-optimized counterparts.
This paper presents some unusual dynamics of the Rabinovich-Fabrikant system, such as ``virtual'' saddles and ``tornado''-like stable cycles. Due to the strong nonlinearity and high complexity, the results are obtained numerically with some insightful descriptions and discussions.
In this paper we numerically investigate the chaotic behaviors of the fractional-order Chen system. A striking finding is that the lowest order for this system to have chaos is 0.3, which is the lowest-order chaotic system among all the found chaotic systems to date.