Control of input-affine nonlinear systems via linear programming

An effective and user-friendly method to control a large portion of input-affine nonlinear systems is proposed. This method works based on transforming the nonlinear control problem to a linear programming (LP) in unknown controls, the state variables of plant, and possibly the constraints imposed on the controls and state variables. The solution of this LP provides the control to be applied to the plant. The main advantages of the proposed method are: simplicity of applying to multi-input multi-output systems, taking into account the actuator saturation and constraints on states, and robustness to uncertainties in the model. Two numerical examples are presented to verify the effectiveness of the proposed method. These are output voltage regulation of a two-input two-output dc-dc boost converter with actuator saturation and position control of a magnetic levitation system with a constraint on the speed of ball.

Automated summary

The proposed method effectively controls input-affine nonlinear systems by transforming the nonlinear control problem into linear programming, making it suitable for multi-input multi-output systems with simplicity, robustness, and consideration of constraints on controls and states. The effectiveness of the method is verified through two numerical examples.