We consider a general class of optimal control problems with regional pole and controller structure constraints. Our goal is to show that for a fairly general class of regional pole and controller structure constraints, such constrained optimal control problems can be transformed to a new one with a canonical structure. A three-step transformation procedure is used to achieve our goal, which essentially amounts to repeated augmentations of plant dynamics and repeated reductions of the controller. The transformed problem is one of the standard optimal static output feedback with a decentralized and repeated structure. KEY WORDS optimal control; controller structure constraint; regional pole constraint; static output feed back
1. Introduction
Optimal control problems generally seek to find a feedback controller which minimizes a certain performance index function. Two predominant examples are H, " and H2, or LQG optimal control problems. Traditionally, performance aspects in optimal control problems have been emphasized exclusively, and mainly steady-state performance is considered. The issues of controller complexity and transient behaviour of the system, however, have been largely ignored. Since low controller complexity is generally in conflict with its performance, and since transient properties compete against steady-state properties, an optimal controller is generally of a significant level of complexity and may lead to poor transient properties.
The controller complexity constitutes an important issue in feedback design and is linked directly to implementation, reliability, and robustness of the system, as more complex systems tend to be more costly, more difficult to implement, less reliable, and less robust. Therefore, it is important to constrain the controller complexity in feedback design, and this imposes a constraint on the achievable performance level. Optimal control problems which take controller complexity explicitly into consideration have been formulated in Reference 17.