Non‐iterative SOS‐based approach for guaranteed cost control design of polynomial systems with input saturation

Vafamand, Navid; Mardani, Mohammad Mehdi; Khayatian, Alireza; Shasadeghi, Mokhtar

doi:10.1049/iet-cta.2017.0096

Cited by 15 publications

(19 citation statements)

References 35 publications

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“…In attitude control, it is called eigenaxis, which is denoted by k, k � n 1 n 2 n 3 T ; the angel of rotation is represented by Φ. In this paper, modified Rodrigue parameters (MRPs) are used to represent the attitude of the satellite [19]. ese parameters can be applied to 360°rotations (about the characteristic axis).…”

Section: Large-angle Satellite Attitude Maneuver Modelmentioning

confidence: 99%

“…In literature [18], a novel SOSbased adaptive sliding mode control for polynomial systems consisting of uncertainties and input nonlinearities is proposed. Vafamand et al [19] propose an approach that uniquely considers the stability of input saturated polynomial systems together with the nonlinear control law. Another advantage of this approach over the recently guaranteed cost controller design methods is that it can solve the proposed conditions without relying on any iterative techniques.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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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.

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Section: Large-angle Satellite Attitude Maneuver Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2019

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“…One effective way for chattering reduction is replacing the discontinuous function ( ) sgn ⋅ with continuous functions [39,45]. Fuzzy logic controllers are widely utilized to stabilize the systems during recent years [28,27,38,30,11,40,7,17]. In this paper, the fuzzy mechanism fs u is employed and incorporated into Equation 20 Letting σ and fs u be the input and the output variables of the FAPISMC, respectively, the instinctive rules can be written as:…”

Section: Control Problemmentioning

confidence: 99%

Fuzzy-Logic-Based Adaptive Proportional-Integral Sliding Mode Control for Active Suspension Vehicle Systems: Kalman Filtering Approach

Zare¹,

Mardani²,

Vafamand

et al. 2019

ITC

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This paper deals with the problem of synthesizing a fuzzy-logic-based adaptive proportional-integral sliding mode control (FAPISMC) for active suspension systems based on Kalman filtering approach. To improve the performance of the controller and eliminate the effect of the chattering, the switching input is designed based on the fuzzy-logic-based approach with a minimum number of rules. In order to facilitate the stability analysis, the estimation of the state variables is used in designing the sliding surface platform. Furthermore, the gain of the controller is updated by an adaptive law to avoid any pre-knowledge of the disturbance amplitude. Subsequently, the proposed approach is more implementable in real-world processes. Finally, in order to illustrate the effectiveness and merits of the proposed approach, a suspension system is considered and simulated by the real-time hardware-in-the-loop (HiL). In this example, a quarter-car model of suspension systems is considered. Then, the obtained real-time results are compared with the linear quadratic regulator approach.

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“…The TS fuzzy models are described by fuzzy blending of some local subsystems (Song et al, 2016). Depending on the consequent part of the fuzzy IF-THEN rules, the TS fuzzy model is called a linear (Zhang et al, 2016), ane (Beyhan, 2017; Wang et al, 2016), bilinear (Chang and Hsu, 2016; Hamdy and Hamdan, 2015) and polynomial (Mardani et al, 2017b; Vafamand et al, 2017b; Zhou and Zeng, 2017) fuzzy model. The simplicity of the TS-based fuzzy control makes this method a very intresting research field (Khooban et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Non-fragile controller design of uncertain saturated polynomial fuzzy systems subjected to persistent bounded disturbance

Mardani¹,

Vafamand²,

Khooban

et al. 2018

Transactions of the Institute of Measurement and Control

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This paper investigates the problem of designing a non-fragile polynomial fuzzy controller for a class of polynomial fuzzy models subjected to persistent bounded disturbances and system uncertainty. The proposed controller is considered to satisfy the input saturation constraint. Furthermore, the resilient controller is affected by linear fractional uncertainties. The overall structure of the controller is obtained by the polynomial parallel distributed compensation concept. The sufficient conditions guarantee an L1 performance of the perturbed system and exponential stability of the non-perturbed system is achieved in terms of sum-of-squares decomposition conditions. Subsequently, the sum-of-squares-based conditions lead to minimization of the L1 performance such that the above-mentioned hard constraints on the control input and robustness of the closed-loop system against the system and controller uncertainties will be guaranteed. The controller gain matrices will be achieved by numerically solving the sum-of-squares-based conditions with the third-party MATLAB toolbox ‘SOSTOOLS’. Finally, extensive studies and hardware-in-the-loop simulations on a ball-and-beam system are presented, which illustrate the proposed controller can accurately and smoothly track the set point frequency. Furthermore, the proposed control approach is more robust over prior-art controllers for all the simulation scenarios.

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Non‐iterative SOS‐based approach for guaranteed cost control design of polynomial systems with input saturation

Cited by 15 publications

References 35 publications

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

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

Fuzzy-Logic-Based Adaptive Proportional-Integral Sliding Mode Control for Active Suspension Vehicle Systems: Kalman Filtering Approach

Non-fragile controller design of uncertain saturated polynomial fuzzy systems subjected to persistent bounded disturbance

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Non‐iterative SOS‐based approach for guaranteed cost control design of polynomial systems with input saturation

Cited by 15 publications

References 35 publications

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

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

Fuzzy-Logic-Based Adaptive Proportional-Integral Sliding Mode Control for Active Suspension Vehicle Systems: Kalman Filtering Approach

Non-fragile controller design of uncertain saturated polynomial fuzzy systems subjected to persistent bounded disturbance

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

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