Adaptive tracking control for a class of stochastic non‐linear systems with input saturation constraint using multi‐dimensional Taylor network

Adaptive multi‐dimensional Taylor network funnel control of a class of nonlinear systems with asymmetric input saturation

“…In this paper, the design of the controller makes full use of the approximating to nonlinear functions capability of MTN. The theory of MTN has been introduced in detail in our recent work, 25,30,42 only a useful Lemma is included here.Lemma (see Reference 30) : Suppose that φ (ℏ 1 , ⋯, ℏ n ) : R n → R is a function defined on a closed interval Ω ⊂ R n , for any given constant τ > 0, there exists a MTN with approximation error γ ( ℏ ) satisfies with ℏ = [ℏ 1 , ⋯, ℏ n ] T , is the ideal constant weights, and .Remark MTN is a feedforward network, including three layers, that is, input layer, middle layer and output layer. The middle layer is constructed by polynomials formed by input, and its main function is information processing.…”

“…More recently, MTN‐based control method also has been generalized to nonlinear systems with input constraints, for example, by employing MTN, authors in Reference 41 studied the problem of dynamic regulation problem for nonlinear systems with actuator saturation and time varying delay. Authors in Reference 42 developed a MTN‐based control scheme for a class of stochastic non‐linear systems with input saturation constraint. For a class of nonlinear switched systems with input sector nonlinearity, authors in Reference 43 proposed an adaptive MTN tracking control scheme.…”

Multi-dimensional Taylor network-based adaptive control for nonlinear systems with unknown parameters

“…In addition, actuators are frequently involved with several restrictions. such as input and output constrained, and many works have been focused on nonlinear systems with input and output constrained (Han, 2020; Sun et al, 2019).…”

Adaptive tracking control for a class of stochastic non‐linear systems with input delay: a novel approach based on multi‐dimensional Taylor network

“…For a class of uncertain stochastic non‐linear systems, Han and Yan [32] developed an MTN‐based control scheme. In addition, based on MTN, by using the adaptive control along with the backstepping technique, the problems of tracking control were addressed in [33–35] for several classes of stochastic non‐linear systems. However, although many successful control methods have been proposed for stochastic non‐linear systems, significant problems remain to be resolved.…”

“…In particular, the input delay and stochastic non‐linear systems are addressed in a unified framework using the MTN‐based control approach for the first time, and a novel MTN‐based adaptive control strategy is proposed. Besides, the methods proposed in [31, 32] cannot be applied to deal with the tracking control problem of stochastic non‐linear systems considered in this paper. (ii) Note that the MTN‐based control results presented in [31–35], without considering the existence of input constraints, are limited to the stochastic non‐linear systems. These control methods cannot be used directly to control of stochastic non‐linear systems with input delay. (iii) Firstly, the method of handling the input delay in [41] for deterministic systems is extended to a stochastic setting.…”