A design method for optimal controllers of minimax problems: a genetic programming approach

Based on the genetic programming approach, a new design method is proposed for optimal controllers of minimax problems, including H_∞ control problems. The state feedback controllers and observer-based output feedback controllers are derived. First, the detailed description is given on the genetic programming, which plays a key role in constructing robust minimax controllers. Then, making use of the emergent property of the genetic programming, the new type of the design method is proposed. The demonstration of its effectiveness is done through some simple numerical examples of the H_∞ control problems. Finally, the inverted pendulum problem is tackled by applying the GP based design method.