Sebastian Noriega-Marquez , Alexander Poznyak , Alejandra Hernandez-Sanchez , Isaac Chairez
{"title":"使用近似动态编程的差分神经网络鲁棒约束控制器","authors":"Sebastian Noriega-Marquez , Alexander Poznyak , Alejandra Hernandez-Sanchez , Isaac Chairez","doi":"10.1016/j.ejcon.2024.101003","DOIUrl":null,"url":null,"abstract":"<div><p>This study focuses on developing a continuous differential neural network (DNN) approximating min–max robust control by applying dynamic neural programming. The suggested controller is applied to a class of nonlinear perturbed systems providing satisfactory dynamics for a given cost function depending on both the trajectories of the perturbed system and the designed constrained control actions. The min–max formulation for dynamic programming offers reliable control for restricted modeling uncertainties and perturbations. The suggested design considers control norm restrictions in the optimization problem. DNN’s approximation of the worst (with respect to the admissible class of perturbations and uncertainties) value function of the Hamilton–Jacobi–Bellman (HJB) equation enables the estimation of the closed-loop formulation of the controller. The robust version of the HJB partial differential equation is studied to create the learning law class for the time-varying weights in the DNN. The controller employs a time-varying Lyapunov-like differential equation and the solution of the corresponding learning laws. A recurrent algorithm based on the Kiefer–Wolfowitz technique can be used by modifying the weights’ initial conditions to fulfill the specified cost function’s end requirements. A numerical example tests the robust control proposed in this study, validating the robust optimal solution based on the DNN approximation for Bellman’s value function.</p></div>","PeriodicalId":50489,"journal":{"name":"European Journal of Control","volume":null,"pages":null},"PeriodicalIF":2.5000,"publicationDate":"2024-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Differential neural network robust constrained controller using approximate dynamic programming\",\"authors\":\"Sebastian Noriega-Marquez , Alexander Poznyak , Alejandra Hernandez-Sanchez , Isaac Chairez\",\"doi\":\"10.1016/j.ejcon.2024.101003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This study focuses on developing a continuous differential neural network (DNN) approximating min–max robust control by applying dynamic neural programming. The suggested controller is applied to a class of nonlinear perturbed systems providing satisfactory dynamics for a given cost function depending on both the trajectories of the perturbed system and the designed constrained control actions. The min–max formulation for dynamic programming offers reliable control for restricted modeling uncertainties and perturbations. The suggested design considers control norm restrictions in the optimization problem. DNN’s approximation of the worst (with respect to the admissible class of perturbations and uncertainties) value function of the Hamilton–Jacobi–Bellman (HJB) equation enables the estimation of the closed-loop formulation of the controller. The robust version of the HJB partial differential equation is studied to create the learning law class for the time-varying weights in the DNN. The controller employs a time-varying Lyapunov-like differential equation and the solution of the corresponding learning laws. A recurrent algorithm based on the Kiefer–Wolfowitz technique can be used by modifying the weights’ initial conditions to fulfill the specified cost function’s end requirements. A numerical example tests the robust control proposed in this study, validating the robust optimal solution based on the DNN approximation for Bellman’s value function.</p></div>\",\"PeriodicalId\":50489,\"journal\":{\"name\":\"European Journal of Control\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.5000,\"publicationDate\":\"2024-05-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"European Journal of Control\",\"FirstCategoryId\":\"94\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0947358024000633\",\"RegionNum\":3,\"RegionCategory\":\"计算机科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"AUTOMATION & CONTROL SYSTEMS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"European Journal of Control","FirstCategoryId":"94","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0947358024000633","RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
Differential neural network robust constrained controller using approximate dynamic programming
This study focuses on developing a continuous differential neural network (DNN) approximating min–max robust control by applying dynamic neural programming. The suggested controller is applied to a class of nonlinear perturbed systems providing satisfactory dynamics for a given cost function depending on both the trajectories of the perturbed system and the designed constrained control actions. The min–max formulation for dynamic programming offers reliable control for restricted modeling uncertainties and perturbations. The suggested design considers control norm restrictions in the optimization problem. DNN’s approximation of the worst (with respect to the admissible class of perturbations and uncertainties) value function of the Hamilton–Jacobi–Bellman (HJB) equation enables the estimation of the closed-loop formulation of the controller. The robust version of the HJB partial differential equation is studied to create the learning law class for the time-varying weights in the DNN. The controller employs a time-varying Lyapunov-like differential equation and the solution of the corresponding learning laws. A recurrent algorithm based on the Kiefer–Wolfowitz technique can be used by modifying the weights’ initial conditions to fulfill the specified cost function’s end requirements. A numerical example tests the robust control proposed in this study, validating the robust optimal solution based on the DNN approximation for Bellman’s value function.
期刊介绍:
The European Control Association (EUCA) has among its objectives to promote the development of the discipline. Apart from the European Control Conferences, the European Journal of Control is the Association''s main channel for the dissemination of important contributions in the field.
The aim of the Journal is to publish high quality papers on the theory and practice of control and systems engineering.
The scope of the Journal will be wide and cover all aspects of the discipline including methodologies, techniques and applications.
Research in control and systems engineering is necessary to develop new concepts and tools which enhance our understanding and improve our ability to design and implement high performance control systems. Submitted papers should stress the practical motivations and relevance of their results.
The design and implementation of a successful control system requires the use of a range of techniques:
Modelling
Robustness Analysis
Identification
Optimization
Control Law Design
Numerical analysis
Fault Detection, and so on.