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Finite-time adaptive dynamic programming control for nonlinear systems based on novel complementary terminal sliding mode surface

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART I-JOURNAL OF SYSTEMS AND CONTROL ENGINEERING 2025年第2期239卷 290-302页

作者： Jia, Chao Li, Xinyu Liu, Xiaohua Shangguan, Xuanyue Tianjin Univ Technol Sch Elect Engn & Automat 391 Binshuixi Rd Tianjin 300191 Peoples R China

For a nonlinear system, a novel complementary terminal sliding mode surface-based finite-time adaptive dynamic programming optimal control scheme (FT-NCTSMS-ADP) is proposed. To begin with, with the aim to improve convergence speed and tracking precision, a novel complementary terminal sliding mode surface (NCTSMS) is developed. Then, a specific cost function related to the NCTSMS is developed, and the initial control problem is then transformed toward a series of optimal control problems. The Hamilton-Jacobi-Bellman (HJB) problem is then solved by a single critic neural network, yielding the estimated optimal controller. Finally, using the finite-time lemma, we design a Lyapunov function and verify the system's fast finite-time convergence. Both the simulation and the real-world experiment validate the practical significance of the proposed method.

关键词： Finite-time adaptive dynamic programming complementary terminal sliding mode optimal control

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Human-Machine Shared Stabilization Control Based on Safe adaptive dynamic programming With Bounded Rationality

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2025年第0期

作者： Tan, Junkai Wang, Jingcheng Xue, Shuangsi Cao, Hui Li, Huan Guo, Zihang Xi An Jiao Tong Univ Sch Elect Engn Xian Peoples R China Xi An Jiao Tong Univ Shaanxi Key Lab Smart Grid Xian Peoples R China Xi An Jiao Tong Univ State Key Lab Elect Insulat & Power Equipment Xian Peoples R China Power Stn Inst New Energy Tech Supervis Dept Tech Supervis Xian Peoples R China

This article considers the shared control of bounded rational human behavior with cooperative autonomous machines. For the collaboration of humans and machines, it is crucial to ensure the safety of the interactive process due to the involvement of human beings. First, a barrier-function-based state transformation is developed to ensure full state safety constraints. A level-k$$ k $$ thinking framework is exploited to obtain bounded rationality. Every single level-k$$ k $$ control policy is approximated by using adaptive dynamic programming. Inspired by the theory of human behavior modeling, a probabilistic distribution based on Softmax is utilized to model human behavior, which imitates the uncertainty of human intelligence in the cooperative game. Through the construction of a shared control framework, the control inputs of humans and machines are blended to achieve stabilization safely and efficiently. Finally, simulations are implemented to test the effectiveness of the proposed cooperation architecture. The result demonstrates that full-state asymmetric constraints and stabilization are guaranteed in commonly safety-critical situations, and the shared control framework ensures the safety of the overall system when one of the participants is not safety-aware.

关键词： adaptive dynamic programming barrier function bounded rationality human-machine collaboration shared control

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dynamic event-triggering adaptive dynamic programming for robust stabilization of partially unknown nonlinear systems

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NEUROCOMPUTING 2025年 628卷

作者： Hong, Yishen Xue, Shan Liu, Derong Wang, Yonghua Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China Hainan Univ Sch Informat & Commun Engn Haikou 570228 Peoples R China Southern Univ Sci & Technol Sch Automat & Intelligent Mfg Shenzhen 518055 Peoples R China Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA

In this paper, anew dynamic event-triggering (DET) mechanism based on adaptive dynamic programming (ADP) is developed to deal with the robust control problem of partially unknown uncertain systems. First, this paper completes the transition from the robust control problem to the optimal control problem by designing a nominal system. Meanwhile, the use of integral reinforcement learning (IRL) eliminates the need for prior knowledge of drift dynamics. Then, to improve resource utilization, a static event-triggering (SET) scheme is designed. Subsequently, a DET scheme is developed on the basis of SET to further improve resource utilization. It is proven that the developed DET controller guarantees the robustness of the partially unknown uncertain system. The neural network (NN) weight estimation errors are uniformly ultimately bounded (UUB) while the Zeno behavior is successfully avoided. Finally, an experiment is provided to demonstrate that the proposed DET algorithm has the fewest triggering samples while guaranteeing robustness.

关键词： adaptive dynamic programming dynamic event-triggering mechanism Robust control Integral reinforcement learning Neural networks

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Optimal Output-Feedback Controller Design Using adaptive dynamic programming: A Permanent Magnet Synchronous Motor Application

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IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2025年第1期72卷 208-212页

作者： Wang, Zhongyang Ye, Huiru Wang, Youqing Shi, Yukun Liang, Li Beijing Univ Chem Technol Coll Informat Sci & Technol Beijing 100029 Peoples R China

This brief introduces a novel adaptive optimal output-feedback controller for permanent magnet synchronous motor (PMSM) systems, eliminating the need for prior knowledge of system dynamics, numerous integral window functions, or unmeasurable states and load torque. Initially, we design an adaptive optimal output-feedback controller by constructing internal states. Then, a policy iteration algorithm based on adaptive dynamic programming approximates the optimal output-feedback gain using only input and trajectory tracking error information. Notably, this method does not require the minimal polynomial of an exosystem or the solution of regulator equations, facilitating the overall design of the feedforward-feedback controller. The effectiveness of the proposed learning algorithm is validated on a PMSM system.

关键词： Regulators Torque dynamic programming System dynamics Symmetric matrices Mathematical models Heuristic algorithms Vectors Circuits Chemical elements Permanent magnet synchronous motor adaptive dynamic programming output-feedback policy iteration

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Output feedback control of anti-linear systems using adaptive dynamic programming

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OPTIMAL CONTROL APPLICATIONS & METHODS 2025年第1期46卷 155-173页

作者： Yu, Li Wang, Hai Guangxi Normal Univ Sch Math & Stat Guilin Guangxi Peoples R China Xidian Univ Sch Math & Stat Xian Peoples R China

This paper introduces an adaptive optimal feedback control approach for discrete-time anti-linear systems (ALSs). The method utilizes sampling and measurable input-output data. By employing the adaptive dynamic programming (ADP) technique, this study iteratively solves the discrete-time algebraic Anti-Riccati equation (AARE). Initially, an output feedback model is established for ALSs, and a model-based algorithm is developed based on this model. The feasibility of this algorithm is based on the premise that the system dynamic information is completely known. Subsequently, for the scenario where the model is unknown, we further developed a model-free ADP algorithm specifically designed to address optimal control problems in the presence of model uncertainty. With this algorithm, we achieve effective control optimization even in cases where detailed system dynamics information is lacking. Finally, through simulation experiments, we validated the feasibility and effectiveness of this algorithm. This paper presents an adaptive optimal feedback control approach for discrete-time anti-linear systems, leveraging adaptive dynamic programming techniques. It introduces a model-based algorithm that solves the Anti-Riccati equation with complete system dynamics and a model-free algorithm that optimizes control using only measurable output data when system dynamics are unknown. Simulation results validate the effectiveness and feasibility of the proposed methods. image

关键词： adaptive dynamic programming anti-linear systems algebraic anti-Riccati equation optimal output feedback

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Data-driven real-time home energy management system based on adaptive dynamic programming

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ELECTRIC POWER SYSTEMS RESEARCH 2025年 238卷

作者： Yuan, Jun Zeng, Xianxian Zhou, Jiayu Li, Jiawen Lv, Jujian Chen, Rongjun Chen, Kairui Yang, Weijun Zhang, Yun Guangdong Polytech Normal Univ Dept Comp Sci & Technol Guang Zhou 510665 Peoples R China Guangzhou Univ Sch Mech & Elect Engn Guang Zhou 510000 Peoples R China Guangzhou City Polytech Sch Mech & Elect Engn Guangzhou 510405 Peoples R China Guangdong Univ Technol Sch Automat Guang Zhou 510000 Peoples R China

Real-time optimal control is crucial for the efficacy of Home Energy Management Systems (HEMS) in residential settings during actual operation. The time-varying and nonlinear nature of smart households - characterized by fluctuations in renewable energy generation, real-time electricity pricing, and load consumption - presents substantial challenges for both prediction and real-time control within HEMS. To tackle these issues, this paper introduces a real-time optimal control algorithm, augmented by predictive scheduling for HEMS. More specifically, the proposed real-time HEMS framework integrates an adaptive dynamic programming (ADP) algorithm, which is complemented by predictions of renewable energy generation and load consumption. Initially, data-driven methodologies generate accurate forecasts using available data collected and processed in real time. Gated Recurrent Unit (GRU) neural networks utilizing a range of data inputs such as electricity prices, battery charge/discharge rates, load consumption, and renewable energy generation, the system computes the optimal performance index function. Following this, we employ the ADP algorithm to reduce total electricity costs. This paper confirms the convergence properties of the value iteration ADP algorithm., demonstrating a monotonic approach of the iterative performance index function towards the optimal solution. The efficacy of the proposed algorithm is supported by numerical experiments, which verify its that solar energy efficiency has increased to 98% and electricity costs have been reduced by 64%.

关键词： Real-time home energy management system adaptive dynamic programming Data-driven Time-varying prediction modeling

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Adjustable behavior-guided adaptive dynamic programming for neural learning control

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NEUROCOMPUTING 2025年 636卷

作者： Tang, Guohan Wang, Ding Liu, Ao Qiao, Junfei Beijing Univ Technol Sch Informat Sci & Technol Beijing 100124 Peoples R China Beijing Univ Technol Beijing Key Lab Computat Intelligence & Intelligen Beijing 100124 Peoples R China Beijing Univ Technol Beijing Inst Artificial Intelligence Beijing 100124 Peoples R China Beijing Univ Technol Beijing Lab Smart Environm Protect Beijing 100124 Peoples R China

In this article, an adjustable behavior-guided adaptive dynamic programming (BGADP) algorithm is designed to solve the optimal regulation problem for discrete-time systems. In conventional adaptive dynamic programming methods, gradient information of system dynamics is necessary for conducting policy improvement. However, these methods face challenges when gradient information cannot be computed or when the system dynamics is non-differentiable. To overcome these limitations, a human-behavior-inspired swarm intelligence approach is used to search for superior policies during the iterative process, eliminating the need for gradient information. Additionally, a relaxation factor is introduced into the value function update to accelerate the convergence speed of the algorithm. The monotonicity and convergence properties of the iterative value function are rigorously analyzed. Finally, the effectiveness and practicality of the adjustable BGADP algorithm are validated through two simulation studies, which are implemented using the actor-critic framework with neural networks.

关键词： adaptive dynamic programming Brain storm optimization Convergence rate Neural networks Optimal control Swarm intelligence

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Event-triggered robust hierarchical control for uncertain multiplayer Stackelberg games via adaptive dynamic programming

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NEUROCOMPUTING 2025年 616卷

作者： Zhang, Yongwei Zhao, Bo Liu, Derong Polycarpou, Marios M. Peng, Shiguo Zhang, Shunchao South China Agr Univ Coll Math & Informat Guangzhou 510642 Peoples R China Beijing Normal Univ Sch Syst Sci Beijing 100875 Peoples R China Southern Univ Sci & Technol Sch Automat & Intelligent Mfg Shenzhen 518055 Peoples R China Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA Univ Cyprus Dept Elect & Comp Engn CY-2109 Nicosia Cyprus Guangdong Univ Technol Sch Automat Guangzhou 510006 Peoples R China Guangdong Univ Finance Sch Internet Finance & Informat Engn Guangzhou 510521 Peoples R China

This paper investigates the event-triggered robust hierarchical control (ETRHC) problem of uncertain multi- player nonlinear systems subject to actuator faults by using adaptive dynamic programming and integral sliding mode technique. Different from existing results where the control policies of all players are updated simultaneously, a hierarchical decision-making problem is considered as a Stackelberg game. The Stackelberg game consists of a single leader and multiple followers, the leader acts a control policy in advance by considering the responses of all the followers, and each follower responds optimally to the leader's policy. The proposed control structure comprises of two components, namely integral sliding mode control and ETRHC. In the first step, the integral sliding mode control policy is developed to cope with actuator faults and matched uncertainties, and then, the fault-free multi-player nonlinear systems with mismatched uncertainties is obtained. In the second step, by designing an appropriate performance index function for each player, the ETRHC of the fault-free multi-player nonlinear system with mismatched uncertainties is converted to an event- triggered approximate optimal control of its nominal form, and the hierarchical decision-making problem is addressed. Subsequently, the ETRHC laws are derived by solving event-triggered Hamilton-Jacobi equations with the critic-only learning. Theoretical analysis demonstrates that the integral sliding mode-based ETRHC scheme guarantees the multi-player uncertain nonlinear systems with actuator faults to be asymptotically stable. Finally, the quadrotor attitude system is adopted to verify the effectiveness of the present scheme.

关键词： adaptive dynamic programming Integral sliding-mode control Event-triggered control Stackelberg games Neural networks

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Force feedback controller of a parallel haptic device via online adaptive dynamic programming

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MECHATRONICS 2025年 106卷

作者： Jin, Zhaopeng Zhao, Yanzhi Sun, Yue Liu, Yajun Yanshan Univ 438 West Hebei Ave Qinhuangdao 066004 Hebei Peoples R China

Haptic devices can replicate real-time force signals, which demand high accuracy and real-time performance. However, several common factors affect the accuracy of system modeling, which potentially limit the performance of haptic devices. These factors include unavoidable errors and unmodeled dynamics in the systems themselves, as well as uncertainties stemming from human-computer interaction (HCI) processes. Considering these unfavorable circumstances, this paper designs and fabricates a novel parallel haptic device with three degrees of freedom (DoF). To enhance modeling accuracy, a model-data driven approach is employed, utilizing the theoretical dynamic model as prior knowledge. A recurrent neural network (RNN) is used to approximate the actual system model. Subsequently, the online adaptive dynamic programming (ADP) technique is applied to achieve force reproduction. Critic-action networks are established to minimize the search for the established value function by continuously updating the weights of both networks in realtime. Through rigorous experimentation, the proposed haptic device successfully reproduces the desired force sensing signal and exhibits excellent adaptability.

关键词： Haptics Parallel device Recurrent neural network adaptive dynamic programming

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Self-Triggered adaptive dynamic programming Suboptimal Control of Unknown Affine Nonlinear Systems With Full-State Constraints and Input Constraints

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INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL 2025年

作者： Liu, Yizhuo Ma, Kemao Harbin Inst Technol Sch Astronaut Harbin Peoples R China Natl Key Lab Complex Syst Control & Intelligent Ag Harbin Peoples R China

A self-triggered approximate suboptimal controller design method is proposed within the adaptive dynamic programming framework. By constructing a novel auxiliary value function and candidate Lyapunov function, this method utilizes the barrier Lyapunov function for the first time in designing an optimal controller for a broader class of affine nonlinear systems with full-state constraints, overcoming the traditional limitation that the barrier Lyapunov function is restricted to strict feedback nonlinear systems. Furthermore, a nonquadratic cost function is employed to simultaneously satisfy the input constraints. By constructing identifier neural networks, optimal performance control is achieved, even with unknown system dynamics. The proposed self-triggered mechanism enables the controller and network weights to be updated only at the predicted moment, which not only reduces communication resource consumption but also eliminates the need for system state monitoring, as required in the event-triggered mechanism. Rigorous convergence analysis establishes a strong theoretical foundation for the stability and safety of the proposed method in practical applications. Simulation experiments confirm the effectiveness of the algorithm.

关键词： adaptive dynamic programming barrier Lyapunov function input constraints neural networks self-triggered control state constraints

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