A Linear-Programming-Based Sliding-Mode Control Design for Stabilization of a Double-Inverted Pendulum

Abstract

A linear programming approach for computation of sliding-mode control inputs is proposed. The method is applied to a double-inverted pendulum system and it takes input and approaching rate constraints into account. The derivation procedure reveals that it is generalizable to a large class of dynamic systems and can take a more general set of constraints into account. The approach preserves the robustness property of the sliding-mode control and enriches it by adding the features of the linear programming. The main feature incorporated into the sliding-mode control is the optimal update of the control inputs under a set of linear constraints. The constraints are specified to meet the sliding-mode conditions and to improve its undesired chattering behaviour.