Finite Horizon Discrete-Time Adaptive Dynamic Programming

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Finite Horizon Discrete-Time Adaptive Dynamic ProgrammingDerong Liu, University of Illinois at ChicagoThe objective of the present project is to make fundamental contributions to the field of intelligent control. In particular, the PI will conduct adaptive dynamic programming research under the following three topics. The first topic is about the analysis of optimal controllers and optimal performance costs under the condition that the number of steps for performing optimal control of nonlinear discrete-time systems is not fixed but is known to be finite. The second topic is to develop adaptive neural dynamic programming algorithms for the optimal control of nonlinear discrete-time systems. The third topic is to establish the stability, convergence, and optimality theory for the adaptive dynamic programming algorithms developed in this project. The first topic is the foundation of the second topic. The third topic provides guarantees of stability, convergence and optimality when applying our adaptive neural dynamic programming algorithms. The second topic is the ultimate goal of this project. The PI will develop stable and convergent algorithms for adaptive dynamic programming of nonlinear discrete-time systems.Intellectual MeritThe PI will investigate adaptive dynamic programming for discrete-time nonlinear systems. Specifically, for discrete-time optimal control problems with finite, but may not be fixed, time horizon, he will establish analysis results of optimal controllers for each control step and investigate properties of these controllers, in order to build a foundation for neural network implementation of adaptive dynamic programming. The main goal of this project is to develop adaptive neural dynamic programming algorithms for nonlinear discrete-time systems. Since the algorithms will be implemented using neural networks, the PI can find the minimum of cost function without solving partial differential equations. Broader Impacts In addition to training Ph.D. students, the PI will work with several undergraduate students on research topics in the present project in the next three years. In the present project, The PI will continue his effort in recruiting minority undergraduate students to his research program. It is believed that the success of the present project will build a solid foundation for adaptive dynamic programming of nonlinear discrete-time systems with finite time horizon. Theoretical results obtained in the present project will help push forward practical applications of adaptive dynamic programming in the years to come.