Nonlinear Systems Adaptive Inverse Optimal Control

In order to avoid solving intricate Hamilton-Jacobi-Belllman(HJB) partial differential equations in the nonlinear optimal control in recent years, the inverse optimal approach has been proposed. Subsequently, a series of profound and significant results have been appeared. On the basis of the following system,some innovation works have been done in this thesis that is organized as follows. Firstly, the strict-feedback nonlinear systems with unknown virtual control coefficients b_i have been studied and the problem of its inverse optimality has been solved, that isThe new solvable theorem of inverse optimal gain assignment problem has been proposed through the method of modular design for the original system.The main contributions in this paper are as follows:1)Adaptive inverse optimal control of strict-feedback systems with unknown virtual control coefficientsAccording to the basic idea of the inverse optimal control, It is solved in this paper that the inverse optimal gain assignment problem for the strict-feedback nonlinear systems not only with unknown constant paraments and unknown time-variant bounded disturbance but also with unknown virtual control coefficients. By virtual of backstepping, the inverse optimal controller is designed, which is continuous and performed more easily. The results of simulations indicate the efficiency of this scheme.2)Adaptive inverse optimal control with modular designThis paper gives the new solvable theorem of inverse optimal gain assignment problem. By means of adaptive backstepping algorithm and the basic idea of modular design for strict-feedback nonlinear continuous systems with unknown time-varing bounded disturbances and constant unknown parameters, an inverse optimal controller is designed. Aiming at such strict-feedback nonlinear continuous systems, the more popular observor has been designed by the key theorem established by us.