This paper investigates the non-overshooting tracking conditions forn-th order nonlinear systems with unmeasurable states. By designing state observers, the problem of unmeasurable states is addressed. The key to non-overshooting control (OC) is how to design appropriate controller to ensure the system is not only stable but also effectively solves the non-OC problem. Based on backstepping, a square root gain control algorithm is proposed in this paper, which ensures global asymptotic stability of the closed-loop system. Meanwhile, two main conclusions are drawn in non-OC: 1) If the initial values of the system states are equal to the initial values of the observer states, the conditions obtained by the proposed algorithm can achieve non-OC, i.e., the system overshoot is zero. Non-OC conditions for$n=1$,$n=2$,$n=3$, and$n\geq 4$order systems are obtained, respectively. And the conditions are relatively rich. Therefore, compared with existing algorithms, this algorithm not only ensures zero system overshoot, but also reduces conservatism; 2) If the initial values of the system states are not equal to the initial values of the observer states, the conditions obtained by this algorithm can achieve mean-non-OC, i.e., the system overshoot can be adjusted to any small value. In terms of simulation, the stability performance algorithm, non-OC algorithm, and mean-non-OC algorithm were verified using the mathematical models of the DC servo motor systems and Chua’s circuit system. Simulation results show that these control algorithms are effective. It also compares existing related results, highlighting the superiority of the algorithm presented in this paper.

In this article, we propose a full-state constraints asymptotic stability control for nonlinear multiple-input-multiple-output (MIMO) systems. This algorithm addresses the full-state constraints problem by restricting the constraint intervals to only the system states, thus compensating for the limitations of barrier Lyapunov functions. Additionally, it ensures the asymptotic stability of the closed-loop system in the presence of unknown functions. In contrast to neural network and fuzzy approximation algorithms, our proposed algorithm facilitates the convergence of system states to the origin without relying on assumptions about unknown functions. This leads to a reduction in conservatism compared to these algorithms. Furthermore, a simulation example is provided to demonstrate the effectiveness and superiority of the proposed algorithm.

In this article, the conditions of ensuring nonovershooting tracking control (NOTC) for nonlinear pure-feedback systems (PFSs) are proposed. Presently, there are almost no results of guaranteed NOTC conditions for nonlinear PFSs. And the results in strict-feedback form are also very narrow. Based on these problems, this article obtains a more extensive conditions of NOTC for nonlinear PFSs. First, a controller is designed to make the closed-loop system (CLS) globally asymptotically stable, and a suitable CLS can be obtained through the designed controller. Then, by analyzing the CLS, the NOTC conditions of the first-order, second-order, and multiorder systems can be obtained, respectively. Finally, through the simulation results of two examples and comparing the simulation results of the existing algorithms, it is concluded that the algorithm in this article is effective and superior. In this article, for more general nonlinear PFSs, a wider range of NOTC conditions are obtained, and the obtained NOTC conditions are also suitable for strict-feedback form. Therefore, this algorithm reduces the conservatism.

This article investigates nonovershooting tracking control for a class of multiple-input–multiple-output (MIMO) nonlinear systems. Nonovershooting tracking control is desired in various practical situations, yet remains a challenging task with limited existing research. While the MIMO nonlinear system better represents real-world scenarios, the specific algorithm for nonovershooting tracking control has not been previously reported. In this study, a controller is designed to ensure system stability initially, while also achieving a closed-loop system for easy tracking error analysis. By deriving the expression of tracking error, a broad range of nonovershooting tracking conditions is identified through analytical analysis. The proposed nonovershooting control is shown to offer more extensive nonovershooting conditions compared to existing approaches, thereby reducing conservatism. Furthermore, this algorithm eliminates overshoot in MIMO nonlinear systems. Its effectiveness is validated through application to a two-degree-of-freedom robot manipulator.

This article studies the output regulation problem (ORP) for nonlinear systems based on prescribed performance control (PPC). The items with the partial derivative of the virtual controller are combined together by using backstepping, and then the fuzzy logic systems (FLSs) are used to approximate these combined items, so that the designed virtual controller does not have the partial derivative of the previous virtual controllers. Therefore, this method not only reduces the calculation burden in the backstepping method, but also avoids the disadvantages of dynamic surface control (DSC). Finally, a function$\Theta $is constructed such that the overall performance (dynamic performance and steady-state performance) of the tracking error (OPTE) is constrained by PP functions. The proposed control algorithm ensures that all the signals are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error achieves the PPC. Simulation examples are provided to illustrate the effectiveness of the proposed method.