Control of periodic sampling systems subject to actuator saturation

Self Cite

Summary In this paper, overall convergence rate is considered for a delta operator system with actuator saturation. A saturation feedback law is presented for the delta operator system to obtain a desired overall convergence rate. Some properties on the overall convergence rate are revealed for time‐optimal actuator saturation delta operator systems. Limitations on the overall convergence rate are also investigated by proposed methods. An optimization problem is solved through a linear matrix inequality method to obtain the domain of attraction and overall convergence rate. Two numerical examples are provided to demonstrate the effectiveness of the proposed techniques. Copyright © 2017 John Wiley & Sons, Ltd.

Section: F /supporting

confidence: 69%

Section: Optimization Problemmentioning

confidence: 89%

“…An open‐loop delta operator system with actuator saturation is given as

δ x (t_{k}) = A x (t_{k}) + B u (t_{k}), ∥ u (t_{k}) ∥ ⩽ 1,

where x ( t k )∈ R n is the plant state, u ( t k )∈ R m is the control input, and ( A , B ) is stabilizable. Under the following saturation feedback law

u (t_{k}) = sat (F x (t_{k})),

where F ∈ R m × n is a feedback gain matrix, a closed‐loop delta operator system with actuator saturation is obtained as

δ x (t_{k}) = A x (t_{k}) + B sat (F x (t_{k})) .

As in , denote the i th row of F as f i and define the linear region of saturation as

L (F) = \{x (t_{k}) \in R^{n} : | f_{i} x (t_{k}) | ⩽ 1, i = 1, 2, \dots, m\} .

Denote a Lyapunov function of system as V ( x ( t k )) = x T ( t k ) P x ( t k ) and a level set associated with V ( x ( t k )) as

normalΩ (P, ρ) = \{x (t_{k}) \in R^{n} : x^{T} (t_{k}) P x (t_{k}) ⩽ ρ\},

wh...…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

See 1 more Smart Citation

Overall convergence rate of delta operator systems subject to actuator saturation

Yang

Xia

Geng

2017

Self Cite

“…An LMI‐based framework is proposed to synthesize the output feedback controller for Lur'e nonlinear systems and Takagi‐Sugeno systems based on Lyapunov theory and the modified sector condition. The controller design problem for switched and sampling systems was investigated in the works of Ma et al and Yang et al, respectively. The technique in the work of Hussain and Rehan proposes AWC synthesis for constrained nonlinear time‐delay systems by employing a delay‐range‐dependent methodology.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous design of AWC and nonlinear controller for uncertain nonlinear systems under input saturation

Hussain

Rehan

Ahn

et al. 2019

Summary This article addresses a novel technique for the simultaneous design of a robust nonlinear controller and static anti‐windup compensator (AWC) for uncertain nonlinear systems under actuator saturation and exogenous L2 bounded input. The system is presumed to have locally Lipschitz nonlinearities, time‐varying uncertainties (appearing both in the linear as well as nonlinear dynamics and both in the state in addition to the output equations), and external norm‐bounded inputs both in the state and the output equations. Several bilinear matrix inequality–based conditions are derived to simultaneously design the robust nonlinear controller and AWC gains for uncertain nonlinear systems by employing the Lyapunov functional, reformulated Lipschitz property, uncertainty bounds, linear parameter‐varying approach, modified local and global sector conditions, iterative linear matrix inequality algorithm, convex optimization procedure, and L2 gain minimization. The proposed multiobjective AWC‐based dynamic robust nonlinear controller guarantees the mitigation of saturation effects, robustness against time‐varying parametric norm‐bounded uncertainties, the asymptotic stability of the closed‐loop nonlinear system under zero external disturbances, and the attenuation of disturbance effects under nonzero external disturbances. The effectiveness of the proposed AWC‐based dynamic robust nonlinear controller synthesis scheme is illustrated by simulation examples.

“…Nowadays, several main approaches have been used to drive the aforementioned problem of the sampled-data control system. The input delay approach is provided in other works [12][13][14][15][16] and is applied to analyze the sampled-data control system via Lyapunov-Krasovskii functionals. The other one is the impulsive model approach, 17 where the sampled-data control system is treated as an impulsive model.…”

Section: Introductionmentioning

confidence: 99%

H_∞ control of memristive neural networks with aperiodic sampling and actuator saturation

Wang

Jiang

et al. 2018

The H ∞ control problem for memristive neural networks with aperiodic sampling and actuator saturation is considered in this paper. A novel approach that is combined with the discrete-time Lyapunov theorem and sampled-data system is proposed to cope with the aperiodic sampling problem. On the basis of such method and choosing a polyhedral set, sufficient conditions to determine the ellipsoidal region of asymptotic stability and exponential stability for the estimation error system are obtained through a saturating sampled-data control. Furthermore, H ∞ performance index of memristive neural networks with disturbance is also analyzed, whereas the observer and controller gains are calculated from stability conditions of linear matrix inequalities. Finally, the effectiveness of the theoretical results is illustrated through the numerical examples.