398 research outputs found
Observer-based Leader-following Consensus for Positive Multi-agent Systems Over Time-varying Graphs
This paper addresses the leader-following consensus problem for discrete-time
positive multi-agent systems over time-varying graphs. We assume that the
followers may have mutually different positive dynamics which can also be
different from the leader. Compared with most existing positive consensus works
for homogeneous multi-agent systems, the formulated problem is more general and
challenging due to the interplay between the positivity requirement and
high-order heterogeneous dynamics. To solve the problem, we present an extended
version of existing observer-based design for positive multi-agent systems. By
virtue of the common quadratic Lyapunov function technique, we show the
followers will maintain their state variables in the positive orthant and
finally achieve an output consensus specified by the leader. A numerical
example is used to verify the efficacy of our algorithms
The minimum spanning tree problem with conflict constraints and its variations
AbstractWe consider the minimum spanning tree problem with conflict constraints (MSTC). The problem is known to be strongly NP-hard and computing even a feasible solution is NP-hard. When the underlying graph is a cactus, we show that the feasibility problem is polynomially bounded whereas the optimization version is still NP-hard. When the conflict graph is a collection of disjoint cliques, (equivalently, when the conflict relation is transitive) we observe that MSTC can be solved in polynomial time. We also identify other special cases of MSTC that can be solved in polynomial time. Exploiting these polynomially solvable special cases we derive strong lower bounds. Also, various heuristic algorithms and feasibility tests are discussed along with preliminary experimental results. As a byproduct of this investigation, we show that if an ϵ-optimal solution to the maximum clique problem can be obtained in polynomial time, then a (3ϵ−1)-optimal solution to the maximum edge clique partitioning (Max-ECP) problem can be obtained in polynomial time. As a consequence, we have a polynomial time approximation algorithm for the Max-ECP with performance ratio O(n(loglogn)2log3n), improving the best previously known bound of O(n)
- …