A New Method for Suboptimal Control of a Class of Non-Linear Systems

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Dehghan, Ali Reza | 2010

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 41072 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Hesaaraki, Mahmoud
Abstract:
In this thesis, a new non-linear control synthsis technique (θ - D) approximation) is discussed. This approach achieves suboptimal solutions to a class of non-linear optimal control problems characterized by a quadratic cost function and a plant model that is a_ne in control. An approximate solution to the Hamilton-Jacobi-Bellman (HJB) equation is sought by adding perturbations to the cost function. By manipulating the perturbation terms both asymptotic stability and suboptimality properties are obtained. The new technique overcomes the large-control-for-large-initial-states problem that occurs in some other Taylor series expansion based methods. Also this method does not require excessive online computations like the recently popular state dependent Riccati equation (SDRE) technique. Furthermore, it provides a closed-form non-linear feedback controller if _nite number of terms are taken in the series expansion. A scalar problem and a 2-D benchmark problem are investigated to demonstrate the e_ectiveness of this new technique. Both stability and convergence proofs are given.
Keywords:
Nonlinear Systems ; Optimal Control ; Hamilton-Jacobi-Bellman Equation ; Feedback Control ; Perturbation Method