A DIFFERENTIAL-ALGEBRAIC PERSPECTIVE ON NONLINEAR CONTROLLER-DESIGN METHODOLOGIES

Considerable activity has occurred independently in the fields of nonl inear geometric controller design and the solution of differential-alg ebraic systems of equations. Recently, a differential-algebraic approa ch to nonlinear controller design has been proposed. In this paper, th e formal relationship between these approaches is identified. In parti cular, it is shown that the index of the nonlinear inversion problem i s equal to rho + 1, where rho is the relative order of the process. Th e merits of the primary nonlinear control algorithms are assessed from a differential-algebraic perspective. Error trajectory controllers of fer the advantage of being index one differential-algebraic problems w ith no associated initialization difficulties. In contrast, the nonlin ear inversion and sliding mode control designs result in higher-order index problems with initialization restrictions. The restrictions iden tified for the nonlinear inverse design are related to the concept of functional controllability from the nonlinear systems literature. The relationship between the differential-algebraic design approach and th e nonlinear geometric approach is extended to a class of processes des cribed by nonlinear differential-algebraic equations. Finally, the non linear controller design problem is analyzed graphically, highlighting the differences between the various approaches.