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An Optimal Control Design for Input-Affine Nonlinear Systems

This presentation addresses the problem of optimal controller design for Input-affine systems for both Open-loop and Close-loop controller. In Open-loop approach the solution has been analytically given in optimal control theory based on nonlinear ordinary differential equation. Having boundary value problems in the optimal control theory make this problem challenging even though for numerical solution approach. First section of presentation is devoted to the method of unraveling this difficulty. The second section involves in finding an optimal solution for Close-loop nonlinear controllers designed by conventional methods such as Feedback Linearization or Sliding Mode. The method is applicable to all nonlinear systems which can be linearized using the method of state-feedback linearization. The alternative is to use linear optimization techniques for the linearized equations but then there is no guarantee that the original nonlinear system behaves optimally. We use feedback linearization technique to linearize the system and then design a state-feedback for the feedback-linearized system in such a way that it ensures optimal performance of the original nonlinear system. The proposed method can optimize any arbitrary smooth function of states and input. The method is successfully applied to control design of a flexible joint dynamic and the results are discussed. Several times of improvement is obtained in this example by employing the proposed method rather than the conventional linear quadratic regulator (LQR). Furthermore, the proposed algorithm easily could be extended to optimally tune the control parameters in a conventional Lyapunov-Based method which shares the same concept of control design with sliding mode approach as applied to the robot manipulators. Finally, other applications of proposed method are discussed.

Type of Seminar:
Ph.D. Seminar
Peyman Mohajerin Esfahani
Sharif University of Technology
Dec 20, 2007   10:45

ETL K 25
Contact Person:

Prof. J. Lygeros
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