Saturated PI Control for Nonlinear System With Provable Convergence: An Optimization Perspective

The saturated PI (proportional-integral) based method is widely applied in nonlinear system control fields. It can be regarded as a black-box type approach with the saturated control input and utilizes the tracking error of the system output with its integral information. However, as precise description of plants' system details is usually difficult, saturated PI control approaches have to empirically tune the proportional and integral parameters to guarantee reliable convergence, making its general convergence mechanism not interpreted. In this brief, for the first time, the convergence of the saturated PI control scheme is proved through an optimization solver based on a primal dual neural network. Illustrate examples including control of an inverted-pendulum mobile vehicle and a manipulator demonstrate the efficiency of the proposed saturated PI control method in such an optimization perspective.