(687d) Performance Evaluation of Two Different Decentralized Control Methods Applied to Reactor Networks

This paper proposes a management layer for performance evaluation of adaptive agent-based control systems for a Continuous Stirred Tank Reactor (CSTR) network, using different decentralized spatial reconfiguration techniques. In each reactor of this network, autocatalytic product species are competing against each other, providing a nice example for population dynamics and social networks. The approach used aims to select the best control method over other candidates, whenever a disturbance hits the system and/or a change is made in the desired grade (composition) of the product. The method is able to keep track of previous performances of different individual control methods by using a k-nearest neighbor (kNN) algorithm for regression, which then gives estimates for the performances of different algorithms depending on the similarity of the state of the network and the behavior exhibited by them in similar conditions.

The operation of highly nonlinear networks may benefit from evolutionary self-organizing control because the optimal operating regime and the required control strategies may not be known ahead of time. Agent-based control systems provide the capability for localized and global control strategies that are both reactive in controlling disturbances and proactive in searching for better operational solutions.

Large-scale spatially distributed systems have the properties of being nonlinear and mostly having a high order. Therefore, they present a unique and difficult control challenge. The control structure, which has to be implied to those systems, has a tendency to include continuous and discrete elements. Additionally, the structure itself is generally both discrete and distributed.

The control structures, the performances of which are evaluated in different operating conditions, are working in a decentralized manner and their objective is to maintain the desired grade. The decentralized control methods have some similarities in their operation. In both control techniques, whenever a control agent desires to change the dominant species within a reactor, it must transport some amount of the desired species from another neighboring reactor to the reactor, the concentration of which is being modified. If none of the immediate neighboring reactors contains the desired species, then the agent must negotiate with several other agents on the network in order to move the species from a more distant reactor. To minimize the disturbance to the operation of the network as a whole, the control agent attempts to find the shortest path between itself and a reactor containing the species that it needs to change the dominant species of its reactor. The similarities mostly end at the heuristics used to control the reactor network. One control approach is using an auction-based mechanism, where each control agent bids on the species that it want to produce on a particular reactor, whereas the other decentralized approach is using a perceptron-based learning for its decision mechanism, in which it observes its environment, compares the current grade with the objective one and calculates its species strength and comes up with a decision of transporting some amount from the reactor it is controlling to a neighboring one.

To acquire the ability to evaluate the performances and to calculate the estimates for picking up the control method suitable for the current state when a disturbance hits the reactor network, both methods should have completed a training phase. Training will continue, until they have enough data points to make the comparison meaningful. The training phase consists of introducing some pre-determined disturbances and picking the method for control, which has less data points in the space, until there are enough data points to make kNN work. We are using in our work 3-NN, hence the training phase continues until each method has been used three times on different scenarios.

The training examples are vectors in a multidimensional feature space. This vector is trying to capture the similarity of the reactor network to a previous one, which is measured by the current grade produced, a quantity called average neighborhood size, which is a measure of the amount of reactor clustering in the network producing same species and another quantity called average network strength, which is indicating how difficult for that reactor network it will be to make a transition from one grade to another. In order to calculate this quantity, individual concentrations of different species in each reactor are compared against each other and their average value is taken.

The training phase of the algorithm consists only of storing the feature vectors and the corresponding performance value, which is a weighted sum of the following measures:

? The algorithm meeting the objective and being able to maintain the desired grade.

? The amount of disturbance that the control method itself is giving to the system.

? The time that it needs to completion.

In the actual regression phase, the test sample is represented as a vector (showing the current reactor network condition) in the feature space. Distances from the new vector to all stored vectors are computed and three (k value in kNN algorithm) closest samples are selected. The performance values associated with those three vectors are weighed in an inversely proportional manner according to the Euclidean distance they have to the new vector location. That average will provide an estimate about how each method will behave on the current condition based on their individual histories of success and failure.

The results of the management layer for performance evaluation is illustrated in a case study where a controlled set of disturbances and set-point changes are introduced to the system for the training phase and others are used to test the performances of different decentralized control algorithms during actual regression phase. The approach enables online switching of different control algorithms based on their previous performances and provides a basis for updating the individual control mechanisms, in case they start behaving poorly because of some unforeseen changes in the network.