scholarly journals Lower bound for the cost of connecting tree with given vertex degree sequence

2019 ◽  
Vol 8 (2) ◽  
Author(s):  
Mikhail Goubko ◽  
Alexander Kuznetsov
Keyword(s):  
Lower Bound ◽  
Heuristic Algorithms ◽  
Degree Sequence ◽  
Real Life ◽  
Inequality Constraints ◽  
Topology Design ◽  
Semidefinite Optimization ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
The Cost

Abstract The optimal connecting network problem generalizes many models of structure optimization known from the literature, including communication and transport network topology design, graph cut and graph clustering, etc. For the case of connecting trees with the given sequence of vertex degrees the cost of the optimal tree is shown to be bounded from below by the solution of a semidefinite optimization program with bilinear matrix inequality constraints, which is reduced to the solution of a series of convex programs with linear matrix inequality constraints. The proposed lower-bound estimate is used to construct several heuristic algorithms and to evaluate their quality on a variety of generated and real-life datasets.

scholarly journals Determinant Maximization with Linear Matrix Inequality Constraints

1998 ◽  
Vol 19 (2) ◽  
pp. 499-533 ◽  
Author(s):  
Lieven Vandenberghe ◽  
Stephen Boyd ◽  
Shao-Po Wu
Keyword(s):  
Linear Matrix Inequality ◽  
Inequality Constraints ◽  
Linear Matrix ◽  
Matrix Inequality

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.

scholarly journals Limited-Budget Formation Control for High-Order Linear Swarm Systems with Fix Topologies

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hongtao Dang ◽  
Le Wang ◽  
Yan Zhang ◽  
Jianye Yang
Keyword(s):  
Formation Control ◽  
Sufficient Conditions ◽  
Inequality Constraints ◽  
High Order ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Order Linear ◽  
Limited Budget ◽  
Communication Topology ◽  
Formation Design

This paper discusses limited-budget time-varying formation design and analysis problems for a high-order linear swarm system with a fixed communication topology. Firstly, the communication topology among agents is modeled as an undirected and connected graph, and a new formation control protocol with an energy integral term is proposed to realize formation control and to guarantee the practical energy assumption is less than the limited energy budget. Then, by the matrix inequality tool, sufficient conditions for limited-budget formation design and analysis are proposed, respectively, which are scalable and checkable since they are independent of the number of agents of a swarm system and can be transformed into linear matrix inequality constraints. Moreover, an explicit expression of the formation center function is given, which contains the formation function part and the cooperative state part and is not associated with the derivatives of the formation functions. Finally, a numerical simulation is shown to demonstrate the effectiveness of theoretical results.

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.

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