Robustness of Hopfield Neural Networks Described by Differential Algebraic Systems of Index-1 under the Conditions of Deviation Argument and Stochastic Disturbance

Robustness refers to the ability of a system to maintain its original state under a continuous disturbance conditions. The deviation argument (DA) and stochastic disturbances (SDs) are enough to disrupt a system and keep it off course. Therefore, it is of great significance to explore the interval length of the deviation function and the intensity of noise to make a system remain exponentially stable. In this paper, the robust stability of Hopfield neural network (VPHNN) models based on differential algebraic systems (DAS) is studied for the first time. By using integral inequalities, expectation inequalities, and the basic control theory method, the upper bound of the interval of the deviation function and the noise intensity are found, and the system is guaranteed to remain exponentially stable under these disturbances. It is shown that as long as the deviation and disturbance of a system are within a certain range, there will be no unstable consequences. Finally, several simulation examples are used to verify the effectiveness of the approach and are described below.

Parameter Identification and The Multi-Switching Sliding Mode Combination Synchronization of Fractional Order Non-Identical Chaotic System Under Stochastic Disturbances

This paper deals with the issue of the multi-switching sliding mode combination synchronization (MSSMCS) of fractional order (FO) chaotic systems with different structures and unknown parameters under double stochastic disturbances (SD) utilizing the multi-switching synchronization method. The stochastic disturbances are considered as nonlinear uncertainties and external disturbances. Our theoretical part is divided into two cases, namely, the dimension of the drive-response system are different (or same). Firstly, a FO sliding surface was established in term of fractional calculus. Secondly, depended on the FO Lyapunov stability theory, the adaptive control technology and sliding mode control technique, the multi-switching adaptive controllers (MSAC) and some suitable multi-switching adaptive updating laws (MSAUL) are designed, so that the state variables of the drive systems are synchronized with the different state variables of the response systems. Simultaneously, the unknown parameters are assessed and the upper bound of stochastic disturbances are examined. Selecting the suitable scale matrices, the multi-switching projection synchronization, multi-switching complete synchronization, and multi-switching anti-synchronization will become special cases of MSSMCS. Finally, examples are displayed to certify the usefulness and validity of the demonstrated scheme via MATLAB.

Robust-adaptive dynamic programming-based time-delay control of autonomous ships under stochastic disturbances using an actor-critic learning algorithm

This paper proposes a hybrid robust-adaptive learning-based control scheme based on Approximate Dynamic Programming (ADP) for the tracking control of autonomous ship maneuvering. We adopt a Time-Delay Control (TDC) approach, which is known as a simple, practical, model free and roughly robust strategy, combined with an Actor-Critic Approximate Dynamic Programming (ACADP) algorithm as an adaptive part in the proposed hybrid control algorithm. Based on this integration, Actor-Critic Time-Delay Control (AC-TDC) is proposed. It offers a high-performance robust-adaptive control approach for path following of autonomous ships under deterministic and stochastic disturbances induced by the winds, waves, and ocean currents. Computer simulations have been conducted under two different conditions in terms of the deterministic and stochastic disturbances and all simulation results indicate an acceptable performance in tracking of paths for the proposed control algorithm in comparison with the conventional TDC approach.