On the Terminal Full Order Sliding Mode Control of Uncertain Chaotic Systems

Abstract

Over the years, several forms of sliding mode control (SMC), such as conventional SMC, terminal SMC (TSMC) and fuzzy SMC (FSMC) have been developed to cater to the control needs of complex, non-linear and uncertain systems. However, the chattering phenomenon in conventional SMC and the singularity errors in TSMC make the application of these schemes relatively impractical. In this chapter, terminal full order SMC (TFOSMC), the recent development in this line, has been explored for efficient control of the uncertain chaotic systems. Two important chaotic systems, Genesio and Arneodo-Coullet have been considered in fractional order as well as integer order dynamics. The investigated fractional and integer order chaotic systems are controlled using fractional order TFOSMC and integer order TFOSMC, respectively and the control performance has been assessed for settling time, amount of chattering, integral absolute error (IAE) and integral time absolute error (ITAE). To gauge the relative performance of TFOSMC, a comparative study with FSMC, tuned by Cuckoo Search Algorithm for the minimum IAE and amount of chattering has also been performed using settling time, amount of chattering, IAE and ITAE performances. The intensive simulation studies presented in this chapter clearly demonstrate that the settling time, amount of chattering and steady-state tracking errors offered by TFOSMC are significantly lower than that of FSMC; therefore, making TFOSMC a superior scheme.