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| Title: | Generalized Hamilton-Jacobi-Bellman formulation-based neural network control of affine nonlinear discrete-time systems | |
| Author (s): | Chen, Zheng Sarangapani, Jagannathan | |
| Department/Lab Affiliations: | Computer Science Electrical and Computer Engineering Engineering Management & Systems Engineering Intelligent Systems Center | |
| Keywords: | generalized Hamilton–Jacobi–Bellman (BHJB) equation neural network (NN) nonlinear discrete-time (DT) system | |
| Issue Date: | 2008-01 | |
| Publisher: | Institute of Electrical and Electronics Engineers IEEE | |
| Citation: | Chen, Z., S. Jagannathan,"Generalized Hamilton-Jacobi-Bellman formulation-based neural network control of affine nonlinear discrete-time systems," IEEE Transactions on Neural Networks, Vol. 19, pp. 90-106,2008. | |
| Abstract: | In this paper, we consider the use of nonlinear networks towards obtaining nearly optimal solutions to the control of nonlinear discrete-time (DT) systems. The method is based on least squares successive approximation solution of the generalized Hamilton-Jacobi-Bellman (GHJB) equation which appears in optimization problems. Successive approximation using the GHJB has not been applied for nonlinear DT systems. The proposed recursive method solves the GHJB equation in DT on a well-defined region of attraction. The definition of GHJB, pre-Hamiltonian function, HJB equation, and method of updating the control function for the affine nonlinear DT systems under small perturbation assumption are proposed. A neural network (NN) is used to approximate the GHJB solution. It is shown that the result is a closed-loop control based on an NN that has been tuned a priori in offline mode. Numerical examples show that, for the linear DT system, the updated control laws will converge to the optimal control, and for nonlinear DT systems, the updated control laws will converge to the suboptimal control. | |
| Type: | Article - Journal text | |
| In Title: | IEEE Transactions on Neural Networks | |
| Copyright Notice: | This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. allows publisher's final version to be uploaded FULL COPYRIGHT INFORMATION: | |
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| title | Generalized Hamilton-Jacobi-Bellman formulation-based neural network control of affine nonlinear discrete-time systems | |
| contributor.author | Chen, Zheng | |
| contributor.author | Sarangapani, Jagannathan | |
| contributor.deptlab | Computer Science | |
| contributor.deptlab | Electrical and Computer Engineering | |
| contributor.deptlab | Engineering Management & Systems Engineering | |
| contributor.deptlab | Intelligent Systems Center | |
| subject | generalized Hamilton–Jacobi–Bellman (BHJB) equation | |
| subject | neural network (NN) | |
| subject | nonlinear discrete-time (DT) system | |
| date.issued | 2008-01 | |
| publisher | Institute of Electrical and Electronics Engineers IEEE | |
| identifier.citation | Chen, Z., S. Jagannathan,"Generalized Hamilton-Jacobi-Bellman formulation-based neural network control of affine nonlinear discrete-time systems," IEEE Transactions on Neural Networks, Vol. 19, pp. 90-106,2008. | |
| identifier.pub.URI | ||
| description.abstract | In this paper, we consider the use of nonlinear networks towards obtaining nearly optimal solutions to the control of nonlinear discrete-time (DT) systems. The method is based on least squares successive approximation solution of the generalized Hamilton-Jacobi-Bellman (GHJB) equation which appears in optimization problems. Successive approximation using the GHJB has not been applied for nonlinear DT systems. The proposed recursive method solves the GHJB equation in DT on a well-defined region of attraction. The definition of GHJB, pre-Hamiltonian function, HJB equation, and method of updating the control function for the affine nonlinear DT systems under small perturbation assumption are proposed. A neural network (NN) is used to approximate the GHJB solution. It is shown that the result is a closed-loop control based on an NN that has been tuned a priori in offline mode. Numerical examples show that, for the linear DT system, the updated control laws will converge to the optimal control, and for nonlinear DT systems, the updated control laws will converge to the suboptimal control. | |
| type | Article - Journal | |
| type.DCMIType | text | |
| type.status | Final version | |
| rights | This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder. | |
| rights | allows publisher's final version to be uploaded | |
| rights.URI | ||
| rights.URI | ||
| rights.URI | ||
| relation.isPartOf | IEEE Transactions on Neural Networks | |
| date.accessioned | 2008-07-08T20:34:25Z | |
| date.available | 2008-07-11T18:36:09Z | |
| identifier.persist.URI | ||
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