On minimum quadratic functional control of affine nonlinear systems

Abstract

The minimization control problem of the quadratic functionals for the class of affine nonlinear systems in the hypothesis of nilpotent associated Lie algebra is analyzed. The optimal control correspondent to the first-, second- and third-order nilpotent operator is determined. H. Bourdache-Siguerdinljane has applied the method of Lie algebras to the study of optimal control regulation of satellites. S. Banks and M. Yew have studied the optimal control of energy consumption minimization for a class of bilinear systems and J.S. Liu et al., have generalized this result for the class of affine nonlinear systems. The optimal control determination of nonlinear system with a nilpotent structure minimizing the quadratic functionals generalizes the results of J.S. Liu, K. Yuan, W.S. Lin, and S.P. Banks, and M.K. Yew regarding the energy minimization of the affine nonlinear and bilinear systems.