ZD Method Based Nonlinear and Robust Control of Agitator Tank

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The optimal control of time-varying nonlinear systems is an important research topic and faces many difficulties and challenges, but also has substantial benefits. In this paper, the output optimization of scalar time-varying nonlinear (STVN) system and 2-dimension time-varying nonlinear (2DTVN) system is considered. The zeroing dynamics (ZD) method, which can solve the time-varying problems flexibly and effectively, has been extensively used in recent years. By introducing the ZD method, the time-varying optimal system state is attained, and the controller with the optimal output is designed. Meanwhile, the direct dynamics (DD) method is presented to further illustrate the superiority of the ZD method. Theoretical analyses prove that the ZD method has a faster convergence rate (that is, exponential convergence). In addition, the effectiveness and feasibility of the ZD method for solving the output optimization of STVN and 2DTVN systems are verified by numerical experiments, and further substantiated via output optimization of a two-wheeled mobile robot.

Section: Introductionmentioning

confidence: 99%

Output optimization of scalar and 2‐dimension time‐varying nonlinear systems using zeroing dynamics

Zhang

Shi

Yang

et al. 2020

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“…More specifically, the ZNN-L model is applied for solving the left Moore-Penrose inverse, while the ZNN-R model is applied for solving the right Moore-Penrose inverse. By using the design method proposed by Zhang et al [14,25,26], the following error function (t) is constructed for the ZNN-L model:…”

Section: Zhang Neural Networkmentioning

confidence: 99%

“…Different from the GNN, (t) is a matrix-formed function, and obviously, (t) becomes zero matrix when X(t) equals the exact value of the left Moore-Penrose inverse A + (i.e., (A T A) −1 A T ). By following the procedure of ZNN [14,25,26], the ZNN-L model is obtained as follows:…”

Section: Zhang Neural Networkmentioning

confidence: 99%

Improved recurrent neural networks for online solution of Moore‐Penrose inverse applied to redundant manipulator kinematic control

Tan

Chen

et al. 2018

In this paper, two novel neural networks (NNNs), namely NNN-L and NNN-R neural models, are proposed to online left and right Moore-Penrose inversion. As compared to GNN (gradient neural network) and the recently proposed ZNN (Zhang neural network) for the left or right Moore-Penrose inverse solving, our models are theoretically proven to possess superior global convergence performance. More importantly, the proposed NNN-R model is successfully applied to path-tracking control of a three-link planar robot manipulator. Illustrative examples well validate the theoretical analyses as well as demonstrate the feasibility of the proposed models, which are adopted and verified their effectiveness in kinematic control of a redundant manipulator, for real-time Moore-Penrose inverse solving.

“…As analyzed above, to minimize the performance index ‖Ċ‖ 2 2 ∕2, we can also define a vector-valued error function as e =̇∈ R n . Following Zhang et al's neural-dynamics method [38,45,55,56], we can seṫe = − e to make e converge to zero exponentially. Thus, we have C̈+Ċ̇+ Ċ= 0.…”

Section: Mke-type Zhang Equivalency (Mke-ze)mentioning

confidence: 99%

“…Following Zhang et al. 's neural‐dynamics method , we can set

\overset{bold-italice}{true} = - λ bold-italice

to make e converge to zero exponentially. Thus, we have

C \overset{bold-italicθ}{true} + Ċ \overset{bold-italicθ}{true} + λ C \overset{bold-italicθ}{true} = bold-italic 0

.…”

Section: Preliminaries and Formulationsmentioning

confidence: 99%

Analysis, Verification and Comparison on Feedback‐Aided MA Equivalence and Zhang Equivalency of Minimum‐Kinetic‐Energy Type for Kinematic Control of Redundant Robot Manipulators

Qiu

Zhang

Yang

2017

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By following and generalizing Ma et al.'s inspiring work and Zhang et al.'s inspiring work, this paper proposes and investigates three kinds of equivalent relationships with error-feedback information incorporated for the minimum-kinetic-energy (MKE) redundancy resolution. Specifically, these three equivalent relationships are divided into two big classes in terms of scheme formulations: one is termed MKE-type Ma equivalence (MKE-ME); the other is MKE-type Zhang equivalency (MKE-ZE), which can be further subdivided into MKE-ZE-I and MKE-ZE-II. Also, the equivalent analyses as well as the primary distinctions about three such equivalent relationships are presented. The simulation results based on a PUMA560 robot manipulator and a three-link planar robot manipulator not only verify the efficacy of the corresponding velocity-level and acceleration-level schemes of MKE-ME, MKE-ZE-I and MKE-ZE-II, but also substantiate their reasonableness and effectiveness of these three equivalent relationships. More importantly, the comparative numerical results show their respective characteristics and advantages for kinematic control of redundant robot manipulators.