ASSIGNMENT OF NONLINEAR SAMPLED-DATA DYNAMICS USING GENERALIZED HOLD FUNCTION CONTROL

This paper considers the problem of assigning the dynamics of a nonlin ear analytic system using nonlinear generalized sampled-data hold func tion (GSHF) control, in the neighborhood of an equilibrium point. On e very sampling interval, the control input consists of a nonlinear time -periodic function applied to the sampled value of the state vector. T he nonlinear monodromy map is the state transition map from one sample time to the next. It is shown that this map is arbitrarily assignable by GSHF feedback if and only if the linear part of the system is cont rollable. Two approaches are proposed to construct a GSHF controller t hat performs the assignment. The first approach matches the coefficien ts of the Taylor series expansion of the monodromy map around the equi librium. The second approach interpolates an optimal control law at se veral points in the vicinity of the equilibrium. These approaches are illustrated on an example.