Finite time analysis based on Sum of Squares Technique: Applied to the super-twisting second order sliding mode control

TL;DR

This paper develops a systematic sum of squares programming approach for finite time stability analysis and control design, applied to super-twisting sliding mode control, verified through simulations and numerical examples.

Contribution

It introduces a novel Lyapunov function construction method and region of reaching estimation using sum of squares techniques for finite time analysis.

Findings

Feasibility conditions formulated as semi-definite programs.

Effective control design demonstrated for super-twisting sliding mode.

Simulation results confirm theoretical predictions.

Abstract

Finite time analysis of the continuous system is investigated through both stability and stabilization based on Sum of squares programming. A systematic approach is proposed to construct Lyapunov function and Control Lyapunov function for this objective. The Region of reaching, the set which has the property that all trajectories starting from initial point inside it reach to the origin in finite time, is introduced, and The largest subset of region of reaching is estimated using Lyapunov based technique. The main results are presented to give sufficient conditions which can be translated by semi-definite program. These conditions are provided a feasibility problem involving sum of squares constraints. The results of the paper are then verified by several simulation and numerical examples. Furthermore, one important practical application namely as a super twisting second order sliding mode control also is presented using the proposed result to illustrate its effectiveness.