Approximate optimal control of affine nonlinear continuous-time systems using event-sampled neurodynamic programming

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dc.contributor.authorSahoo, Avimanyu
dc.contributor.authorXu, Hao
dc.contributor.authorSarangapani, Jagannathan
dc.date.accessioned2022-02-28T20:47:11Z
dc.date.available2022-02-28T20:47:11Z
dc.date.issued2016-04-07
dc.description.abstractThis paper presents an approximate optimal control of nonlinear continuous-time systems in affine form by using the adaptive dynamic programming (ADP) with event-sampled state and input vectors. The knowledge of the system dynamics is relaxed by using a neural network (NN) identifier with event-sampled inputs. The value function, which becomes an approximate solution to the Hamilton–Jacobi–Bellman equation, is generated by using event-sampled NN approximator. Subsequently, the NN identifier and the approximated value function are utilized to obtain the optimal control policy. Both the identifier and value function approximator weights are tuned only at the event-sampled instants leading to an aperiodic update scheme. A novel adaptive event sampling condition is designed to determine the sampling instants, such that the approximation accuracy and the stability are maintained. A positive lower bound on the minimum inter-sample time is guaranteed to avoid accumulation point, and the dependence of inter-sample time upon the NN weight estimates is analyzed. A local ultimate boundedness of the resulting nonlinear impulsive dynamical closed-loop system is shown. Finally, a numerical example is utilized to evaluate the performance of the near-optimal design. The net result is the design of an event-sampled ADP-based controller for nonlinear continuous-time systems.en_US
dc.description.abstractThis paper presents an approximate optimal control of nonlinear continuous-time systems in affine form by using the adaptive dynamic programming (ADP) with event-sampled state and input vectors. The knowledge of the system dynamics is relaxed by using a neural network (NN) identifier with event-sampled inputs. The value function, which becomes an approximate solution to the Hamilton–Jacobi–Bellman equation, is generated by using event-sampled NN approximator. Subsequently, the NN identifier and the approximated value function are utilized to obtain the optimal control policy. Both the identifier and value function approximator weights are tuned only at the event-sampled instants leading to an aperiodic update scheme. A novel adaptive event sampling condition is designed to determine the sampling instants, such that the approximation accuracy and the stability are maintained. A positive lower bound on the minimum inter-sample time is guaranteed to avoid accumulation point, and the dependence of inter-sample time upon the NN weight estimates is analyzed. A local ultimate boundedness of the resulting nonlinear impulsive dynamical closed-loop system is shown. Finally, a numerical example is utilized to evaluate the performance of the near-optimal design. The net result is the design of an event-sampled ADP-based controller for nonlinear continuous-time systems.
dc.identifier.citationSahoo, A., Xu, H. and Jagannathan, S., 2016. Approximate optimal control of affine nonlinear continuous-time systems using event-sampled neurodynamic programming. IEEE transactions on neural networks and learning systems, 28(3), pp.639-652.en_US
dc.identifier.citationSahoo, A., Xu, H. and Jagannathan, S., 2016. Approximate optimal control of affine nonlinear continuous-time systems using event-sampled neurodynamic programming. IEEE transactions on neural networks and learning systems, 28(3), pp.639-652.
dc.identifier.doihttps://doi.org/10.1109/TNNLS.2016.2539366
dc.identifier.urihttps://hdl.handle.net/1969.6/90210
dc.language.isoen_USen_US
dc.language.isoen_US
dc.publisherIEEEen_US
dc.publisherIEEE
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International*
dc.rightsAttribution-NonCommercial-NoDerivatives 4.0 International
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/*
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.subjectartificial neural networksen_US
dc.subjectoptimal controlen_US
dc.subjectadaptive systemsen_US
dc.subjectnonlinear dynamical systemsen_US
dc.subjectsystem dynamicsen_US
dc.subjectstability analysisen_US
dc.subjectdynamic programmingen_US
dc.subjectartificial neural networks
dc.subjectoptimal control
dc.subjectadaptive systems
dc.subjectnonlinear dynamical systems
dc.subjectsystem dynamics
dc.subjectstability analysis
dc.subjectdynamic programming
dc.titleApproximate optimal control of affine nonlinear continuous-time systems using event-sampled neurodynamic programmingen_US
dc.titleApproximate optimal control of affine nonlinear continuous-time systems using event-sampled neurodynamic programming
dc.typeArticleen_US
dc.typeArticle

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