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Nonlinear Optimal Control Design Considering a Class of System Constraints With Validation on a Magnetic Levitation System

In this letter, based on the theory developed, a nonlinear optimal controller is designed via stable manifold theory making use of Lagrange multipliers to take into account a class of system constraints. A feature of this method is that a discontinuous Hamiltonian system has to be solved. The existence and uniqueness of solutions of the Hamiltonian system are proven in this letter with a discussion on the stability of the designed controller. The effectiveness of the method is experimentally validated on a Quanser magnetic levitation system. The result shows that the designed nonlinear controller is able to handle the acceleration constraints with better control performance compared with the linear optimal one.