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Quadratic minimization (QM) has been investigated for many years, which is generally supposed to be time-invariant and at the same level. Nevertheless, the QM which arises in practical applications, is usually time-varying and may be at the different levels. Different from general QM, a novel different-level time-varying QM (DLTVQM) is proposed and investigated in this paper. Firstly, the DLTVQM solving...
Discrete time-varying problems are frequently encountered in mathematics and engineering fields, such as numerical analysis, signal processing and computer computing. However, conventional algorithms mainly solve time-invariant problems. Employed for discrete time-varying problems solving, conventional algorithms may generate quite large and unacceptable lagging errors. In this paper, discrete time-varying...
In this paper, to achieve the fault-tolerant capability for redundant manipulators, a dimension-reduction method is presented and investigated at the joint-acceleration level. By incorporating such a dimension-reduction method and the limits of joint angle, joint velocity as well as joint acceleration (i.e., the physical constraints on joints), an acceleration fault-tolerant scheme for redundant manipulator...
In this paper, the displacement control and angle control of helicopter sling load system are investigated respectively by using zeroing-dynamics (ZD) method and zeroing-gradient (ZG) method, through which we yield corresponding ZD controller and ZG controller. More importantly, the recently new formula termed Taylor-Zhang discretization (TZD) formula is derived and applied to the discrete control...
Ordinary differential equations (ODEs) are commonly used in physical system and automation researches, describing the relationship among variables. Hence there are practical significances to discuss and to research the solutions of ODEs. The initial value problem (IVP) is one of the important parts, and we usually use traditional methods, e.g. Euler method, to obtain the solutions. In this paper,...
In this paper, a new Zhang finite difference (ZFD) formula with higher accuracy, termed 4-node g-square finite difference (4NgSFD), is presented and applied to solving ordinary differential equations (ODEs). Such a method is thus considered as ZFD 4NgSFD method. For comparison, the conventional Euler method is also presented. In addition, numerical experiments are carried out, of which the results...
In this paper, we propose and investigate a new Euler-precision 3-node g-proportional finite difference formula [also named Zhang finite difference (ZFD) formula 3NgPFD_G], which achieves an error pattern of O(g), where g denotes the sampling gap. Moreover, the proposed formula is extended to future minimization (FM). Specifically, the ZFD formula 3NffPFD_G and its extension to discretize continuous-time...
To avoid Jacobian inversion existing in the conventional pseudo inverse solution effectively and to obtain the solution of minimum two-norm tracking error to the inverse kinematics of the two-wheeled mobile robot system (TWMRS), an inverse-free solution using gradient dynamics (GD) method is presented and investigated in this paper. As we probably know, the inversion of Jacobian matrix is required...
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