Self-Triggered Scheme Design for Takagi-Sugeno Fuzzy Model Based on Mismatch Premise Variable With Time-Varying Delay

Abstract

Over the last 20 years, numerous experts in the manufacturing companies have become interested in controlling <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">flexible joint robots</i>. The control design process using a networked framework has played a significant role in the industrial sector. This research addresses the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">self–triggered</i> control problem for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Takagi–Sugeno (T–S) fuzzy systems</i> based on time delay is established in this research. A new <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">self–triggered</i> mechanism determines when the plant state is transmitted. Instead of continuously tracking predefined triggering conditions, the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">self–triggered</i> system determines the next triggering instant based on the most recently triggered state information. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">self–triggered</i> mechanism relying on <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T–S fuzzy controller</i> is then created using the triggered state, allowing for flexible configuration of its fuzzy rules and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">membership operations (MOs)</i> that are not dependent on the controlled fuzzy system. Furthermore, it precisely demonstrates the interaction between the triggered condition and the plant state under the constraint of mismatched premise variables. To ensure system stability and performance, delay–dependent requirements are derived using a novel <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lyapunov–Krasovskii functional</i> based on fuzzy concepts to develop the fuzzy control design. The presence of the required controller is then shown under <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LMI–based conditions</i>. Lastly, a simulation of a flexible robotic arm example is provided along with an evaluation of other triggered methods.