Guaranteed cost control of uncertain systems with a time-multiplied quadratic cost function: An approach based on linear matrix inequalities

1997 ◽  
Author(s):  
S. O. R. Moheimani ◽  
I. R. Petersen
Keyword(s):  
Cost Function ◽  
Linear Matrix Inequalities ◽  
Uncertain Systems ◽  
Cost Control ◽  
Linear Matrix ◽  
Matrix Inequalities ◽  
Quadratic Cost ◽  
Guaranteed Cost ◽  
Quadratic Cost Function ◽  
Control Of Uncertain Systems

Time-Multiplied Guaranteed Cost Control of Linear Delay Systems

2008 ◽  
Vol 130 (6) ◽  
Author(s):  
Junling Wang ◽  
James Lam ◽  
Shengyuan Xu ◽  
Zhan Shu
Keyword(s):  
Cost Function ◽  
Linearization Method ◽  
Delay Systems ◽  
Linear Matrix ◽  
Linear Quadratic ◽  
Quadratic Cost ◽  
Linear Delay ◽  
Guaranteed Cost ◽  
Delay Dependent ◽  
Quadratic Cost Function

This paper investigates the design of guaranteed cost controllers for a class of linear systems with a state delay using a time-multiplied linear quadratic cost function. Based on delay-dependent and delay-independent stability criteria, guaranteed cost controllers can be constructed via solutions to linear matrix inequalities (LMIs) such that the resulting closed-loop system is stable and a specified time-multiplied linear integral-quadratic cost function has an upper bound. By the cone complementary linearization method, delay-dependent state feedback controllers can be derived in terms of LMIs. A numerical example is provided to demonstrate the effectiveness of the proposed method.

The Optimal Regulations of the Interconnection-Degrees of Large Scale Systems under Instable Case

2012 ◽  
Vol 235 ◽  
pp. 107-110
Author(s):  
Ying Ge Wo
Keyword(s):  
Cost Function ◽  
Linear Matrix Inequalities ◽  
Large Scale ◽  
Large System ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Stabilization Problem ◽  
Large Scale Systems ◽  
The Cost

This paper discusses the stabilization problem of a large-scale system via cutting off the connections or decreasing the degree of interconnections among its subsystems subject to a cost function. Under the assumption that the large system is unstable but its sub-systems are all stable, a sufficient condition about the degree of interconnection is presented via cutting off the connections or decreasing the degree of interconnections among its subsystems such that the new large system is stable. This condition can be expressed by linear matrix inequalities (LMIs). Based on this analysis, an optimal regulation for such controls is obtained ensures the minimization of the cost function. An illustrating example is also given to show the effectiveness of the proposed method.

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.

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