scholarly journals Sufficient global optimality conditions for multi-extremal smooth minimisation problems with bounds and linear matrix inequality constraints

2006 ◽  
Vol 47 (4) ◽  
pp. 439-450 ◽  
Author(s):  
N. Q. Huy ◽  
V. Jeyakumar ◽  
G. M. Lee
Keyword(s):  
Linear Matrix Inequality ◽  
Optimality Conditions ◽  
Model Problem ◽  
Inequality Constraints ◽  
Linear Matrix ◽  
Feasible Region ◽  
Global Optimality ◽  
Global Optimality Conditions ◽  
Matrix Inequality ◽  
Analysis And Design

AbstractIn this paper, we present sufficient conditions for global optimality of a general nonconvex smooth minimisation model problem involving linear matrix inequality constraints with bounds on the variables. The linear matrix inequality constraints are also known as “semidefinite” constraints which arise in many applications, especially in control system analysis and design. Due to the presence of nonconvex objective functions such minimisation problems generally have many local minimisers which are not global minimisers. We develop conditions for identifying global minimisers of the model problem by first constructing a (weighted sum of squares) quadratic underestimator for the twice continuously differentiable objective function of the minimisation problem and then by characterising global minimisers of the easily tractable underestimator over the same feasible region of the original problem. We apply the results to obtain global optimality conditions for optinusation problems with discrete constraints.

A linear matrix inequality–based proportional-derivative sliding mode control tuning method in robotic systems subjected to external disturbance

2020 ◽  
Vol 26 (23-24) ◽  
pp. 2297-2315
Author(s):  
Valiollah Ghaffari
Keyword(s):  
Sliding Mode Control ◽  
Linear Matrix Inequality ◽  
Sliding Mode ◽  
Robot Manipulator ◽  
External Disturbance ◽  
Inequality Constraints ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Tuning Method ◽  
Mode Control

The proportional-derivative sliding-mode control will be designed and tuned in the trajectory tracking of a robot manipulator which operates on uncertain dynamic environments. For achieving these goals, first, a linear matrix inequality–based framework is suggested to design a robust proportional-derivative sliding-mode control in the presence of external disturbances. Next, the parameters of the proportional-derivative sliding-mode control law will be tuned via another minimization problem subjected to some linear matrix inequality constraints. Thus, the controller parameters can be automatically updated via the solution of the optimization problem. The results are successfully used in the robot manipulator with considering two reference paths and some different loads. The simulation results show the effectiveness of the proposed method in comparison with the same technique.

Linear Matrix Inequality and its Application in Control Theory

2013 ◽  
Vol 853 ◽  
pp. 636-640
Author(s):  
Hai Yan Wang
Keyword(s):  
Linear Matrix Inequality ◽  
Solution Method ◽  
System Analysis ◽  
Linear Matrix ◽  
General Description ◽  
Matrix Inequality ◽  
Closed Loop System ◽  
Analysis And Design ◽  
Good Nature ◽  
Basic Content

As a result of linear matrix inequality (LMI) and its good nature of mathematics as well as the breakthrough of solution method, many control problems can be transformed into a standard LMI problem to solve. Linear matrix inequality has received widely attention and applications in control system analysis and design. This paper introduces some of the basic content of LMI, such as the general description, the relevant algorithms and software. The controller will be designed using LMI such that the closed-loop system is asymptotically stable, and simulation will be given using Matlab. Finally, the population model will be given and analyzed.

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