Precise Point-to-Point Control for Nonlinear Systems

A novel control strategy for designing point-to-point controllers for nonlinear systems is proposed. The control law combines feedback and feedforward for the purpose of finite time settling of a non-linear system to its desired state. The feedback is designed separately to satisfy certain performance specifications in the time domain. The feedforward control law is determined from the feedback part and it is approximated via numerical methods. The point-to-point control problem is shown to be reduced to a boundary value problem in time, where its solution can be estimated via classical numerical methods, such as using the Galerkin, the least square, and the finite element techniques. Two methods for approximating the feedforward control part with the aid of the least-square technique are proposed. In the first method, the point-to-point control problem reduces to minimizing the norm of an error vector as integrated from zero to the final time. The size of the error vector is equal to the system´s dimension. In the second method a truncation in the size of the error vector is suggested. It has been shown that the second method leads to better approximations and less computation times. The robustness of the proposed control strategy is addressed, and computer simulations are presented to justify the viability of the proposed control strategy.