On Output Regulation Of Affine Singular Nonlinear Systems

Output regulation for nonlinear system is the core topic of control theory.Most of existing results on output regulation problem of singular nonlinear systems are limited to local solutions,while the global/semi-global output regulation problem is not ful-ly studied.This dissertation addresses global/semi-global output regulation problems for some classes of affine singular nonlinear systems,and extends the general frame-work for output regulation problem of normal nonlinear systems to singular nonlinear systems.The main contents of the dissertation lie in the below:?.Global output regulation for a class of affine singular nonlinear systems.First-ly,this dissertation considers a class of singular nonlinear systems which is precisely known.An input and coordinate transformation is introduced to transfer the singular nonlinear system into a reduced-order normal system.Secondly,we prove that the so-lution of the global stabilization problem for the normal system implies the solution of the global output regulation problem for the considered singular nonlinear system.Finally,we establish the sufficient conditions for the global stabilization problem for the normal system,which means that the solvability conditions of the global output regulation problem are obtained.?.Global robust output regulation for a class of uncertain singular nonlinear sys-tems with unknown parameter vector.A class of affine singular nonlinear system with unknown parameter vector is considered.Assume that the singular nonlinear system has a strong relative degree,a corresponding global diffeomorphism map is designed.Then we transfer the singular nonlinear system into a new singular nonlinear system with a special structure based on the input-output linearization.The augmented system is composed of a linear internal model and the new singular nonlinear system.We show that the global robust stabilization solution of the augmented system implies the glob-al robust output regulation solution of the original singular nonlinear system.Finally,under some appropriate assumptions,the global robust stabilization problem is solved by using small gain theorem.Hence,the solvability conditions of global robust output regulation problem are established.?.Semi-global robust output regulation for a class of singular nonlinear systems via nonlinear internal model.The linear internal model is based on a polynomial as-sumption which is quite restrictive because it requires the considered nonlinear systems contain only the polynomial nonlinearity.A class of affine singular nonlinear systems with unknown parameter vector is investigated by using a nonlinear internal model.A nonlinear internal model is given to weaken the polynomial assumption,and an aug-mented system is obtained which is composed of the nonlinear internal model and the singular nonlinear system.The augmented system's semi-global robust stabilization solution also leads to the solution of the semi-global robust output regulation problem of the singular nonlinear system.By investigating the semi-global robust stabilization problem via high-gain feedback control,the solvability conditions of the semi-global output regulation problem are established.?.Semi-global robust output regulation for a class of singular nonlinear systems with unknown algebraic equations.When the singular nonlinear systems can be re-duced into a normal nonlinear system,the output regulation problem of singular non-linear system can be converted into the output regulation problem of a corresponding normal nonlinear system.But it is usually hard to solve the algebraic equations.Es-pecially,when algebraic equations of the singular nonlinear system are not precisely known,it is almost impossible to solve the algebraic equations.A class of singular nonlinear systems with unknown algebraic equations is considered.Based on a linear internal model,the problem is converted into a robust stabilization problem of an aug-mented singular nonlinear system.The augmented singular nonlinear system also can't be reduced to a normal nonlinear system.Under some reasonable assumptions,it is shown that the augmented system can be semi-globally stabilized by using a high gain output feedback control law.Hence,the semi-global robust output regulation problem is solved.