Rinaldo A. Jose and Lyle H. Ungar
University of Pennsylvania
Philadelphia, PA 19104
We propose an auction-based method for coordinating a group of distributed control units (DCUs) such as those operating the process units in a single plant. If control responsibilities can be divided such that each DCU is entirely independent of the others, then optimizing each DCU locally will optimize the operation of the plant as a whole. Global resource constraints normally preclude such a division, and any particular distributed control system structure will most likely involve DCU interaction.
Resource constraints, for example maximum available steam or cooling water, make up one class of global constraints common in chemical processes. Since DCUs operate as if in the absence of global constraints, the total usage for a particular resource, such as steam, may exceed the current supply, i.e. some of the global resource constraints may be violated. Typically, these problems are solved using a Dantzig-Wolfe decomposition which essentially assigns ``prices'' to the limiting resources. One drawback to this approach is that accurate local objective functions may be unknown. Humans in the optimization loop may be inclined to ``misrepresent'' their objective functions in order to acquire limited resources at the expense of others.
Auction-based methods have some important advantages over other distributed control or decomposition methods. A properly designed auction motivates participants to use accurate objective functions. The auction is independent of the solution methods of the DCUs. The auctioning process is not computationally intensive nor does it involve the formulation or solution of large-scale optimization problems. The primary difficulty with this approach is that local optimization criteria must be consistent with the global objective function. To ensure this consistency requires the incorporation of ``incentive compatible mechanisms'' which reward DCUs for acting in a globally beneficial manner.
A resource auction consists of two types of players: an auctioneer which manages the limited resource and agents which represent the interests of a particular DCU. Before every auction, each DCU determines an optimal amount of resource required for the next unit of operating time. Each DCU agent then computes the gain in utility associated with acquiring the resource and converts this into some amount of ``money'' it is willing to pay --- this constitutes a bid. The auctioneer collects the bids from all agents and sorts them based on price per unit, forming a demand curve. The intersection of the demand curve and the auctioneer's supply curve defines an auction price. Each component whose bid is above the auction price pays its bid amount less the auction price while each component below the auction price pays nothing and receives nothing. The component whose bid is at the auction price pays nothing, but receives only part of what was requested.
In order to demonstrate some of the features of an auction-based scheme relative to other solution methods, we consider the problem of temperature control of a set of process units which share a common steam supply. We examine three approaches: