Application of Sum of Squares Method in Nonlinear H_∞ Control for Satellite Attitude Maneuvers

Abstract

e Hamilton-Jacobi-Issacs (HJI) inequality is the most basic relation in nonlinear H ∞ design, to which no e ective analytical solution is currently available. e sum of squares (SOS) method can numerically solve nonlinear problems that are not easy to solve analytically, but it still cannot solve HJI inequalities directly. In this paper, an HJI inequality suitable for SOS is rstly derived to solve the problem of nonconvex optimization. en, the problems of SOS in nonlinear H ∞ design are analyzed in detail. Finally, a two-step iterative design method for solving nonlinear H ∞ control is presented. e rst step is to design an adjustable nonlinear state feedback of the gain array of the system using SOS. e second step is to solve the L 2 gain of the system; the optimization problem is solved by a graphical analytical method. In the iterative design, a diagonally dominant design idea is proposed to reduce the numerical error of SOS. e nonlinear H ∞ control design of a polynomial system for large satellite attitude maneuvers is taken as our example. Simulation results show that the SOS method is comparable to the LMI method used for linear systems, and it is expected to nd a broad range of applications in the analysis and design of nonlinear systems.

Towards Precision Fertilization: Multi-Strategy Grey Wolf Optimizer Based Model Evaluation and Yield Estimation

“…The performance of the proposed GWO-based method is not limited to yield estimation, and it can also be tested based on other real-world applications, such as energy storage planning and scheduling [147], service ecosystem [148,149], image editing [150][151][152], epidemic prevention and control [153,154], social recommendation and QoS-aware service composition [155][156][157], active surveillance [158], large scale network analysis [159], spatial analysis [160], crop evapotranspiration prediction [161], control engineering [162,163], pedestrian dead reckoning [164] and evaluation of human lower limb motions [165]. The SLEGWO proposed is based on the improved GWO multi-strategy optimization method and it is applied to solve the fertilizer effect function, which is a new idea based on the traditional precision fertilizer application operation technology.…”

Some new logarithmic aggregation operators and their application to group decision making problem based on t-norm and t-conorm

“…Gou (2016) established the idea of exponential operational laws and develop several operators using IFS and IFNs. Meng et al (2019), Yang et al (2021), Li et al (2021), Ding et al (2020), Kordestani et al (2021), He et al (2020), Zhang et al (2021), Zhao et al (2020), Sun et al (2021), Sun et al (2015) introduced many new methods related to fuzzy set theory and intuitionistic fuzzy set theory. After the positive applications of exponential operational laws (EOL) it was necessary to be developing the idea of logarithmic operational laws (LOL).…”

Analytical Solutions to Two-Dimensional Nonlinear Telegraph Equations Using the Conformable Triple Laplace Transform Iterative Method

“…Therefore, using the described method one can obtain the exact solution to nonlinear partial fractional derivatives with less computational size. Moreover, the proposed approach allows the user with analytical approximation, and it is applied directly to the problems without requiring any discretization, linearization, or perturbation parameters like Adomian polynomials and SOS polynomials ( [42,47] see the references therein). This is the main advantage of the proposed method CFTLTIM over the other existing approaches in the literature.…”