###### Abstract
A unified approach to fixed-time tracking control of stochastic high-order nonlinear systems (HONSs) with or without full-state constraints is studied in [17]. In this paper, to consider the running speed and stability of the manipulator, the time-optimal trajectory planning (TOTP) of the manipulator is transformed into a nonlinear optimal value search problem under multiple constraints, and a time-search algorithm based on fuzzy control is proposed, so that the end of the manipulator can run along the given path in Cartesian space for the shortest time, and the angular velocity and angular acceleration of each joint is within a limited range [18]. To begin with, a discrete LQR controller with feedforward and feedback components is designed based on the error model of vehicle lateral dynamics constructed by the natural coordinate system. Then, a fuzzy control method is applied to adjust the weight coefficients of the LQR in real time according to the state of the vehicle [19]. In another paper, an indirect hybrid solar-electric dryer was used to be able to dry a wide range of agriproducts and to ensure a continuous drying operation [20]. The shadowed type-2 fuzzy system (ST2-FHS) can be seen as an option to simplify fuzzy systems as they provide a solution by representing a fuzzy set based on two points (cuts), where the essential values are retained, and insignificant values are eliminated. The purpose of this approach is to minimize the issue of excessive precision in defining uncertainty. The aim of this work was to model a GT2 FLS based on shadowed type-2 fuzzy sets (ST2 FS) and apply this approach to control problems. The ST2 FS consists of approximating the secondary membership function with shadowed sets and it is because of this that we present an analytic approach to obtain the shadowed set for triangular and Gaussian membership functions for any parameters [21]. Traffic networks are getting big and complex day by day with a rapid traffic growth. Existing type-2 (T2) fuzzy logic works well in optimizing the waiting time of traffic at a big junction, but the rule base of T2 fuzzy logic is heavily dependent on previous traffic data, rather than real-time data. Moreover, it fails in changing and updating the waiting time in any junction with a high rate of traffic. In addition, very big junctions contain dynamic traffic data that are characterized by a high level of uncertainty, which is difficult to be handled with type-2 fuzzy logic. To cope with this situation, shadowed type-2 (ST2) fuzzy logic is proposed as it works well in a domain having very clumsy and uncertain data. It increases the uncertainty of a fuzzy set by partitioning it into a different region [22], and the ST2 FIS is based on the ideas of shadowed fuzzy sets and is an approximation of general type-2 fuzzy inference systems (GT2 FIS). The fundamental rationale for utilizing ST2 FIS instead of GT2 FIS is that the computational cost of GT2 FIS is too high for this application. The simulation results for the FTC using IT2 FIS and FTC using ST2 FIS for the Coupled Conical Tank Level Control (CCTLC) system with a 30% and 40% loss of effectiveness in the main actuator are presented in this study. In addition, this article compares the proposed FTC approach using ST2 FIS to FTC using IT2 FIS in terms of fault-recovery time [23]. This paper presents a novel methodology to obtain the shadowed set for all the secondary membership functions embedded in a general type-2 membership function. In this paper, we present an approach to obtain the shadowed set for a triangular and a Gaussian membership function. The idea is to model and perform a general type-2 fuzzy system based on shadowed type-2 fuzzy sets. The results are compared against the performance when a general-type fuzzy inference system is approximate when used on \(\alpha\)-planes [24]. General type-2 fuzzy sets (GT2 FSs) have been originally proposed to allow for modeling uncertainty associated with the membership grades of type-1 (T1) FSs.