A new approach for optimal control using market-based algorithms

A new method for distributed resource allocation is called market-based control. Market-based control systems imitate the behavior of an economic system; some applications of this method exist in the field of distributed computer and telecommunications systems. A new field of application is the control of dynamic systems. In this work, the market-based approach is used for optimal control which is still one of the important methods of control theory. Unfortunately, even though most researchers in this area deal with complex systems, they omit the mathematical background. For this reason, our work focuses on a mathematical description of a market-based control algorithm especially for linear dynamic systems in order to explain the relationship between economic and control systems. It is shown that the optimal control problem can be considered as a special kind of a resource distribution problem. Therefore, the fact that in economic systems resources are optimally distributed in a decentralized manner even in large and complex systems is very interesting. The obtained algorithm in the case of a linear system is characterized by a very effective computation and easy understanding.