Design of LQ regulator for linear systems with algebraic-equation constraints

The problem of linear quadratic (LQ) optimal control of linear systems with algebraic-equation constraint is considered in this paper. Based on the stabilized constraint relation, this problem is transformed to an optimal control problem with equality constraints of the control and state variables. Then, using optimal control theory, the LQ regulator is derived which minimizes the given quadratic performance criterion and simultaneously forces the closed-loop system to satisfy the constraints. The sufficient condition for the existence of an LQ regulator and the stability of the corresponding closed-loop system are studied, which show that the closed-loop poles consist of the poles of the stabilized constraint relation and the other stable poles which are independent of the stabilized constraint relation. The application to a constrained mechanical system is discussed, and two examples are also given to illustrate the validity of the design method presented.