On sensor quantization in linear control systems: Krasovskii solutions meet semidefinite programming

2019 ◽  
Vol 37 (2) ◽  
pp. 395-417 ◽  
Author(s):  
Francesco Ferrante ◽  
Frédéric Gouaisbaut ◽  
Sophie Tarbouriech
Keyword(s):  
Control Systems ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Loop System ◽  
State Feedback Control ◽  
Linear Control Systems ◽  
Compact Set ◽  
Closed Loop System ◽  
Feedback Control Systems ◽  
Linear State

Abstract Stability and stabilization for linear state feedback control systems in the presence of sensor quantization are studied. As the closed-loop system is described by a discontinuous right-hand side differential equation, Krasovskii solutions (to the closed-loop system) are considered. Sufficient conditions in the form of matrix inequalities are proposed to characterize uniform global asymptotic stability of a compact set containing the origin. Such conditions are shown to be always feasible whenever the quantization-free closed-loop system is asymptotically stable. Building on the obtained conditions, computationally affordable algorithms for the solution to the considered problems are illustrated. The effectiveness of the proposed methodology is shown in three examples.

scholarly journals Decentralized design of interconnected H∞ feedback control systems with quantized signals

2013 ◽  
Vol 23 (2) ◽  
pp. 317-325 ◽  
Author(s):  
Guisheng Zhai ◽  
Ning Chen ◽  
Weihua Gui
Keyword(s):  
Feedback Control ◽  
Control Systems ◽  
Closed Loop ◽  
Loop System ◽  
Disturbance Attenuation ◽  
Closed Loop System ◽  
Attenuation Level ◽  
Feedback Control Systems ◽  
Decentralized Design ◽  
Disturbance Attenuation Level

In this paper, we consider the design of interconnected H∞ feedback control systems with quantized signals. We assume that a decentralized dynamic output feedback has been designed for an interconnected continuous-time LTI system so that the closed-loop system is stable and a desired H∞ disturbance attenuation level is achieved, and that the subsystem measurement outputs are quantized before they are passed to the local controllers. We propose a local-output-dependent strategy for updating the parameters of the quantizers, so that the overall closed-loop system is asymptotically stable and achieves the same H∞ disturbance attenuation level. Both the pre-designed controllers and the parameters of the quantizers are constructed in a decentralized manner, depending on local measurement outputs.

scholarly journals Fault-Tolerant Control for Networked Control Systems with Limited Information in Case of Actuator Fault

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Wang Yan-feng ◽  
Wang Pei-liang ◽  
Li Zu-xin ◽  
Chen Hui-ying
Keyword(s):  
Control Systems ◽  
Closed Loop ◽  
Networked Control Systems ◽  
Fault Tolerant ◽  
Transition Probabilities ◽  
Sufficient Conditions ◽  
Loop System ◽  
Networked Control ◽  
Actuator Fault ◽  
Closed Loop System

This paper is concerned with the problem of designing a fault-tolerant controller for uncertain discrete-time networked control systems against actuator possible fault. The step difference between the running stepkand the time stamp of the used plant state is modeled as a finite state Markov chain of which the transition probabilities matrix information is limited. By introducing actuator fault indicator matrix, the closed-loop system model is obtained by means of state augmentation technique. The sufficient conditions on the stochastic stability of the closed-loop system are given and the fault-tolerant controller is designed by solving a linear matrix inequality. A numerical example is presented to illustrate the effectiveness of the proposed method.

Finite-time dissipative control for networked control systems with hybrid-triggered scheme

2020 ◽  
pp. 014233122094650
Author(s):  
Qian Zhang ◽  
Huaicheng Yan ◽  
Shiming Chen ◽  
Xisheng Zhan ◽  
Xiaowei Jiang
Keyword(s):  
Control Systems ◽  
Finite Time ◽  
Closed Loop ◽  
Controller Design ◽  
Networked Control Systems ◽  
Sufficient Conditions ◽  
Networked Control ◽  
Closed Loop System ◽  
Network Resources ◽  
Dissipative Control

This paper is concerned with the problem of finite-time dissipative control for networked control systems by hybrid triggered scheme. In order to save network resources, a hybrid triggered scheme is proposed, which consists of time-triggered scheme and event-triggered scheme simultaneously. Firstly, sufficient conditions are derived to guarantee that the closed-loop system is finite-time bounded (FTBD) and [Formula: see text] dissipative. Secondly, the corresponding controller design approach is presented based on the derived conditions. Finally, a numerical example is presented to show the effectiveness of the proposed approach.

P-D Feedback for Decoupling and Pole Assignment of Singular Systems

1998 ◽  
Vol 120 (3) ◽  
pp. 378-388 ◽  
Author(s):  
F. N. Koumboulis ◽  
B. G. Mertzios
Keyword(s):  
Closed Loop ◽  
Singular Systems ◽  
Sufficient Conditions ◽  
Pole Assignment ◽  
Loop System ◽  
Necessary And Sufficient Conditions ◽  
Algebraic Equations ◽  
Input Output ◽  
Closed Loop System ◽  
Necessary And Sufficient

The problem of reducing a multi input-multi output system to many single input-single output systems, namely the problem of input-output decoupling, is studied for the case of singular systems i.e., for systems described by dynamic and algebraic equations. The problem of input-output decoupling with simultaneous arbitrary pole assignment, via proportional plus derivative (P-D) state feedback, is extensively solved. The general explicit expression of all P-D controllers solving the decoupling problem is determined. The general form of the diagonal elements of the decoupled closed-loop system is proven to be in a form having a fixed numerator polynomial and an arbitrary denominator polynomial. The necessary and sufficient conditions for the solvability of the problem of decoupling with simultaneous asymptotic stabilizability or arbitrary pole assignment are established. Furthermore, the necessary and sufficient conditions for decoupling with simultaneous impulse elimination, as well as the necessary and sufficient conditions for decoupling with arbitrary assignment of the finite and infinite poles of the closed-loop system, are established.

Event-triggered Hꝏ control for NCS with time-delay and packet losses

2019 ◽  
Vol 37 (3) ◽  
pp. 918-934
Author(s):  
Jing Bai ◽  
Ying Wang ◽  
Li-Ying Zhao
Keyword(s):  
Time Delay ◽  
Closed Loop ◽  
Discrete Event ◽  
Sufficient Conditions ◽  
Loop System ◽  
Linear Matrix ◽  
Time Varying ◽  
Closed Loop System ◽  
Packet Losses ◽  
Event Triggered

Abstract This paper is concerned with the discrete event-triggered dynamic output-feedback ${H}_{\infty }$ control problem for the uncertain networked control system, where the time-varying sampling, network-induced delay and packet losses are taken into account simultaneously. The random packet losses are described via the Bernoulli distribution. And then, the closed-loop system is modelled as an augmented time-delay system with interval time-varying delay. By using the Lyapunov stability theory and the augmented state space method, the sufficient conditions for the asymptotic stability of the closed-loop system are proposed in the form of linear matrix inequalities. At the same time, the design method of the ${H}_{\infty }$ controller is created. Finally, a numerical example is employed to illustrate the effectiveness of the proposed method.

Output Feedback Algorithm for Nonlinear Systems with Compensation of Bounded Disturbances and Measurement Noises

2019 ◽  
Vol 20 (1) ◽  
pp. 3-15 ◽  
Author(s):  
I. B. Furtat ◽  
P. A. Gushchin ◽  
A. A. Peregudin
Keyword(s):  
Output Feedback ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Loop System ◽  
Partial Recovery ◽  
Closed Loop System ◽  
External Disturbances ◽  
Control Schemes ◽  
Measurement Noises ◽  
Feedback Algorithm

The output feedback algorithm for dynamic plants with compensation of parametric uncertainty, external disturbances and measurement noises is synthesized. The plants are described by a nonlinear system of differential equations with vector input and output signals. Unlike most existing control schemes in this paper the dimensions of the measurement interference and the output signal are equal, the sources of the signals of disturbances and disturbances are different, parametric and external disturbances can be present in any equation of the plant model. For simultaneous compensation of disturbances and measurement noises it is proposed to consider two channels. On the first channel a part of the measurement noises will be estimated which will allow partial recovery the information about the plant noisy output. On the second channel the disturbances will be compensated. Thus, at least two independent measurement channels are required for simultaneous compensation of disturbances and measurement noises. Sufficient conditions for calculating the parameters of the algorithm in the form of solvability of the linear matrix inequality are obtained. It is shown that the equation of a closed-loop system obtained on the basis of the proposed algorithm depends on the disturbances and the smallest component of the measurement noise. However, if the smallest component cannot be identified a priory, the results of the transients depend on the component of the noise that will be selected in the synthesis of the control system. Thus, unlike most existing control schemes, where the equation of a closed-loop system depends on disturbance and noise, the resulting algorithm provides better transients, because they do not depend on the entire noise vector, but only on its smallest (one) component. The simulations for a third-order nonlinear plant and the synchronization of an electrical generator connected to the power grid are presented. Numerical examples illustrate the effectiveness of the proposed scheme and the robustness with respect to random components in the noises and disturbances.

Robust nonfragile observer-based H2/H∞ controller

2016 ◽  
Vol 24 (4) ◽  
pp. 722-738 ◽  
Author(s):  
Atta Oveisi ◽  
Tamara Nestorović
Keyword(s):  
Control System ◽  
Real Time ◽  
Closed Loop ◽  
Linear Time ◽  
Sufficient Conditions ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Real Time System ◽  
Structured Uncertainty

A robust nonfragile observer-based controller for a linear time-invariant system with structured uncertainty is introduced. The [Formula: see text] robust stability of the closed-loop system is guaranteed by use of the Lyapunov theorem in the presence of undesirable disturbance. For the sake of addressing the fragility problem, independent sets of time-dependent gain-uncertainties are assumed to be existing for the controller and the observer elements. In order to satisfy the arbitrary H2-normed constraints for the control system and to enable automatic determination of the optimal [Formula: see text] bound of the performance functions in disturbance rejection control, additional necessary and sufficient conditions are presented in a linear matrix equality/inequality framework. The [Formula: see text] observer-based controller is then transformed into an optimization problem of coupled set of linear matrix equalities/inequality that can be solved iteratively by use of numerical software such as Scilab. Finally, concerning the evaluation of the performance of the controller, the control system is implemented in real time on a mechanical system, aiming at vibration suppression. The plant under study is a multi-input single-output clamped-free piezo-laminated smart beam. The nominal mathematical reduced-order model of the beam with piezo-actuators is used to design the proposed controller and then the control system is implemented experimentally on the full-order real-time system. The results show that the closed-loop system has a robust performance in rejecting the disturbance in the presence of the structured uncertainty and in the presence of the unmodeled dynamics.

On Passive Implementation of Feedback Control Systems

1989 ◽  
Vol 111 (2) ◽  
pp. 339-342
Author(s):  
R. Shoureshi
Keyword(s):  
Feedback Control ◽  
Control Systems ◽  
State Feedback ◽  
Closed Loop ◽  
State Feedback Control ◽  
Closed Loop Control ◽  
Linear Quadratic ◽  
Loop Control ◽  
Feedback Control Systems ◽  
Linear Quadratic Regulators

Closed-loop control systems, especially linear quadratic regulators (LQR), require feedbacks of all states. This requirement may not be feasible for those systems which have limitations due to geometry, power, required sensors, size, and cost. To overcome such requirements a passive method for implementation of state feedback control systems is presented.

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