Decentralized robust control of unknown systems using tuning regulators

The problem of determining a decentralized robust controller for a general servomechanism problem, in which the system to be regulated is unknown, is considered in this paper. In this problem, the unknown system is subject to disturbances and it is desired to find a decentralized controller so that the outputs track given specified reference inputs, independent of any disturbances occurring in the system, and such that this occurs for any perturbations in the parameters of the system (which do not cause instability). The only assumptions made regarding the system to be regulated are that 1) the system is described by a finite linear time-invariant multivariable model and 2) the system is stable. Note that the order of the system is not assumed to be known. The approach taken to solve the problem is in the same spirit of some results recently obtained on "multivariable tuning regulators" for centralized control systems [1]. In this problem formulation, the constraint is imposed that only one controller (at a given control station) may be adjusted at any time (and that when adjusted, this controller will remain fixed), and that the closed-loop system must remain stable at all times during the tuning procedure. It is shown that necessary and sufficient conditions for a solution to exist to the problem can be obtained by performing some simple experiments on the plant, and that a robust decentralized controller can then be synthesized using the results of these experiments in conjunction with a series of one-dimensional parameter searches performed on the closed-loop system. This later procedure is called "tuning the controller on line." The most interesting feature of this problem which differs from the centralized control problem is that the controller synthesis must be carded out in a certain preassigned order with respect to each controller agent (not necessarily unique); if this ordering is not carried out, then there may not exist a controller synthesis for the problem.