{"title":"Constrained optimal control for a class of nonlinear systems with uncertainties","authors":"Jie Ding, S. Balakrishnan","doi":"10.1109/ACC.2011.5990893","DOIUrl":null,"url":null,"abstract":"Approximate dynamic programming formulation (ADP) implemented with an Adaptive Critic (AC) based neural network (NN) structure has evolved as a powerful technique for solving the Hamilton-Jacobi-Bellman (HJB) equations. As interest in the ADP and the AC solutions are escalating, there is a dire need to consider enabling factors for their possible implementations. A typical AC structure consists of two interacting NNs which is computationally expensive. In this paper, a new architecture, called the \"Cost Function Based Single Network Adaptive Critic (J-SNAC)\" is presented that eliminates one of the networks in a typical AC structure. This approach is applicable to a wide class of nonlinear systems in engineering. Many real-life problems have controller limits. In this paper, a non-quadratic cost function is used that incorporates the control constraints. Necessary equations for optimal control are derived and an algorithm to solve the constrained-control problem with J-SNAC is developed. A benchmark nonlinear system is used to illustrate the working of the proposed technique. Extensions to optimal control constrained problems in the presence of uncertainties are also considered.","PeriodicalId":225201,"journal":{"name":"Proceedings of the 2011 American Control Conference","volume":"28 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2011-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 2011 American Control Conference","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ACC.2011.5990893","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
Approximate dynamic programming formulation (ADP) implemented with an Adaptive Critic (AC) based neural network (NN) structure has evolved as a powerful technique for solving the Hamilton-Jacobi-Bellman (HJB) equations. As interest in the ADP and the AC solutions are escalating, there is a dire need to consider enabling factors for their possible implementations. A typical AC structure consists of two interacting NNs which is computationally expensive. In this paper, a new architecture, called the "Cost Function Based Single Network Adaptive Critic (J-SNAC)" is presented that eliminates one of the networks in a typical AC structure. This approach is applicable to a wide class of nonlinear systems in engineering. Many real-life problems have controller limits. In this paper, a non-quadratic cost function is used that incorporates the control constraints. Necessary equations for optimal control are derived and an algorithm to solve the constrained-control problem with J-SNAC is developed. A benchmark nonlinear system is used to illustrate the working of the proposed technique. Extensions to optimal control constrained problems in the presence of uncertainties are also considered.