Fault diagnosis for semilinear distributed parameter systems with actuator/sensor based on iterative learning control

The problem of adaptive consensus is addressed for a class of second‐order nonlinear multi‐agent systems with aperiodically time‐varying parameters and unknown control directions. Firstly, a new adaptive control approach, so‐called congelation of variables method, is adopted to deal with aperiodically time‐varying parameters which are fast‐varying in an unknown compact set with only their radii known a priori. Secondly, a novel Nussbaum‐type function approach is utilized to address the problem of unknown control directions. It is noteworthy that the control directions investigated in this paper are allowed to be completely unknown and nonidentical, whereas the unknown control directions in the most existing works are assumed to be identical. Thirdly, the unknown nonlinear function in each follower's dynamics is approximated by radial basis function neural network approximation technique. The approximation error, external disturbance in the follower's dynamics, as well as the leader's unknown acceleration dynamics are suppressed as an adaptive robust term, which can alleviate the online computational burden. Then, by designing time‐varying control gains updated adaptively with only local information, a fully distributed adaptive consensus control scheme is designed to guarantee that the multi‐agent systems achieve consensus asymptotically in the presence of unknown aperiodically time‐varying parameters, unknown nonidentical control directions, unknown nonlinearities, and external disturbances. Two simulation examples are provided to validate the effectiveness of the proposed consensus protocol.

Section: Discussionmentioning

confidence: 99%

Adaptive consensus of second‐order nonlinear MASs with aperiodically time‐varying parameters and unknown control directions

Yi,

2023

“…For some large 𝓁, the eigenvalues of operator  + 𝓁 can not be ensured to fall within the area | arg(spec( + 𝓁))| ≥ 𝛼𝜋 2 , which indicates that (1)-( 3) with U(t) = 0 isn't M-L stable by Matignon [33]. Thus, the following main objective is to design an effective boundary controller U(t) to M-L stabilize system (1)- (3). In other words, by designing a suitable controller U(t) such that the closed-loop system (1)-( 3) has a unique solution v(•, t), and ||v(…”

Section: Lemma 23 ([31]) Suppose That V(t) Satisfyingmentioning

confidence: 99%

“…Therefore, the study of DPSs has aroused widespread concern. Since reaction-diffusion is one of the most common phenomena in nature, the control design of reaction-diffusion systems described by parabolic PDEs has produced rich results [3][4][5][6] and so on. However, the modeling of these systems is based on the fact that the diffusion of the system takes place in a homogeneous medium and follows Fick's law.…”

Section: Introductionmentioning

confidence: 99%

“…In that the characteristics of the spatial distribution of the DPSs, the control design includes boundary control and intra-domain control (point and distributed) [18], which makes the control problem of DPSs physically attractive and mathematically challenging. In contrast to the distributed intra-domain control strategy [3,19], boundary control is generally regarded as a simple and easy-to-implement control scheme in industrial processes, especially the introduction of the backstepping method as a systematical approach for control of DPSs, which results that boundary control of linear DPSs has been a well-established subject; see Smyshlyaev and Krstic [20] and Tang and Xie [21] and the reference therein. For instance, in Krstic and Smyshlyaev [4,20], by utilizing the backstepping approach, the boundary stabilization of a class of linear DPSs has been solved and in Tang and Xie [21], the same method is used to solve the stabilization problem of a class of coupled systems.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Boundary Mittag–Leffler stabilization of a class of time fractional‐order nonlinear reaction–diffusion systems

Zhao

Lei

et al. 2023

Boundary control design of a class of time fractional‐order nonlinear reaction–diffusion systems (FNRDSs) is considered in three cases: domain‐averaged measurement, collocated boundary point measurement, and anti‐collocated boundary point measurement. For domain‐averaged measurement and collocated boundary point measurement, boundary controllers are designed directly based on the measurements, respectively. For the anti‐collocated boundary point measurement, to overcome the difficulty that the measurement cannot be used for the controller design directly, an observer is constructed firstly, and then, an observer‐based boundary controller is designed. Sufficient conditions for Mittag–Leffler (M‐L) stability of the closed‐loop system are all provided in terms of linear matrix inequalities (LMIs). Numerical simulation results are provided to illustrate the feasibility and effectiveness of the proposed methods.

“…However, many systems considered are governed by ordinary differential systems (ODSs) [9][10][11][12] or parabolic distributed parameter systems (DPSs) [13][14][15][16]. Results on ILC for hyperbolic DPSs are still limited; hence, there are merely a few related works.…”

Section: Introductionmentioning

confidence: 99%

Iterative learning control for hyperbolic distributed parameter systems based on sensor–actuator networks

Zhang

Cui

Lou

et al. 2022

This paper proposes two kinds of iterative learning control (ILC) schemes for a class of the distributed parameter systems based on sensor–actuator networks which can be described by hyperbolic partial differential equations. A D‐type ILC algorithm is first considered and the convergent condition of the output error is obtained via the contraction mapping methodology. Then, the PD‐type ILC algorithm is considered in this hyperbolic distributed parameter systems based on sensor–actuator networks. Finally, a cable equation with air and structural damping is given to illustrate the effectiveness of the proposed methods.