Abstract:This paper studies the problem of adaptive fuzzy asymptotic tracking control for multiple input multiple output nonlinear systems in nonstrict-feedback form.Full state constraints, input quantization, and unknown control direction are simultaneously considered in the systems. By using the fuzzy logic systems, the unknown nonlinear functions are identified. A modified partition of variables is introduced to handle the difficulty caused by nonstrict-feedback structure. In each step of the backstepping design, th… Show more
“…Based on the excellent performance of adaptive control method, over the last decades, it has been widely employed to handle a variety of nonlinear systems, such as single-input and single-output (SISO) nonlinear systems, [1][2][3][4][5] multiple-input and multiple-output (MIMO) nonlinear systems, [6][7][8][9][10] and so on. Among them, MIMO nonlinear systems have attracted considerable attention on account of the complex interactions among sorts of inputs, outputs, and uncertain states.…”
In this article, the command filter based adaptive event-triggered control problem for multiple-input and multiple-output multiple time-delay stochastic nonlinear systems is considered. First, a state observer is constructed to estimate the unmeasured states of systems. Then, in the framework of backstepping design, the command filtered and event-triggered techniques are employed to avoid the problem of "explosion of complexity" and save the communication resources, respectively. Meanwhile, by utilizing the command filters, a novel variable separation method is constructed to address the algebraic-loop problem, which caused by the nonstrict-feedback item. The boundedness of the whole signals in systems can be remained, and the given desired trajectories can be followed by the system outputs. Finally, a numerical example is shown to demonstrate the effectiveness of the proposed control method.
“…Based on the excellent performance of adaptive control method, over the last decades, it has been widely employed to handle a variety of nonlinear systems, such as single-input and single-output (SISO) nonlinear systems, [1][2][3][4][5] multiple-input and multiple-output (MIMO) nonlinear systems, [6][7][8][9][10] and so on. Among them, MIMO nonlinear systems have attracted considerable attention on account of the complex interactions among sorts of inputs, outputs, and uncertain states.…”
In this article, the command filter based adaptive event-triggered control problem for multiple-input and multiple-output multiple time-delay stochastic nonlinear systems is considered. First, a state observer is constructed to estimate the unmeasured states of systems. Then, in the framework of backstepping design, the command filtered and event-triggered techniques are employed to avoid the problem of "explosion of complexity" and save the communication resources, respectively. Meanwhile, by utilizing the command filters, a novel variable separation method is constructed to address the algebraic-loop problem, which caused by the nonstrict-feedback item. The boundedness of the whole signals in systems can be remained, and the given desired trajectories can be followed by the system outputs. Finally, a numerical example is shown to demonstrate the effectiveness of the proposed control method.
“…Among them, the methods to deal with UFVs are mainly approximation control methods, that is, fuzzy approximation control and neural network approximation control. These methods successfully deal with the nonlinear UFVs problem 18‐24 . It is worth mentioning that in References 21 and 25, direct fuzzy control method and direct neural network control method are proposed to be applied to SISO and MIMO nonlinear systems, respectively.…”
In this article, a control algorithm is proposed to solve the global stabilization control problem of multiple input multiple output (MIMO) nonlinear systems with unknown function vectors (UFVs). Firstly, a Lemma dealing with UFVs is proposed. Then, combined with the backstepping method, the controller is designed such that all signals of the closed‐loop system are globally stable. Compared with the approximation method, the algorithm in this article solves the global stabilization control problem. Compared with the assumptions of UFVs, the algorithm in this article reduces the conservatism problem. At the same time, the algorithm in this article also solves the “explosion of terms” problem of backstepping. Compared with the methods to solve this problem: dynamic surface control (DSC) and direct fuzzy control, the algorithm in this article can make all signals of the closed‐loop system converge to the origin. Finally, the algorithm is applied to the model of spacecraft with modified Rodrigues parameters, and the simulation results show the effectiveness of this algorithm.
“…An adaptive backstepping output feedback control scheme for nonstrict‐feedback nonlinear systems was designed in Reference 48. The variable separation method was extended to MIMO nonstrict‐feedback systems by Du et al in Reference 49. The problem of including all states in stochastic nonstrict‐feedback systems was dealt with by Chen and Zhang using the properties of Gaussian function in Reference 50.…”
In this article, a new decentralized adaptive neural output feedback control scheme based on first‐order command filter is proposed for stochastic nonstrict‐feedback interconnected systems with prescribed performance, input quantization, actuator failures and unmodeled dynamics. The unknown smooth functions are eliminated by using the radial basis function neural networks. The immeasurable states in the system are estimated using the decentralized K‐filters, unmodeled dynamics is processed using dynamic signal, and the hyperbolic tangent function is applied to the construction of the prescribed performance function. The hysteretic quantizer and actuator failure are denoted in the form of linearization, and a smoothing function is introduced to compensate for the effects of quantization and bounded stuck faults. Based on the dynamic surface control (DSC) method and using the properties of Gaussian function to deal with stochastic nonstrict‐feedback interconnected systems, the first‐order command filter is used to replace the first‐order filter in the traditional DSC to eliminate the influence of filtering error on the systems, and an error compensation signal is introduced at the recursive each step of the design to construct a new error dynamic surface, which simplifies the derivation process and the design of the controller. Finally, the Lyapunov method is used to prove that all the signals in the whole controlled system are semiglobally uniformly ultimately bounded in probability and the tracking error is within the time‐varying constraint. The effectiveness of the proposed decentralized adaptive control method is verified by a numerical simulation and an example simulation.
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