Mathematics

Research

Jump to: Review

23 pages, 1001 KB

Open AccessArticle

ThinkDrive: Adaptive Dual-Process Reasoning for Autonomous Driving via Uncertainty-Triggered Causal Deliberation

by Bowen Yang, Bingxu Yao, Tianyi Fu and Hubing Du

Mathematics 2026, 14(11), 1806; https://doi.org/10.3390/math14111806 - 23 May 2026

Viewed by 567

Abstract

End-to-end autonomous driving remains fragile in long-tail scenarios, while incorporating vision-language models (VLMs) introduces substantial deliberation latency that cannot interfere with the real-time planning loop. We present ThinkDrive, a dual-process driving framework designed under explicit real-time queuing constraints. The framework contains four coordinated [...] Read more.

End-to-end autonomous driving remains fragile in long-tail scenarios, while incorporating vision-language models (VLMs) introduces substantial deliberation latency that cannot interfere with the real-time planning loop. We present ThinkDrive, a dual-process driving framework designed under explicit real-time queuing constraints. The framework contains four coordinated components. First, a Scene Complexity Estimator regulates System-2 activation through a trigger cool-down mechanism, allowing at most one asynchronous request every

⌈ L_{2} / Δ t ⌉

frames and thereby preventing queue saturation under a System-2 latency of

L_{2} = 565

ms. Second, a multi-modal System-1 planner generates

K_{1} = 5

candidate trajectories within 44 ms and is trained with winner-takes-all imitation learning together with explicit score supervision. Third, a two-stage Causal-CoT module uses the VLM to identify risk agents and predict a preferred spatial goal

G_{VLM}

, after which a single batched scm_rollout selects the safest candidate and extracts its endpoint as a world-coordinate goal anchor

g_{S 2}

. Fourth, a Goal-Anchor Replanning module transforms

g_{S 2}

into the current ego frame and selects the candidate whose waypoint at the remaining time horizon is closest to the transformed goal. This design avoids coordinate-space mixing, mitigates bias caused by mismatched temporal horizons, and prevents semantic instability across replanning cycles. On nuPlan test14-hard, ThinkDrive with InternVL2-8B and a 6.8% trigger rate achieves 74.9 PDMs, outperforming AdaThinkDrive at 73.1 while maintaining a nominal latency of 44 ms. Full article

(This article belongs to the Special Issue Intelligent Control and Applications of Nonlinear Dynamic System)

► Show Figures

Figure 1

22 pages, 1451 KB

Open AccessArticle

Design of Decoupling Control Based TSK Fuzzy Brain-Imitated Neural Network for Underactuated Systems with Uncertainty

by Duc Hung Pham and V. T. Mai

Mathematics 2026, 14(1), 102; https://doi.org/10.3390/math14010102 - 26 Dec 2025

Viewed by 782

Abstract

This paper proposes a Takagi–Sugeno–Kang Elliptic Type-2 Fuzzy Brain-Imitated Neural Network (TET2FNN)-based decoupling control strategy for nonlinear underactuated mechanical systems subject to uncertainties. A sliding-mode framework is employed to construct a decoupled control architecture, in which an intermediate variable is introduced to separate [...] Read more.

This paper proposes a Takagi–Sugeno–Kang Elliptic Type-2 Fuzzy Brain-Imitated Neural Network (TET2FNN)-based decoupling control strategy for nonlinear underactuated mechanical systems subject to uncertainties. A sliding-mode framework is employed to construct a decoupled control architecture, in which an intermediate variable is introduced to separate two second-order sliding surfaces, thereby forming a decoupled slip surface. The TET2FNN acts as the main controller and approximates the ideal control law online, while a robust compensator is incorporated to suppress approximation errors and guarantee closed-loop stability. Simulation studies conducted on a double inverted pendulum system demonstrate that the proposed method achieves improved tracking accuracy and disturbance rejection compared with representative state-of-the-art controllers. Furthermore, the computational burden remains reasonable, indicating that the proposed scheme is suitable for real-time implementation and practical nonlinear control applications. Full article

(This article belongs to the Special Issue Intelligent Control and Applications of Nonlinear Dynamic System)

► Show Figures

Figure 1

16 pages, 670 KB

Open AccessArticle

Data-Driven Fully Distributed Fault-Tolerant Consensus Control for Nonlinear Multi-Agent Systems: An Observer-Based Approach

by Yuyang Zhao, Dongnan Li, Yunlong Li, Dawei Gong, Jiaoyuan Chen, Shijie Song and Minglei Zhu

Mathematics 2025, 13(22), 3582; https://doi.org/10.3390/math13223582 - 7 Nov 2025

Cited by 1 | Viewed by 1118

Abstract

This paper introduces a novel observer-based, fully distributed fault-tolerant consensus control algorithm for model-free adaptive control, specifically designed to tackle the consensus problem in nonlinear multi-agent systems. The method addresses the issue of followers lacking direct access to the leader’s state by employing [...] Read more.

This paper introduces a novel observer-based, fully distributed fault-tolerant consensus control algorithm for model-free adaptive control, specifically designed to tackle the consensus problem in nonlinear multi-agent systems. The method addresses the issue of followers lacking direct access to the leader’s state by employing a distributed observer that estimates the leader’s state using only local information from the agents. This transforms the consensus control challenge into multiple independent tracking tasks, where each agent can independently follow the leader’s trajectory. Additionally, an extended state observer based on a data-driven model is utilized to estimate unknown actuator faults, with a particular focus on brake faults. Integrated into the model-free adaptive control framework, this observer enables real-time fault detection and compensation. The proposed algorithm is supported by rigorous theoretical analysis, which ensures the boundedness of both the observer and tracking errors. Simulation results further validate the algorithm’s effectiveness, demonstrating its robustness and practical viability in real-time fault-tolerant control applications. Full article

(This article belongs to the Special Issue Intelligent Control and Applications of Nonlinear Dynamic System)

► Show Figures

Figure 1

16 pages, 4127 KB

Open AccessArticle

A Stacking-Based Fusion Framework for Dynamic Demand Forecasting in E-Commerce

by Lei Ni, Zhonglin Huang and Ning Fu

Mathematics 2025, 13(21), 3436; https://doi.org/10.3390/math13213436 - 28 Oct 2025

Cited by 6 | Viewed by 1960

Abstract

In response to the growing complexity of e-commerce warehouse management driven by the expansion of live-streaming and cross-border businesses, this study tackles the critical challenge of product demand forecasting. We propose an intelligent forecasting approach based on a multi-model fusion framework, constructing a [...] Read more.

In response to the growing complexity of e-commerce warehouse management driven by the expansion of live-streaming and cross-border businesses, this study tackles the critical challenge of product demand forecasting. We propose an intelligent forecasting approach based on a multi-model fusion framework, constructing a Stacking ensemble that integrates XGBoost, LightGBM, and CatBoost as base learners. Hyperparameter optimization is systematically conducted using grid search combined with cross-validation. To account for periodic trends, seasonal fluctuations are modeled as explicit temporal features, and a Seasonal Autoregressive Integrated Moving Average (SARIMA) model is incorporated to perform joint forecasting by capturing residual time-dependent patterns. Experimental results show that the proposed fusion model consistently outperforms all individual base learners across multiple metrics, including R², RMSE, MAE, MAPE, Precision, Recall, and Accuracy. Furthermore, the mean cosine similarity of the forecast sequences reaches 0.986, underscoring both the stability of seasonal representations and the model’s robustness in capturing demand variations. This method effectively improves the accuracy of e-commerce product demand forecasts, offering reliable data support for inventory management and allocation strategies. Full article

(This article belongs to the Special Issue Intelligent Control and Applications of Nonlinear Dynamic System)

► Show Figures

Figure 1

22 pages, 2225 KB

Open AccessArticle

A Chord Error-Priority Bilevel Interpolation Optimization Method for Complex Path Planning

by Pengxuan Wei, Liping Wang, Dan Wang, Jun Qi and Xiaolong Ye

Mathematics 2025, 13(21), 3385; https://doi.org/10.3390/math13213385 - 24 Oct 2025

Viewed by 976

Abstract

To address path deviation and efficiency reduction issues in traditional interpolation optimization algorithms for complex path machining, this paper proposes a chord error-priority bilevel interpolation optimization method (CPBI). First, arc length parametric modeling of the machining path is performed within the Frenet–Serret framework, [...] Read more.

To address path deviation and efficiency reduction issues in traditional interpolation optimization algorithms for complex path machining, this paper proposes a chord error-priority bilevel interpolation optimization method (CPBI). First, arc length parametric modeling of the machining path is performed within the Frenet–Serret framework, yielding curvature and torsion information. After introducing geometric-based multi-machining constraints in the outer layer, the velocity upper limit is established by controlling chord error to dynamically adjust regions with curvature mutation. In the inner layer, combining the velocity limit with bidirectional scanning achieves adaptive optimization of interpolation step size and optimal velocity planning that balances precision and smoothness. Simulation results demonstrate that CPBI effectively reduces the number of interpolation points by 30–50% while ensuring the chord error. Compared with the reference method, the CPBI improved efficiency by 14.31% and 34.72% in machining experiments on S-shaped and wave-shaped paths, respectively. The results validated the CPBI’s high precision and efficiency advantages in complex path machining, providing an effective solution for CNC path optimization in high-end manufacturing. Full article

(This article belongs to the Special Issue Intelligent Control and Applications of Nonlinear Dynamic System)

► Show Figures

Figure 1

33 pages, 15730 KB

Open AccessFeature PaperArticle

Design and Analysis of Modular Reconfigurable Manipulator System

by Yutong Wang, Junjie Li, Ke Wang and Shaokun Wang

Mathematics 2025, 13(7), 1103; https://doi.org/10.3390/math13071103 - 27 Mar 2025

Cited by 2 | Viewed by 2129

Abstract

With the continuous development of modern robotics technology, in order to overcome the obstacles to the ability to complete tasks due to the fixed structure of the robot itself, to realize the reconfigurable purpose of the manipulator, it can be assembled into different [...] Read more.

With the continuous development of modern robotics technology, in order to overcome the obstacles to the ability to complete tasks due to the fixed structure of the robot itself, to realize the reconfigurable purpose of the manipulator, it can be assembled into different degrees of freedom or configurations according to the needs of different tasks, which has the characteristics of a compact structure, high integrability, and low cost. The overall design scheme of a cable-free modular reconfigurable manipulator is proposed, and based on the target design parameters, the structural design of each module is completed, and the module library is constructed. Each module realizes rapid assembly or disassembly through a new type of docking mechanism module, which improves the flexibility and reliability of the manipulator. Meanwhile, a finite element analysis is carried out on the whole manipulator to optimize the structure that does not meet the strength and stiffness requirements. The wireless energy transmission module is integrated into the joint module to realize the cable-free design of the manipulator in the structure. The kinematic models of each module are established separately, providing a method to quickly construct the kinematics of different configurations of the manipulator, and the dexterity of the workspace is analyzed. Then, two methods, joint space planning and Cartesian space planning, are adopted to generate the corresponding motion paths and kinematic curves, which successfully verifies the reasonableness of the kinematics of the designed manipulator. Finally, combined with the results of the dynamics simulation, the corresponding dynamics curves of the end of each joint are generated to further verify the reliability of its design. It provides a new way of thinking for the research and development of highly intelligent and highly integrated manipulators. Full article

(This article belongs to the Special Issue Intelligent Control and Applications of Nonlinear Dynamic System)

► Show Figures

Figure 1

17 pages, 6358 KB

Open AccessArticle

Continuous Multi-Target Approaching Control of Hyper-Redundant Manipulators Based on Reinforcement Learning

by Han Xu, Chen Xue, Quan Chen, Jun Yang and Bin Liang

Mathematics 2024, 12(23), 3822; https://doi.org/10.3390/math12233822 - 3 Dec 2024

Cited by 6 | Viewed by 2328

Abstract

Hyper-redundant manipulators based on bionic structures offer superior dexterity due to their large number of degrees of freedom (DOFs) and slim bodies. However, controlling these manipulators is challenging because of infinite inverse kinematic solutions. In this paper, we present a novel reinforcement learning-based [...] Read more.

Hyper-redundant manipulators based on bionic structures offer superior dexterity due to their large number of degrees of freedom (DOFs) and slim bodies. However, controlling these manipulators is challenging because of infinite inverse kinematic solutions. In this paper, we present a novel reinforcement learning-based control method for hyper-redundant manipulators, integrating path and configuration planning. First, we introduced a deep reinforcement learning-based control method for a multi-target approach, eliminating the need for complicated reward engineering. Then, we optimized the network structure and joint space target points sampling to implement precise control. Furthermore, we designed a variable-reset cycle technique for a continuous multi-target approach without resetting the manipulator, enabling it to complete end-effector trajectory tracking tasks. Finally, we verified the proposed control method in a dynamic simulation environment. The results demonstrate the effectiveness of our approach, achieving a success rate of 98.32% with a 134% improvement using the variable-reset cycle technique. Full article

(This article belongs to the Special Issue Intelligent Control and Applications of Nonlinear Dynamic System)

► Show Figures

Figure 1

Review

Jump to: Research

22 pages, 397 KB

Open AccessReview

Compliant Force Control for Robots: A Survey

by Minglei Zhu, Dawei Gong, Yuyang Zhao, Jiaoyuan Chen, Jun Qi and Shijie Song

Mathematics 2025, 13(13), 2204; https://doi.org/10.3390/math13132204 - 6 Jul 2025

Cited by 24 | Viewed by 10295

Abstract

Compliant force control is a fundamental capability for enabling robots to interact safely and effectively with dynamic and uncertain environments. This paper presents a comprehensive survey of compliant force control strategies, intending to enhance safety, adaptability, and precision in applications such as physical [...] Read more.

Compliant force control is a fundamental capability for enabling robots to interact safely and effectively with dynamic and uncertain environments. This paper presents a comprehensive survey of compliant force control strategies, intending to enhance safety, adaptability, and precision in applications such as physical human–robot interaction, robotic manipulation, and collaborative tasks. The review begins with a classification of compliant control methods into passive and active approaches, followed by a detailed examination of direct force control techniques—including hybrid and parallel force/position control—and indirect methods such as impedance and admittance control. Special emphasis is placed on advanced compliant control strategies applied to structurally complex robotic systems, including aerial, mobile, cable-driven, and bionic robots. In addition, intelligent compliant control approaches are systematically analyzed, encompassing neural networks, fuzzy logic, sliding mode control, and reinforcement learning. Sensorless compliance techniques are also discussed, along with emerging trends in hardware design and intelligent control methodologies. This survey provides a holistic view of the current landscape, identifies key technical challenges, and outlines future research directions for achieving more robust, intelligent, and adaptive compliant force control in robotic systems. Full article

(This article belongs to the Special Issue Intelligent Control and Applications of Nonlinear Dynamic System)

► Show Figures

Figure 1

Journal Menu

Journal Browser

Intelligent Control and Applications of Nonlinear Dynamic System

Share This Special Issue

Editors

Special Issue Information

Keywords

Benefits of Publishing in a Special Issue

Published Papers (8 papers)

Research

Review

Further Information

Guidelines

MDPI Initiatives

Follow MDPI