Conflicting Multi-Objective Compatible Optimization Control

It is clear that there exist many practical control problems in which the consideration of multiple objectives is typically required, and these objectives may conflict with each other. For example, in many practical control systems, control error often conflicts with energy consumption. In the past ten years, we have been studying the greenhouse environment control problem and have gained a considerable understanding of greenhouse dynamics. In a greenhouse, we must keep the temperature and humidity in certain range that is suitable for the plants. However, we are simultaneously required to minimize energy consumption to reduce the cost. The control means include ventilation, heating and spraying, of which heating and spraying are high-energy-consumption methods. In winter, we can improve the temperature by heating and decrease the humidity by heating and ventilating. With the traditional control strategy, we could maintain the temperature and humidity at a very precise point, but the high energy consumption and expensive cost of this strategy would make the greenhouse unprofitable, which implies that this control strategy would not to be chosen by any users. This type of problem is also widely found in industrial control. There have existed two main traditional methods to solve the above-mentioned multiobjective problem. One is the trade-off weight method (Masaaki, 1997), which translates this multi-objective problem into a single-objective one by adding a set of trade-off weights (Masaaki, 1997; Rangan & Poolla, 1997; Eisenhart, 2003). The major advantage of this method is that the translated single-objective control problem is very easy to deal with, but the disadvantage is that the control result will be strongly associated with the trade-off weights chosen, and the controlled objectives may not be satisfactory if we provide bad weights. In addition, the selection of weights is very difficult for users and engineers in the practical situation. Another approach is the constraints method, which optimizes the most important control objective and translates the others into system constraints (Scherer, 1995; Scherer et al, 1997; Sznaier et al, 2000). The advantage of this approach is to satisfy all controlled objectives through constraints; however, the constraint bounds are very difficult for users or control engineers to determine suitably in a practical problem. Bounds that are too tight may bar the existence of a feasible solution for the optimization problem, while too loose bounds may make the optimization problem lose practical significance.