Semi‐global containment of discrete‐time high‐order multi‐agent systems with input saturation via intermittent control

Collaborative Control of Multimotor Systems for Fixed‐Time Optimisation Based on Virtual Main‐Axis Speed Compensation Structure

“…e synchronous control algorithm mainly includes multiagent consensus [18,19] and sliding mode variable structure control [20,21] algorithms due to different design ideas of multimotor synchronous control. Xu and Li evaluated the multiagent consensus algorithm and proposed a semiglobal consensus control protocol based on low-gain state feedback with consideration for the intermittent semiglobal consensus problem of high-order multiagent system under input saturation [22]. Wang et al analysed the structure of distributed observer of continuous linear timeinvariant system and reduced the dependence of the system on topology structure information using adaptive rule [23].…”

Global Existence and Extinction Singularity for a Fast Diffusive Polytropic Filtration Equation with Variable Coefficient

“…Problem (1) can be used to describe the compressible fluid flows in a homogeneous isotropic rigid porous medium with u(x, t) being the density of the fluid and α(x) � |x| − s acting as the volumetric moisture content. On the other hand parabolic models like (1), together with differential equation models, stochastic differential equations, and linear systems, are regarded as the powerful tools to solve lots of problems from control engineering, image processing, and other areas (see [4][5][6][7][8]). Because of the degeneracy and the singularity, problem (1) might not have classical solution in general, and hence, we introduce definition of the weak solution as follows.…”

“…(54)If q � m(p − 1). From(8), one knows that E(u) is nonincreasing with respect to t. en, for any t ≥ 0, one hasM ′ (t) ≥ − pE u 0 . (55)Integrating, one obtainsM(t) ≥ M(0) − pE u 0 t, for t ≥ 0,(56)which tells us that M(t) > 0 since M(0) > 0 and E(u 0 ) ≤ 0; that is, the solution u(x, t) of problem (1) does not possess extinction phenomenon.…”

The Extension of the GVW Algorithm to Valuation Domains

“…e theory of Gröbner has been widely applied in numerous fields such as engineering, signal processing, neuroscience, coding theory, complexity, and control of networked dynamical systems and so on. For example, in the theory of symbolic dynamic systems, the problems of determining whether there is a shift equivalence of lag from one nonnegative matrix to another can be transferred into solving large-scale equations, while the latter can be solved by the Gröbner basis theory [2][3][4][5][6][7][8][9][10][11][12][13].…”