Reachable Set Estimation of Delayed Markovian Jump Neural Networks Based on an Improved Reciprocally Convex Inequality

Parametric Stability Criteria for Delayed Recurrent Neural Networks via Flexible Delay-Dividing Method

This article focuses on investigating the stability issue for recurrent neural networks (RNNs) with interval time-varying delays (TVDs) based on a flexible delay-dividing method with parameters, which are related to the delay derivative. First, an interval of delay is separated into parametric subintervals via the linear combination technique. Then, an establishment of Lyapunov-Krasovskii functional (LKF) is connected to the parameters, and a novel linear technology is suggested to dispose of integral terms in the derivatives of the constructed function. Finally, the validity and advantage of the inferred criteria are interpreted by the comparison of representative simulation examples.

Improved switching condition for reachable set estimation of discrete-time switched delayed neural networks

This research delves into the reachable set estimation (RSE) problem for general switched delayed neural networks (SDNNs) in the discrete-time context. Note that existing relevant research on SDNNs predominantly relies on either time-dependent or state-dependent switching approaches. The time-dependent versions necessitate the stability of each subnetwork beforehand, whereas the state-dependent switching strategies solely depend on the current state, thus disregarding the historical information of the neuron states. For fully harnessing the historical information pertaining to neuron states, a delicate combined switching strategy (CSS) is formulated with the explicit goal of furnishing a relaxed and less conservative design framework tailored for discrete-time SDNNs, where all subnetworks can also be unstable. By resorting to the established time-dependent multiple Lyapunov-Krasovskii functional (TDMLF) technique, the improved criteria are subsequently presented, ensuring that the reachable set encompassing all potential states of SDNNs is confined to an anticipated bounded set. Ultimately, the practicality and superiority of the presented RSE approach are thoroughly validated by two illustrative simulation examples.

Disturbance Observer-Based Adaptive Intelligent Control of Marine Vessel With Position and Heading Constraint Condition Related to Desired Output

This article studies the adaptive control about the geodetic fixed positions and heading of three-degree-of-freedom dual-propeller vessel. During the navigation of a vessel at sea, due to the unpredictable sea, on the one hand, it is important to ensure that the vessel can smoothly follow the desired geodesic fixed position and heading; on the other hand, when the sailing environment is harsh, it is even more important that the vessel can adapt to the desired geodesic fixed position and heading that change at any time for safe driving. Therefore, this article selects the time-varying function related to the desired geodesic fixed position and heading as the constraint condition, and the constraint condition will change in real time as the expected position and heading change. The design of the control strategy is difficult, and the designed control strategy will be more suitable for complex maritime navigation conditions. First, the article constructs a log-type barrier Lyapunov function. Second, by introducing an unknown external disturbance observer, the external disturbances caused by the environment that may be encountered during the vessel's voyage can be observed. Then, combined with the backstepping algorithm, a neural network (NN) control strategy and adaptive law are designed. Among them, for the uncertain function in the process of designing the control strategy, the NN is used to approximate it. Furthermore, through the Lyapunov stability analysis, it is shown that applying the designed control strategy to the vessel system in this article can ensure that the system is closed-loop stable. The final simulation experiment shows the effectiveness of the designed control strategy.

Sequential Fusion Estimation for Multirate Complex Networks With Uniform Quantization: A Zonotopic Set-Membership Approach

In this article, the sequential fusion estimation problem is investigated for multirate complex networks (MRCNs) with uniformly quantized measurements. The process and measurement noises, which are unknown-yet-bounded (UYB), are restrained into a family of zonotopes, and the multiple sensors are allowed to have different sampling periods. To facilitate digital transmissions, the sensor measurements are uniformly quantized before being sent to the remote estimator. The purpose of this article is to design a sequential set-membership estimator such that, in the simultaneous presence of UYB noises, multirate samplings, and uniform quantization effects, the estimation error (after each measurement update) is confined to a zonotope with minimum F -radius at each time instant. By introducing certain virtual measurements, the MRCNs are first transformed into single-rate ones exhibiting a switching phenomenon. Then, by utilizing the properties of zonotopes, the desired zonotopes are derived, which contain the estimation error dynamics after each measurement update. Subsequently, the gain matrices of the sequential estimator are derived by minimizing the F -radii of these zonotopes, and the uniform boundedness is analyzed for the F -radius of the zonotope containing the estimation error after all measurement updates. Furthermore, sufficient conditions are derived to ensure the existence of the desired uniform upper/lower bounds. Finally, an illustrated example is proposed to show the effectiveness of the proposed sequential fusion estimation method.

Stability Analysis of Recurrent Neural Networks With Time-Varying Delay by Flexible Terminal Interpolation Method

This brief studies the stability problem of recurrent neural networks with time-varying delay. Based on one tunable parameter α , a flexible terminal interpolation method is proposed to change the interval with fixed terminals as 2k+1-3 ones with flexible terminals. Associated with the flexible subintervals, a novel Lyapunov-Krasovskii functional with more delay information is constructed. In order to estimate the Lyapunov-Krasovskii functional, a quadratic reciprocally convex inequality is proposed, which covers some existing ones as its special cases. Based on these ingredients, a new stability criterion is derived in the form of linear matrix inequalities. A comprehensive comparison of results is given to illustrate the newly proposed stability criterion.

Event-Triggered Cooperative Model-Free Adaptive Iterative Learning Control for Multiple Subway Trains With Actuator Faults

This article investigates the issue of speed tracking and dynamic adjustment of headway for the repeatable multiple subway trains (MSTs) system in the case of actuator faults. First, the repeatable nonlinear subway train system is transformed into an iteration-related full-form dynamic linearization (IFFDL) data model. Then, the event-triggered cooperative model-free adaptive iterative learning control (ET-CMFAILC) scheme based on the IFFDL data model for MSTs is designed. The control scheme includes the following four parts: 1) the cooperative control algorithm is derived by the cost function to realize cooperation of MSTs; 2) the radial basis function neural network (RBFNN) algorithm along the iteration axis is constructed to compensate the effects of iteration-time-varying actuator faults; 3) the projection algorithm is employed to estimate unknown complex nonlinear terms; and 4) the asynchronous event-triggered mechanism operated along the time domain and iteration domain is applied to lessen the communication and computational burden. Theoretical analysis and simulation results show that the effectiveness of the proposed ET-CMFAILC scheme, which can ensure that the speed tracking errors of MSTs are bounded and the distances of adjacent subway trains are stabilized in the safe range.

Joint angle estimation with wavelet neural networks

This paper presents a wavelet neural network (WNN) based method to reduce reliance on wearable kinematic sensors in gait analysis. Wearable kinematic sensors hinder real-time outdoor gait monitoring applications due to drawbacks caused by multiple sensor placements and sensor offset errors. The proposed WNN method uses vertical Ground Reaction Forces (vGRFs) measured from foot kinetic sensors as inputs to estimate ankle, knee, and hip joint angles. Salient vGRF inputs are extracted from primary gait event intervals. These selected gait inputs facilitate future integration with smart insoles for real-time outdoor gait studies. The proposed concept potentially reduces the number of body-mounted kinematics sensors used in gait analysis applications, hence leading to a simplified sensor placement and control circuitry without deteriorating the overall performance.