In Section 2, we briefly review the basic models of [S.sup.3]VM and show how to reformulate the corresponding MIQP problem as a completely positive programming problem.
Note that this problem is a MIQP problem which is generally difficult to solve.
Therefore, we propose a new approximating way to get an e-optimal solution of the original mixed integer constrained quadratic programming (MIQP) problem in the next section.
By using the virtual control input, the MIQP problem is approximately rewritten as a quadratic programming (QP) problem, which can be relatively solved faster than the MIQP problem.
Therefore, Problem 1 can be rewritten as a mixed integer quadratic programming (MIQP) problem (see the appendix for further details).
In the above procedure, Problem 1, that is, the MIQP problem must be solved at each time.
The proposed solution method for Problem 1 can be regarded as the method that the MIQP problem corresponding to Problem 1 is divided into one QP problem (Problem 2) and s ILP problems (Problem 3 for each subsystem).
In addition, the fact that Problem 1 is directly solved (in other words, Problem 1 is rewritten as an MIQP problem) corresponds to centralized control of large-scale systems.