Connections in control strategy

Abstract

We present an infinitesimal interpretation of the control theory, particularly of the part concerning dynamic systems. We use the original concept of a bundle connection, which lies in the idea of fibre transportation along a path on the base manifold. The control of a process leads also to the transportation of fibres, and the control strategy, i.e. the choice of a suitable system control in order to optimize the process corresponds to the choice of a path on the base manifold. The triple of crucial terms of control, aim–control–strategy, translates in the terms of connections as fibre–connection–curve. Such a scheme is quite convincing, but it also works well in dynamic systems analysis.We present an infinitesimal interpretation of the control theory, particularly of the part concerning dynamic systems. We use the original concept of a bundle connection, which lies in the idea of fibre transportation along a path on the base manifold. The control of a process leads also to the transportation of fibres, and the control strategy, i.e. the choice of a suitable system control in order to optimize the process corresponds to the choice of a path on the base manifold. The triple of crucial terms of control, aim–control–strategy, translates in the terms of connections as fibre–connection–curve. Such a scheme is quite convincing, but it also works well in dynamic systems analysis.