scholarly journals LMI-Based Analysis and Stabilization of Nonlinear Descriptors with Multiple Delays via Delayed Nonlinear Controller Schemes

2021 ◽  
Vol 2021 ◽  
pp. 1-19
Author(s):  
Javier Adrián Romero-Vega ◽  
Raúl Villafuerte-Segura ◽  
Víctor Estrada-Manzo
Keyword(s):  
Closed Loop ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Multiple Delays ◽  
Control Input ◽  
Nonlinear Controller ◽  
Closed Loop System ◽  
Exponential Estimates ◽  
Nonlinear Controllers ◽  
The Given

This paper presents a convex approach for nonlinear descriptor systems with multiple delays; it allows designing delayed nonlinear controllers such that the closed-loop system holds exponential estimates for convergence. The proposal takes advantage of an equivalent convex representation of the given descriptor model together with Lyapunov-Krasovskii functionals; thus, the conditions are in the form of linear matrix inequalities, which can be efficiently solved by commercially available software. To avoid possible saturation in the actuators, conditions for bounding the control input are also given. Numerical and academic examples illustrate the performance of the proposal.

scholarly journals Design of delay observer-based controllers for uncertain time-lag systems

1999 ◽  
Vol 5 (2) ◽  
pp. 121-137 ◽  
Author(s):  
Magdi S. Mahmoud ◽  
Mohamed Zribi
Keyword(s):  
Uncertain Systems ◽  
Closed Loop ◽  
Time Lag ◽  
Linear Matrix ◽  
Time Lags ◽  
Matrix Inequalities ◽  
Closed Loop System ◽  
Delayed Measurements ◽  
Uncertain Time ◽  
Theoretical Developments

In this paper, the problem of designing observers and observer-based controllers for a class of uncertain systems with input and state time lags is considered. We construct delay-type observers in which both the instantaneous as well as the delayed measurements are utilized. Using feedback control based on the reconstructed state, the behavior of the closed-loop system is investigated. It is established that the uncertain time-lag system with delay observer-based control is asymptotically stable. Expressions for the gain matrices are given based on two linear-matrix inequalities. A numerical example is given to illustrate the theoretical developments.

DETERMINING ROBUST PARAMETERS IN STABILIZING SET OF BACKSTEPPING BASED NONLINEAR CONTROLLER FOR SHIP COURSE KEEPING

2021 ◽  
Vol 158 (A3) ◽  
Author(s):  
X K Zhang ◽  
G Q Zhang
Keyword(s):  
Closed Loop ◽  
Simulation Experiment ◽  
Empirical Knowledge ◽  
Backstepping Method ◽  
Nonlinear Controller ◽  
Closed Loop System ◽  
Robust Performance ◽  
System A ◽  
Uniformly Asymptotic Stability ◽  
Novel Method

In order to solve the problem that backstepping method cannot effectively guarantee the robust performance of the closed-loop system, a novel method of determining parameter is developed in this note. Based on the ship manoeuvring empirical knowledge and the closed-loop shaping theory, the derived parameters belong to a reduced robust group in the original stabilizing set. The uniformly asymptotic stability is achieved theoretically. The training vessel “Yulong” and the tanker “Daqing232” are selected as the plants in the simulation experiment. And the simulation results are presented to demonstrate the effectiveness of the proposed algorithm.

Robust Adaptive Nonlinear Controller for Robotic Systems: Linear Matrix Inequality Approach

2008 ◽  
Author(s):  
Itzhack Levy ◽  
Nadav Berman ◽  
Amit Ailon
Keyword(s):  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Nonlinear Controller ◽  
Closed Loop System ◽  
Storage Function ◽  
Linear Matrix Inequality Approach ◽  
Case Simulation ◽  
Robust Adaptive ◽  
Two Degree Of Freedom

In this paper the tracking problem of a robotic system with model uncertainty is considered via an application of the H∞ control theory for nonlinear systems. In particular, we develop a state feedback controller which yields a global exponential stability of the underlying system and provides the closed loop system with relatively low gains. The main ingredient which facilitates our development is the choice of a particular storage function (which serves as a Lyaponov function). This particular storage function leads to certain linear matrix inequalities, the solution of which yields the desired controller. Moreover, the resulting LMIs (Linear Matrix Inequalities) turn out to be of the same form of the LMIs achieved in the analogous linear case. Simulation results and implementation of the control algorithm in a two-degree of freedom robot illustrate the controller efficiency.

scholarly journals Robust LFC Strategy for Wind Integrated Time-Delay Power System Using EID Compensation

Energies ◽  
2019 ◽  
Vol 12 (17) ◽  
pp. 3223 ◽  
Author(s):  
Liu ◽  
Zhang ◽  
Zou
Keyword(s):  
Time Delay ◽  
Power System ◽  
Closed Loop ◽  
Frequency Control ◽  
Loop System ◽  
Load Frequency Control ◽  
System Stability ◽  
Linear Matrix ◽  
Closed Loop System ◽  
The Stability

This paper presents an active disturbance rejection control (ADRC) technique for load frequency control of a wind integrated power system when communication delays are considered. To improve the stability of frequency control, equivalent input disturbances (EID) compensation is used to eliminate the influence of the load variation. In wind integrated power systems, two area controllers are designed to guarantee the stability of the overall closed-loop system. First, a simplified frequency response model of the wind integrated time-delay power system was established. Then the state-space model of the closed-loop system was built by employing state observers. The system stability conditions and controller parameters can be solved by some linear matrix inequalities (LMIs) forms. Finally, the case studies were tested using MATLAB/SIMULINK software and the simulation results show its robustness and effectiveness to maintain power-system stability.

Gain Scheduled Control of Gas Turbine Engines: Stability and Verification

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Mehrdad Pakmehr ◽  
Nathan Fitzgerald ◽  
Eric M. Feron ◽  
Jeff S. Shamma ◽  
Alireza Behbahani
Keyword(s):  
Convex Optimization ◽  
Gas Turbine ◽  
Closed Loop ◽  
Gas Turbine Engine ◽  
Loop System ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Turbine Engine ◽  
Gain Scheduled Controller ◽  
Gain Scheduled

A stable gain scheduled controller for a gas turbine engine that drives a variable pitch propeller is developed and described. A stability proof is developed for gain scheduled closed-loop system using global linearization and linear matrix inequality (LMI) techniques. Using convex optimization tools, a single quadratic Lyapunov function is computed for multiple linearizations near equilibrium and nonequilibrium points of the nonlinear closed-loop system. This approach guarantees stability of the closed-loop gas turbine engine system. To verify the stability of the closed-loop system on-line, an optimization problem is proposed, which is solvable using convex optimization tools. Simulation results show that the developed gain scheduled controller is capable to regulate a turboshaft engine for large thrust commands in a stable fashion with proper tracking performance.

Positive Finite-Time Stabilization for Discrete-Time Linear Systems

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Wenping Xue ◽  
Kangji Li
Keyword(s):  
Linear Systems ◽  
Discrete Time ◽  
Finite Time ◽  
State Feedback ◽  
Closed Loop ◽  
Linear Matrix ◽  
Closed Loop System ◽  
Initial State ◽  
Finite Time Stability ◽  
Time Linear

In this paper, a new finite-time stability (FTS) concept, which is defined as positive FTS (PFTS), is introduced into discrete-time linear systems. Differently from previous FTS-related papers, the initial state as well as the state trajectory is required to be in the non-negative orthant of the Euclidean space. Some test criteria are established for the PFTS of the unforced system. Then, a sufficient condition is proposed for the design of a state feedback controller such that the closed-loop system is positively finite-time stable. This condition is provided in terms of a series of linear matrix inequalities (LMIs) with some equality constraints. Moreover, the requirement of non-negativity of the controller is considered. Finally, two examples are presented to illustrate the developed theory.

Stable Nonlinear Control Allocation for Aircraft with Multiple Control Effectors

2011 ◽  
Vol 138-139 ◽  
pp. 404-409 ◽  
Author(s):  
Heng Li ◽  
Jin Yong Yu ◽  
You An Zhang
Keyword(s):  
Closed Loop ◽  
Dynamic Control ◽  
Lyapunov Stability Theory ◽  
Invariant Set ◽  
Control Law ◽  
Control Allocation ◽  
Nonlinear Controller ◽  
Closed Loop System ◽  
Multiple Control ◽  
Simulation Results

With respect to aircraft with redundant multiple control effectors, a nonlinear controller, which is composed of a virtual control law and a dynamic control allocation with position constraints of each effector, is designed. Based on Lyapunov stability theory and LaSalle invariant set theorem, asymptotic stabilities of upper control subsystem, dynamic control allocation subsystem and overall closed-loop system are proved respectively. Simulation results show the effectiveness of the proposed method.

Design of Output Feedback Controller for Switched Fuzzy Systems with Time-Delay

2014 ◽  
Vol 635-637 ◽  
pp. 1443-1446
Author(s):  
Hong Yang ◽  
Huan Huan Lü ◽  
Le Zhang
Keyword(s):  
Time Delay ◽  
Output Feedback ◽  
Fuzzy Systems ◽  
Closed Loop ◽  
Feedback Controller ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Closed Loop System ◽  
Output Feedback Controller ◽  
And Control

This paper investigates the problems of stabilization and control for time-delay switched fuzzy systems using output feedback controller. Based on the linear matrix inequality (LMI) technique, multiple Lyapunov method is used to obtain a sufficient condition for the existence of the controller for the output feedback. Then an algorithm is constructed to transform the sufficient condition into a LMI form, thus obtaining a method for designing the controller. The designed controller guarantees the closed-loop system to be asympototically stable. A numerical example is given to show the effectiveness of our method.

Admissible Conditions for T-S Fuzzy Descriptor Systems with Non-Differentiable Membership Functions

2013 ◽  
Vol 415 ◽  
pp. 259-266
Author(s):  
Peng Lin ◽  
Gang Hu
Keyword(s):  
Continuous Time ◽  
Lyapunov Functions ◽  
Closed Loop ◽  
Structural Information ◽  
Descriptor Systems ◽  
Linear Matrix ◽  
Membership Functions ◽  
Matrix Inequalities ◽  
Closed Loop Systems ◽  
Takagi Sugeno

In this paper, the admissible conditions (regular, impulse-free and stable) for a class of continuous-time Takagi-Sugeno (T-S) fuzzy descriptor systems are investigated. Sufficient admissible conditions for the closed-loop systems under non-parallel distributed compensation (non-PDC) feedback are proposed. This approach is mainly based on the state space division properly to make the membership functions continuous differentiable. Moreover, in order to make good use of the systems’ structural information in rules, the provided conditions are obtained through fuzzy Lyapunov functions candidate and can be formulated in terms of dilated Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed approach is shown through numerical example by using the optimization toolbox.

scholarly journals Probabilistic Control for Uncertain Systems

2012 ◽  
Vol 134 (2) ◽  
Author(s):  
Randa Herzallah
Keyword(s):  
Control Algorithm ◽  
Probabilistic Models ◽  
Closed Loop ◽  
Inverse Dynamics ◽  
Loop System ◽  
Model Parameters ◽  
Control Input ◽  
Closed Loop System ◽  
Optimal Control Strategy ◽  
Mixture Density

In this paper a new framework has been applied to the design of controllers which encompasses nonlinearity, hysteresis and arbitrary density functions of forward models and inverse controllers. Using mixture density networks, the probabilistic models of both the forward and inverse dynamics are estimated such that they are dependent on the state and the control input. The optimal control strategy is then derived which minimizes uncertainty of the closed loop system. In the absence of reliable plant models, the proposed control algorithm incorporates uncertainties in model parameters, observations, and latent processes. The local stability of the closed loop system has been established. The efficacy of the control algorithm is demonstrated on two nonlinear stochastic control examples with additive and multiplicative noise.

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