Exact Linearization with Configuration Optimization

In this paper, we study the exact linearization and control of a MIMO nonlinear system which consists of chains of integrators. In such a system, if the number of outputs is greater than number of chains and control inputs, the linearized system will have less number of states than that of the original system. In this case, a subsystem (called zero dynamics) is created by the state feedback. As shown in the paper, this zero dynamics affects the I/O system in an implicit way. We propose a scheme that linearizes the I/O system and, at the same time, controls the zero dynamics to follow a gradient flow so that a desirable condition on the overall system can be reached. Applications of this theory include the control of redundant manipulator and multiple-joint space robot.