scholarly journals Synthesis of Adaptive Robust Controllers for a Class of Nonlinear Systems with Input Saturations

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Kenta Oba ◽  
Hidetoshi Oya ◽  
Tomohiro Kubo ◽  
Tsuyoshi Matsuki
Keyword(s):  
Nonlinear System ◽  
Nonlinear Systems ◽  
Linear Matrix Inequalities ◽  
Design Problem ◽  
Sufficient Conditions ◽  
Matching Condition ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Robust Controllers ◽  
Robust Controller

This paper deals with a design problem of an adaptive robust controller for a class of nonlinear systems with specified input saturations. For the nonlinear system under consideration, the nonlinearity means unknown perturbations and satisfies the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed adaptive robust controller giving consideration to input saturations are given in terms of linear matrix inequalities (LMIs). Finally, simple illustrative examples are shown.

scholarly journals Synthesis of Decentralized Variable Gain Robust Controllers with GuaranteedL2Gain Performance for a Class of Uncertain Large-Scale Interconnected Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Shunya Nagai ◽  
Hidetoshi Oya
Keyword(s):  
Linear Matrix Inequalities ◽  
Large Scale ◽  
Sufficient Conditions ◽  
Matching Condition ◽  
Interconnected Systems ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Robust Controller ◽  
Interconnected System ◽  
Variable Gain

We consider a design problem of a decentralized variable gain robust controller with guaranteedL2gain performance for a class of uncertain large-scale interconnected systems. For the uncertain large-scale interconnected system, the uncertainties and the interactions satisfy the matching condition. In this paper, we show that sufficient conditions for the existence of the proposed decentralized variable gain robust controller with guaranteedL2gain performance are given in terms of linear matrix inequalities (LMIs). Finally, simple illustrative examples are shown.

Global dissipativity of stochastic Lotka–Volterra system with feedback controls

2017 ◽  
Vol 10 (02) ◽  
pp. 1750022 ◽  
Author(s):  
Qimin Zhang ◽  
Xinjing Zhang ◽  
Hongfu Yang
Keyword(s):  
Linear Matrix Inequalities ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Jensen Inequality ◽  
Linear Matrix ◽  
Mean Square ◽  
Matrix Inequalities ◽  
Volterra System ◽  
Feedback Controls ◽  
The Mean

In this paper, a class of stochastic Lotka–Volterra system with feedback controls is considered. The purpose is to establish some criteria to ensure the system is globally dissipative in the mean square. By constructing suitable Lyapunov functions as well as combining with Jensen inequality and It[Formula: see text] formula, the sufficient conditions are established and they are expressed in terms of the feasibility to a couple linear matrix inequalities (LMIs). Finally, the main results are illustrated by examples.

Mixed H2/H∞ Control for State-Delayed Linear Systems and a LMI Approach to the Solution of Coupled AREs

2003 ◽  
Vol 125 (2) ◽  
pp. 249-253 ◽  
Author(s):  
M. D. S. Aliyu
Keyword(s):  
Control Problem ◽  
Linear Systems ◽  
Linear Matrix Inequalities ◽  
State Feedback ◽  
Sufficient Conditions ◽  
Riccati Equations ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Lmi Approach ◽  
Alternative Approach

In this paper, the state-feedback mixed H2/H∞ control problem for state-delayed linear systems is considered. Sufficient conditions for the solvability of this problem are given in terms of the solution to a pair of algebraic Riccati equations similar to the nondelayed case. However, these Riccati equations are more difficult to solve than those arising in the pure H2,H∞ problems, and an alternative approach is to solve a pair of linear matrix inequalities (LMIs).

scholarly journals Guaranteed Cost Nonfragile Robust Controller for Walking Simulation of Quadruped Search Robot on a Slope of VRML Model

2014 ◽  
Vol 6 ◽  
pp. 948795
Author(s):  
Peng Wang ◽  
Jixiang Li ◽  
Yuan Zhang
Keyword(s):  
Linear Matrix Inequalities ◽  
Linear Matrix ◽  
Modeling Language ◽  
Displacement Curve ◽  
Model Structure ◽  
Matrix Inequality ◽  
Matrix Inequalities ◽  
Robust Controller ◽  
3D Terrain ◽  
Guaranteed Cost

The problem of walking simulation for the quadruped search robot on a slope is described as an uncertainty system. In order to create the virtual ramp road environment, VRML modeling language is used to build a real environment, which is a 3D terrain scene in Matlab platform. According to the VRML model structure of the quadruped search robot, a guaranteed cost nonfragile robust controller is designed for ramp road walking simulation. The constraint inequation is transformed into a strict linear inequality by using two equalities; the controller and the guaranteed cost upper bound are given based on the solutions of the linear matrix inequality. And the approaches of designing the controller are given in terms of linear matrix inequalities. The walking stability of quadruped search robot is observed using the VRML model established with the change of gravity curve. Simulation results show that the gravity displacement curve of the robot is smooth. The results given by linear matrix inequalities indicate that the proposed guaranteed cost controller is correct and effective.

Robust controller synthesis via non-linear matrix inequalities

1999 ◽  
Vol 72 (11) ◽  
pp. 971-980 ◽  
Author(s):  
Emmanuel G. Collins ◽  
Debashis Sadhukhan ◽  
Layne T. Watson
Keyword(s):  
Linear Matrix Inequalities ◽  
Controller Synthesis ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Robust Controller ◽  
Non Linear

scholarly journals An Improved Antiwindup Design Using an Anticipatory Loop and an Immediate Loop

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Qing Wang ◽  
Maopeng Ran ◽  
Chaoyang Dong ◽  
Maolin Ni
Keyword(s):  
Linear Matrix Inequalities ◽  
Continuous Time ◽  
Actuator Saturation ◽  
Sufficient Conditions ◽  
The Other ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Continuous Time Systems ◽  
Linear Invariant ◽  
Time Systems

We present an improved antiwindup design for linear invariant continuous-time systems with actuator saturation nonlinearities. In the improved approach, two antiwindup compensators are simultaneously designed: one activated immediately at the occurrence of actuator saturation and the other activated in anticipatory of actuator saturation. Both the static and dynamic antiwindup compensators are considered. Sufficient conditions for global stability and minimizing the inducedL2gain are established, in terms of linear matrix inequalities (LMIs). We also show that the feasibility of the improved antiwindup is similar to the traditional antiwindup. Benefits of the proposed approach over the traditional antiwindup and a recent innovative antiwindup are illustrated with well-known examples.

Delayed Output Feedback Control for Nonlinear Systems With Fuzzy Observers

2012 ◽  
Author(s):  
Mansour Karkoub ◽  
Tzu Sung Wu
Keyword(s):  
Feedback Control ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Output Feedback ◽  
Tracking Error ◽  
Sufficient Conditions ◽  
Output Feedback Control ◽  
Linear Matrix ◽  
External Disturbances ◽  
Control Scheme

In this paper, the design problem of delayed output feedback control scheme using two-layer interval fuzzy observers for a class of nonlinear systems with state and output delays is investigated. The Takagi-Sugeno type fuzzy linear model with an on-line update law is used to approximate the nonlinear system. Based on the fuzzy model, a two-layer interval fuzzy observer is used to reconstruct the system states according to equal interval output time delay slices. Subsequently, a delayed output feedback adaptive fuzzy controller is developed to override the nonlinearities, time delays, and external disturbances such that the H∞ tracking performance is achieved. The linguistic information is developped by setting the membership functions of the fuzzy logic system and the adaptation parameters to estimate the model uncertainties directly for using linear analytical results instead of estimating nonlinear system functions. The filtered tracking error dynamics are designed to satisfy the Strictly Positive Realness (SPR) condition. Based on the Lyapunov stability criterion and linear matrix inequalities (LMIs), some sufficient conditions are derived so that all states of the system are uniformly ultimately bounded and the effect of the external disturbances on the tracking error can be attenuated to any prescribed level and consequently an H∞ tracking control is achieved. Finally, a numerical example of a two-link robot manipulator is given to illustrate the effectiveness of the proposed control scheme.

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