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Policy Iterative-Based adaptive optimal control for Unknown Continuous-Time Nonlinear Systems

IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS 2025年第4期55卷 2859-2869页

作者： Fang, Haiyang He, Shuping Liu, Fei Ding, Zhengtao Anhui Univ Sch Elect Engn & Automat Informat Mat & Intelligent Sensing Lab Anhui Prov Hefei 230601 Peoples R China Chinese Univ Hong Kong Dept Mech & Automat Engn Hong Kong Peoples R China Hefei Comprehens Natl Sci Ctr Inst Artificial Intelligence Hefei 230026 Peoples R China Jiangnan Univ Key Lab Adv Proc Control Light Ind Minist Educ Wuxi 214122 Peoples R China Univ Manchester Sch Elect & Elect Engn Manchester M13 9PL England

This study addresses the optimal control problem for continuous-time nonlinear systems with unknown dynamics. A policy iterative-based optimization algorithm is proposed to solve this problem by leveraging a novel neural network representation termed multivariable neural network linear differential inclusion (MVNNLDI). MVNNLDI approximates the initial nonlinear model with a linear differential equation formulation that includes bounded disturbances. Based on this linearized representation, the relevant adaptive optimal control and disturbance compensation approach are derived to tackle the nonlinear optimization problem. Capitalizing on model-free control principles, the optimal solutions can be obtained using only measured state and input data, thus simplifying algorithmic complexity and accelerating convergence speed substantially. Finally, we use two simulation experiments to demonstrate the feasibility and effectiveness of the proposed method.

关键词： optimal control Mathematical models Artificial neural networks Heuristic algorithms Adaptation models adaptive systems Neurons Stability analysis Nonlinear dynamical systems Approximation algorithms adaptive optimal control continuous-time nonlinear systems multivariable neural network linear differential inclusion (MVNNLDI) policy iteration (PI)

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Transient-State adaptive optimal control of Aircraft Engine Systems With Input Saturation

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IEEE TRANSACTIONS ON AEROSPACE AND ELECTRONIC SYSTEMS 2025年第2期61卷 1764-1774页

作者： Liu, Shuoshuo Shi, Yan Sun, Tao Li, Peng Zhao, Xudong Dalian Univ Technol Key Lab Intelligent Control & Optimizat Ind Equipm Minist Educ Dalian 116024 Liaoning Peoples R China Dalian Univ Technol Sch Control Sci & Engn Dalian 116024 Peoples R China Tsinghua Univ Dept Automat Beijing 100084 Peoples R China

control for transition-state dynamics of aircraft engine systems is one of the foremost challenges in the field of aerospace engineering. Herein, the primary challenge lies in how to design transient-state control strategies to achieve the rapid and safe state transition of an aircraft engine, especially when the wide-range dynamics of the engine system are unknown. In this article, a data-driven adaptive optimal control strategy is proposed for the aircraft engine systems with input saturation constraints. Through the application of the Bellman optimality principle, the task of achieving optimal control is reformulated as solving the Hamilton-Jacobi-Bellman (HJB) equation. Following this, by introducing an epsilon-optimal method and a basis function approximation approach, a data-driven adaptive dynamic programming algorithm that can handle input saturation is designed to solve the HJB equation. By converting the dynamic optimization problem into a static constrained optimization problem and solving it iteratively, the algorithm presented can efficiently update the optimal control strategy. Finally, a comprehensive simulation was carried out on the JT9D engine simulation platform, a nonanalytic and nonlinear virtual prototype model, to assess its practical applicability. The obtained results reveal that the proposed design can achieve promising transition performance and ensure that critical parameters of the system remain within a reasonable range.

关键词： Aircraft propulsion optimal control Engines Aerodynamics Optimization Atmospheric modeling Fans adaptive optimal control aircraft engine systems data-driven transient-state control

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adaptive optimal control of switched linear systems with input constraints

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INTERNATIONAL JOURNAL OF control 2025年第2期98卷 260-268页

作者： Wang, Yuliang Fu, Jun Fu, Yue Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110819 Peoples R China

In this paper, an adaptive optimal control scheme is proposed for a class of switched linear systems with input constraints and unknown dynamics. Firstly, in the case that the system dynamics is known, the optimal controller and optimal switching condition are determined by introducing a non-quadratic cost function and employing the embedding transformation technique. After that, an adaptive algorithm is established for estimating the unknown dynamics of the switched linear systems. Then, when the system dynamics is unknown, the adaptive optimal controller and optimal switching condition are deduced by resorting to the certainty equivalent principle. A common Lyapunov function is constructed, by using which, it is proved that the closed-loop system is globally uniformly asymptotically stable. Simulations are finally conducted to further illustrate the effectiveness of the proposed method.

关键词： Switched linear system input constraints adaptive optimal control embedding transformation

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Online adaptive optimal control Algorithm Based on Weighted Policy Iteration

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2025年 PP卷 PP页

作者： Tan, Wanlin Luo, Rui Peng, Zhinan Ling, Qiang Univ Sci & Technol China Dept Automat Hefei 230027 Peoples R China Chengdu Univ Sch Elect Informat & Elect Engn Chengdu 610106 Peoples R China Univ Elect Sci & Technol China Sch Automat Engn Chengdu 611731 Peoples R China

In this article, we propose a novel online learning algorithm based on weighted policy iteration (WPI) for addressing optimal control problems of nonlinear systems. WPI is proposed to deal with the influence of the neural network (NN) approximation error on the admissibility of the improved control policy. It is shown that the new iterative method can converge to the optimal solution uniformly. Utilizing NN approximation and experience replaying techniques, a WPI-based online learning algorithm is proposed. The new online algorithm distinguishes from previously known ones in that there can be fewer neurons in the hidden layer, giving rise to significant computational improvement. The assumption that the number of neurons needs to be sufficiently large can be dropped. Besides, instead of a standard persistently excited (PE) condition, only a relaxed PE condition is needed, which is also easier to check. Finally, numerical experiments are conducted to verify the effectiveness of our method.

关键词： Artificial neural networks optimal control Approximation algorithms Neurons Approximation error Jacobian matrices Convergence Nonlinear systems Heuristic algorithms Vectors adaptive optimal control affine nonlinear system neural network (NN) approximation policy iteration (PI)

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adaptive optimal control for Unknown Constrained Nonlinear Systems With a Novel Quasi-Model Network

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2022年第7期33卷 2867-2878页

作者： Han, Xiumei Zhao, Xudong Karimi, Hamid Reza Wang, Ding Zong, Guangdeng Dalian Univ Technol Minist Educ Key Lab Intelligent Control & Optimizat Ind Equip Dalian 116024 Peoples R China Politecn Milan Dept Mech Engn I-20156 Milan Italy Beijing Univ Technol Fac Informat Technol Beijing 100124 Peoples R China Beijing Univ Technol Beijing Key Lab Computat Intelligence & Intellige Beijing 100124 Peoples R China Qufu Normal Univ Sch Engn Rizhao 276826 Peoples R China

A policy-iteration-based algorithm is presented in this article for optimal control of unknown continuous-time nonlinear systems subject to bounded inputs by utilizing the adaptive dynamic programming (ADP). Three neural networks (NNs), called critic network, actor network, and quasi-model network, are utilized in the proposed algorithm to give approximations of the control law, the cost function, and the function constituted by partial derivatives of value functions with respect to states and unknown input gain dynamics, respectively. At each iteration, based on the least sum of squares method, the parameters of critic and quasi-model networks will be tuned simultaneously, which eliminates the necessity of separately learning the system model in advance. Then, the control law is improved by satisfying the necessary optimality condition. Then, the proposed algorithm's optimality and convergence properties are exhibited. Finally, the simulation results demonstrate the availability of the proposed algorithm.

关键词： Heuristic algorithms optimal control Cost function System dynamics Mathematical model Artificial neural networks Dynamic programming adaptive optimal control constrained inputs neural networks (NNs) unknown continuous-time nonlinear systems

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adaptive optimal control of Highly Dissipative Nonlinear Spatially Distributed Processes With Neuro-Dynamic Programming

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2015年第4期26卷 684-696页

作者： Luo, Biao Wu, Huai-Ning Li, Han-Xiong Beihang Univ Sci & Technol Aircraft Control Lab Beijing 100191 Peoples R China Chinese Acad Sci Inst Automat State Key Lab Management & Control Complex Syst Beijing 100190 Peoples R China City Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Hong Kong Peoples R China

Highly dissipative nonlinear partial differential equations (PDEs) are widely employed to describe the system dynamics of industrial spatially distributed processes (SDPs). In this paper, we consider the optimal control problem of the general highly dissipative SDPs, and propose an adaptive optimal control approach based on neuro-dynamic programming (NDP). Initially, Karhunen-Loeve decomposition is employed to compute empirical eigenfunctions (EEFs) of the SDP based on the method of snapshots. These EEFs together with singular perturbation technique are then used to obtain a finite-dimensional slow subsystem of ordinary differential equations that accurately describes the dominant dynamics of the PDE system. Subsequently, the optimal control problem is reformulated on the basis of the slow subsystem, which is further converted to solve a Hamilton-Jacobi-Bellman (HJB) equation. HJB equation is a nonlinear PDE that has proven to be impossible to solve analytically. Thus, an adaptive optimal control method is developed via NDP that solves the HJB equation online using neural network (NN) for approximating the value function;and an online NN weight tuning law is proposed without requiring an initial stabilizing control policy. Moreover, by involving the NN estimation error, we prove that the original closed-loop PDE system with the adaptive optimal control policy is semiglobally uniformly ultimately bounded. Finally, the developed method is tested on a nonlinear diffusion-convection-reaction process and applied to a temperature cooling fin of high-speed aerospace vehicle, and the achieved results show its effectiveness.

关键词： adaptive optimal control empirical eigenfunction (EEF) highly dissipative partial differential equations (PDEs) neuro-dynamic programming (NDP) spatially distributed processes (SDPs)

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adaptive optimal control of CVCF Inverters With Uncertain Load: An adaptive Dynamic Programming Approach

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IEEE ACCESS 2021年 9卷 89276-89286页

作者： Wang, Zhongyang Yu, Yunjun Fuzhou Inst Technol Sch Appl Sci & Engn Fuzhou 350506 Peoples R China Nanchang Univ Sch Informat Engn Nanchang 330031 Jiangxi Peoples R China Nanchang Univ AI Inst Nanchang 330031 Jiangxi Peoples R China

This paper proposed a data-driven adaptive optimal control approach for CVCF (constant voltage, constant frequency) inverter based on reinforcement learning and adaptive dynamic programming (ADP). Different from existing literature, the load is treated as a dynamic uncertainty and a robust optimal state-feedback controller is proposed. The stability of the inverter-load system has been strictly analyzed. In order to obtain accurate output current differential signal, this paper designs a tracking differentiator. It is ensured that the tracking error asymptotically converges to zero through the proposed output-feedback controllers. A standard proportional integral controller and linear active disturbance rejection control strategy are also designed for the purpose of comparison. The simulation results show that the proposed controller has inherent robustness and does not require retuning with different applications.

关键词： Inverters Voltage control Mathematical model Reinforcement learning optimal control Load modeling Licenses adaptive optimal control CVCF inverter reinforcement learning adaptive dynamic programming

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adaptive optimal control of multi-modular floating platforms in random seas

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NONLINEAR DYNAMICS 2018年第2期91卷 863-876页

作者： Xu, Daolin Xia, Shuyan Zhang, Haicheng Wu, Yousheng Hunan Univ Coll Mech & Vehicle Engn State Key Lab Adv Design & Mfg Vehicle Body Changsha 410082 Hunan Peoples R China China Ship Sci Res Ctr Wuxi 214082 Peoples R China

This paper presents an adaptive optimal control method to suppress the oscillation of a floating platforms system in random seas. The system consists of multiple modules which are connected by flexible connectors with strong geometrical nonlinearity. To cope with the uncertain waves, a disturbance estimator is introduced to assess the actual wave excitation. This adaptive scheme of the estimator is integrated with an optimal control method subject to a limitation on the control outputs of actuators, where the optimal control process is carried out by the sequential quadratic program method. In numerical experiments, a floating platform with five semi-submersible modules is considered. control process deals with 20 control variables to stabilize the surge, sway and yaw motions of a 30-DOF floating system, subject to unknown irregular waves and limitation of control output. Numerical results have verified the efficiency of the control strategy and show that the proposed control method performs very well.

关键词： Multi-modular floating platform Uncertain wave disturbance High-dimensional nonlinearity adaptive optimal control

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adaptive optimal control of Networked Nonlinear Systems With Stochastic Sensor and Actuator Dropouts Based on Reinforcement Learning

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2024年第3期35卷 3107-3120页

作者： Jiang, Yi Liu, Lu Feng, Gang City Univ Hong Kong Dept Biomed Engn Hong Kong Peoples R China

This article investigates the adaptive optimal control problem for networked discrete-time nonlinear systems with stochastic packet dropouts in both controller-to-actuator and sensor-to-controller channels. A Bernoulli model-based Hamilton-Jacobi-Bellman (BHJB) equation is first developed to deal with the corresponding nonadaptive optimal control problem with known system dynamics and probability models of packet dropouts. The solvability of the nonadaptive optimal control problem is analyzed, and the stability and optimality of the resulting closed-loop system are proven. Two reinforcement learning (RL)-based policy iteration (PI) and value iteration (VI) algorithms are further developed to obtain the solution to the BHJB equation, and their convergence analysis is also provided. Furthermore, in the absence of a priori knowledge of partial system dynamics and probabilities of packet dropouts, two more online RL-based PI and VI algorithms are developed by using critic-actor approximators and packet dropout probability estimator. It is shown that the concerned adaptive optimal control problem can be solved by the proposed online RL-based PI and VI algorithms. Finally, simulation studies of a single-link manipulator are provided to illustrate the effectiveness of the proposed approaches.

关键词： Mathematical models optimal control Heuristic algorithms Closed loop systems Adaptation models Approximation algorithms adaptive systems adaptive optimal control Bernoulli model-based Hamilton-Jacobi-Bellman (BHJB) equation networked discrete-time nonlinear systems reinforcement learning (RL)

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adaptive optimal control Using Frequency Selective Information of the System Uncertainty With Application to Unmanned Aircraft

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IEEE TRANSACTIONS ON CYBERNETICS 2018年第1期48卷 165-177页

作者： Maity, Arnab Hoecht, Leonhard Heise, Christian Holzapfel, Florian Indian Inst Technol Dept Aerosp Engn Bombay 400076 Maharashtra India Tech Univ Munich Inst Flight Syst Dynam D-85748 Garching Germany

A new efficient adaptive optimal control approach is presented in this paper based on the indirect model reference adaptive control (MRAC) architecture for improvement of adaptation and tracking performance of the uncertain system. The system accounts here for both matched and unmatched unknown uncertainties that can act as plant as well as input effectiveness failures or damages. For adaptation of the unknown parameters of these uncertainties, the frequency selective learning approach is used. Its idea is to compute a filtered expression of the system uncertainty using multiple filters based on online instantaneous information, which is used for augmentation of the update law. It is capable of adjusting a sudden change in system dynamics without depending on high adaptation gains and can satisfy exponential parameter error convergence under certain conditions in the presence of structured matched and unmatched uncertainties as well. Additionally, the controller of the MRAC system is designed using a new optimal control method. This method is a new linear quadratic regulator-based optimal control formulation for both output regulation and command tracking problems. It provides a closed-form control solution. The proposed overall approach is applied in a control of lateral dynamics of an unmanned aircraft problem to show its effectiveness.

关键词： adaptive optimal control frequency selective learning (FSL) linear quadratic regulator (LQR) model reference adaptive control (MRAC)

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