## 1 Introduction
Therefore, this kind of thinking is quite conservative. Then, reference [26] used the backstepping method to design an improved controller, and the CLS was the same as the linear CLS in reference [19], and then the conditions of NOTC were discussed based on the Laplace transform. Compared with references [19], reference [26] obtained wider conditions of non-overshooting, which reduced the conservatism. Reference [27] studied the problem of output tracking with non-overshooting of a feedback linearization nonlinear system, and proposed a controller design program using feedback linearization and global coordinate transformation technology. Compared with references [19; 26], the nonlinear function in the controlled system in reference [27] not only needs to be assumed to be known, but also needs to be bounded, so this increases the conservatism. In addition, references [28; 29; 30; 31] have studied the problem of non-overshooting control of nonlinear systems. It is worth mentioning that in recent years, there have been some breakthroughs in NOTC of nonlinear systems. Reference [32] first proposed the mean-non-overshooting tracking control design for stochastic strict-feedback nonlinear systems. The obtained results ensure that the overshoot can be adjusted to be as small as possible under the condition that all the states of the CLS remain bounded. At the same time, reference [33] designs a finite-time control algorithm for nonlinear strict-feedback systems, which makes the overshoot arbitrarily small. However, compared with the NOTC algorithm, this method fails to achieve the control goal of non-overshooting, thus reducing the accuracy of non-overshooting. The method in this paper is mainly aimed at a class of nonlinear systems, and the problem of NOTC with FSCs is studied. Compared with the existing related literature, this paper has the following differences:  
1. Compared with the BLF [11], this paper uses the mapping constraint function, which is a direct constraint method, thus reducing the calculation burden of constraint parameters. 2. On the basis of FSCs, the problem of NOTC is discussed, which makes the FSCs method realize the result of NOTC. Compared with the existing FSCs method [11; 12; 13; 14; 15; 16; 17], the overshoot of tracking error can be 0. 3. Regarding NOTC, because the expression of tracking error is adopted in this paper, a wider range of non-overshooting in conditions can be obtained compared with that of the existing methods [19; 26; 27; 32; 33], which reduces the conservatism. 4. The most difficult problem that arises when designing the algorithm in this paper relates to obtaining a CLS that can solve the expression of tracking error. To obtain a CLS that can easily calculate the expression of tracking error, this paper needs to convert the situation in which each subsystem is nonlinear into a system that only contains the \(n\)-th subsystem as nonlinear (such as (25)). Otherwise, it is difficult to calculate the expression of tracking error for the obtained CLS. Then, this algorithm provides a method to transform the controlled system into a system that is simpler to deal with. Compared with the existing control results with NOTC, this algorithm is simpler. The layout of the rest of this article is as follows: The problem formulation is given in Section 2. The full-state constraints control and control design are shown in Section 3. The NOTC is written in Section 4. An example is given in Section 5, and the conclusions of this paper are provided in Section 6.