Abstract
The problem of finite time adaptive control for stochastic nonlinear system is studied in this paper, where the system has a non-strict feedback structure. Under the sense of finite time stability, the authors propose a new neural network (NN) adaptive controller for stochastic nonlinear systems by backstepping technique. To overcome the difficulties that arise from the non-strict feedback structure of system, a key lemma is introduced. All the signals of the closed-loop systems are bounded in finite time in probability under the adaptive controller. At the same time good tracking performance can be achieved. A simulation example further shows the effectiveness of the control strategy in this thesis.
Highlights
In recent decades, many neural networks(NNs)/ fuzzy logic systems(FLSs) adaptive control strategies have been successfully applied to nonlinear systems with triangle structures, see [1]–[9]
By combining NNs/FLSs approximators with backstepping technique, many important adaptive control strategies are presented for single-input and singleoutput (SISO) strict-feedback nonlinear systems, see [1]–[6], [10]–[15]
The problems of adaptive NNs/FLSs control for multi-input and multi-output (MIMO) nonlinear systems have been studied in [6], [16], respectively, where the systems are in form of strict feedback
Summary
Many neural networks(NNs)/ fuzzy logic systems(FLSs) adaptive control strategies have been successfully applied to nonlinear systems with triangle structures, see [1]–[9]. When the system function is unknown, Sun et al [42] proposed an approximation-based adaptive control strategy These literatures did not study the finite-time control problem of stochastic systems but deterministic systems. According to what we know that few results have been achieved about the problem of finite time state output control for non-strict feedback stochastic systems. Y. Sun et al.: Finite-Time Adaptive Control for Non-Strict Feedback Stochastic Nonlinear Systems. Based on the aforementioned discussion, this thesis is devoted to proposed the finite time tracking control method for non-strict feedback stochastic nonlinear systems. Compared with existing results on the finite time control problem, the paper will study the finite time tracking control problem of stochastic nonlinear systems with non-strict feedback form.
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