This paper is concerned with the control design of adaptive fuzzy fixed-time high-order sliding mode (HOSM) under asymmetric output constraints. The main objective of the paper is to construct a control scheme to build the HOSM in a fixed time and fulfill the pre-set constraint condition. For this purpose, initially to conquer this obstacle regarding the output constraint, a barrier Lyapunov function is developed to keep the output variable within the predefined constraint during operation. Then, the unknown functional bounds of uncertainties in the considered system are modeled by invoking fuzzy logic systems. With the integrated use of adaptive fuzzy control and backstepping-like techniques, a novel protocol for the fixed-time HOSM control with asymmetric output constraints is developed. Through the strictly theoretical clarification, the HOSM is fixed-time established under the suggested control strategy. The effectiveness of the derived results is eventually testified by some comparative simulation results.

Recently, to ensure product quality in high-mix semiconductor manufacturing processes, run-to-run (R2R) control algorithms have received increasing attention. Difficult challenges have been met with new and advanced approaches that address the real-world operating conditions exhibited in high-mix production environments (e.g., different products with different frequencies and high numbers of threads). In this paper, various proposed controllers for high-mix semiconductor manufacturing processes are surveyed from an application and theoretical point of view. Remaining challenges and directions for future work are also summarized with the intent of drawing attention to these problems in the systems and process control communities.