In practical quad-rotor applications, complex operational environments make it exceedingly difficult to establish accurate dynamic models and determine the upper bounds of external disturbances. To overcome these challenges, this paper proposes a novel barrier function-based super-twisting terminal sliding mode control (TSMC) strategy integrated with a multiple-layer recurrent neural network (MLRNN). Specifically, the MLRNN is utilized to approximate the equivalent control law, thereby circumventing the reliance on precise model parameters. By leveraging a double-hidden-layer architecture, the network achieves rapid approximation with a reduced number of neurons, significantly lowering the computational overhead compared to conventional model matrix approximation techniques. Additionally, the integration of a barrier function into the super-twisting algorithm (STA) eliminates the need for prior knowledge of disturbance bounds, effectively suppressing chattering while ensuring rapid tracking performance. The practical finite-time stability of the closed-loop system under bounded neural approximation errors is theoretically established via Lyapunov analysis. Comprehensive simulation results validate the effectiveness and superiority of the proposed control framework.
Overhead cranes are inherently subject to model uncertainties and external disturbances during operation, which present significant challenges to the practical implementation of existing control strategies. To overcome these issues, this paper proposes a non-parametric control method without velocity sensors for three-dimensional overhead cranes (3DOC) system with double-pendulum dynamics, addressing trajectory tracking accuracy and payload oscillation suppression during motion. The crane model investigated in this paper has received limited attention in the literature, as it is distinctly underactuated, complex, and highly nonlinear. First, to eliminate velocity sensors, a fixed-time non-parametric state observer is designed to estimate the system states and their velocities without relying on model knowledge. The estimation errors are guaranteed to converge to the origin (or a neighborhood of the origin) within a fixed time, regardless of initial conditions. Based on this observer, a non-parametric adaptive controller is developed to achieve reference trajectory tracking without requiring precise model knowledge. The key novelty of the proposed approach lies in the introduction of a time-varying control gain, which eliminates the need for parameter estimators or neural networks to handle uncertainties and disturbances. To the best of our knowledge, this is among the first adaptive control schemes for the 3DOC system with double-pendulum dynamics that do not depend on accurate model parameters, while ensuring simplicity and delivering superior control performance. The stability of the closed-loop system is rigorously established using Lyapunov theory. Simulation results on a semi-physical model, benchmarked against state-of-the-art methods, validate the superior performance of the proposed control scheme.
A probabilistic logical control system (PLCS) is a switched Markov chain in which the control input serves as the switching signal. Such a system is extensively adopted to describe the evolutionary process of biological networks. This study addresses the asymptotical reachability of PLCSs under state feedback, termed the asymptotical feedback reachability. Specifically, we aim to determine whether a state feedback exists under which a destination set is asymptotically reachable from a initial set. To analyze the asymptotical reachability of continuous-time PLCSs (CT-PLCSs) under sampled-data state feedback, we introduce the concepts of attraction domain and largest feedback attraction domain (LFAD) of a CT-PLCS with respect to a given set, and propose an algorithm to determine the LFAD. Based on this, we obtain a necessary and sufficient criterion for the asymptotical feedback reachability of CT-PLCSs. For a pair of initial and destination sets satisfying the asymptotical feedback reachability condition, we propose an algorithm for designing a sampled-data state feedback under which any solution from the initial set converges to the destination set. Following a similar idea, the asymptotical reachability of discrete-time PLCSs under state feedback is addressed. The obtained theoretical results are supported by examples.
This paper addresses the asynchronous sliding mode control (SMC) problem for discrete-time Markovian jump systems subject to finite communication bandwidth. A comprehensive design framework is proposed to accommodate multiple constraints, including partially measurable mode information, limited bandwidth, and probabilistic bit flips in the communication channel. Mode asynchronism is characterized by partitioning the mode detection probabilities into known and unknown subsets. To mitigate the effects of limited bandwidth, a closed-loop state coding-decoding mechanism based on a fixed bit-rate uniform quantizer is constructed. By incorporating a binary symmetric channel (BSC) model, the statistical properties and boundedness of both quantization errors and decoding errors induced by probabilistic bit flips are analyzed within a unified framework. On this basis, a detected-mode-dependent asynchronous SMC law is developed together with a stochastic Lyapunov functional. Sufficient conditions ensuring exponential mean-square ultimate boundedness and sliding-mode reachability are derived in terms of linear matrix inequalities. The analysis shows that the controller drives the sliding variables into and confines them within a neighborhood of the sliding surface. Numerical simulations demonstrate the effectiveness and robustness of the proposed method under finite bandwidth.
This paper addresses the finite-time synchronization control problem for complex networks and proposes a data-driven finite-time synchronization control method. When node dynamics are unknown or difficult to model accurately, traditional control methods often fail to achieve fast and accurate synchronization. To tackle this issue, this paper constructs a complete framework by integrating data-driven control and finite-time control theory. Specifically, a dual-network structure consisting of an evaluation network and an action network is designed to achieve the data-driven approximation of the performance function and control strategy. The Lyapunov method is employed to rigorously prove that the synchronization error converges in finite time. Simulation results demonstrate that the proposed method can effectively achieve fast synchronization of drive-response networks under unknown model conditions.
