Implementing nonquadratic control on the nonlinear modal manifold

A unified optimality-based framework was developed to address the problem of nonlinear nonquadratic control of a class of nonlinear modal system. Unlike the traditional IMSC (Independent Modal Space Control) method, which is restricted to linear oscillatory system, the presented control method can be applied to the nonlinear oscillatory system. By using a set of nonlinear coordinate transformation, based on modal invariance theory, the system is translated onto the nonlinear modal manifold; also the nonlinear modally coupled terms can be effectively approximated by the modal variables in the respective nonlinear modal space. Then, by properly assuming a nonlinear-nonquadratic performance criteria to account for the closed-loop control on each modal space. Specifically, the performance criterion is related to the structure of the Lyapunov function which is the solution of the steady-state form of the Hamilton-Jacobi-Bellman equation for addressing the design of optimal controller. Simulation results show that the nonlinear optimal control provides better control effects over the LQR controller.