Partial containment control over signed graphs

In this paper, we deal with the containment control problem in presence of antagonistic interactions. In particular, we focus on the cases in which it is not possible to contain the entire network due to a constrained number of control signals. In this scenario, we study the problem of selecting the nodes where control signals have to be injected to maximize the number of contained nodes. Leveraging graph condensations, we find a suboptimal and computationally efficient solution to this problem, which can be implemented by solving an integer linear problem. The effectiveness of the selection strategy is illustrated through representative simulations.Comment: 6 pages, 3 figures, accepted for presentation at the 2019 European Control Conference (ECC19), Naples, Ital

Evolution of the Gini coefficient <i>G</i>(<i>k</i>) in a market without interaction (black line), in a market with random interaction (magenta line), and in the rational market (blue line).

<p>Evolution of the Gini coefficient <i>G</i>(<i>k</i>) in a market without interaction (black line), in a market with random interaction (magenta line), and in the rational market (blue line).</p

Indegree distribution <i>P</i>(<i>k</i>_<i>in</i>) of the network in the rational market at <i>k</i> = 1 (a) and at <i>k</i> = 15000 (b).

<p>Indegree distribution <i>P</i>(<i>k</i>_<i>in</i>) of the network in the rational market at <i>k</i> = 1 (a) and at <i>k</i> = 15000 (b).</p

Average wealth of an agent as a function of its indegree in the rational market at <i>k</i> = 1 (a) and at <i>k</i> = 15000 (b), and in the partially rational market (c) and irrational market (d) at <i>k</i> = 15000.

<p>Average wealth of an agent as a function of its indegree in the rational market at <i>k</i> = 1 (a) and at <i>k</i> = 15000 (b), and in the partially rational market (c) and irrational market (d) at <i>k</i> = 15000.</p

Average risk attitude in the rational (in blue), partially rational (in green) and irrational (in red) markets.

<p>Average risk attitude in the rational (in blue), partially rational (in green) and irrational (in red) markets.</p

Average risk attitude of the network in the reference scenarios (magenta line) and in the rational market (blue line).

<p>Average risk attitude of the network in the reference scenarios (magenta line) and in the rational market (blue line).</p

Potential driving the edge evolution with <i>b</i> = 16. The red dotted arrow corresponds to an inactive edge, while the blue solid arrow to an active one.

<p>Potential driving the edge evolution with <i>b</i> = 16. The red dotted arrow corresponds to an inactive edge, while the blue solid arrow to an active one.</p

Evolution of the Gini coefficient <i>G</i>(<i>k</i>) in the rational (blue line), partially rational (green line), and irrational (red line) markets.

<p>Evolution of the Gini coefficient <i>G</i>(<i>k</i>) in the rational (blue line), partially rational (green line), and irrational (red line) markets.</p