Article ID: | iaor1994231 |
Country: | United Kingdom |
Volume: | 14 |
Issue: | 2 |
Start Page Number: | 111 |
End Page Number: | 124 |
Publication Date: | Apr 1993 |
Journal: | Optimal Control Applications & Methods |
Authors: | Locatelli A., Nicolao G. de |
Keywords: | programming: multiple criteria, optimization |
The infinite horizon, multiobjective linear quadratic control problem for continuous time systems is considered. Following a utopian approach, the optimal solution is defined as the solution that minimizes the distance from the utopian point in the cost space. It is shown that under standard stabilizability and detectability assumptions the optimal solution always exists. The solution coincides with the solution of a scalar LQ problem in which the cost matrices are given by a suitably weighted sum of their counterparts in the individual criteria. By exploiting the characterization and properties of the optimal solution, it is shown that the problem can be efficiently solved by means of a Newton-type algorithm.