Abstract
In the past time several designs of nonlinear regulator were proposed. Infinite expansion of state series was used in these methods, so convergence of the infinite series was difficult problem. This paper shows the rigorous design of nonlinear regulator using genetic algorithms. When the controlled object has (2N-1) order of state, and peformance function has quadratic form of power state vector of which polynomial order is (2N-1), the optimal control law can be obtained as the feedback of (2N-1) order power state vector. The coefficent matrix of feedback is constracted by a solution of an extended Riccati equation. An extended Riccati equation can not be solved mathematically because the number of variable is less than the number of equation. Genetic algorithms are used in searching method of the solution of an extended Riccati equation. Using the solution of an extended Riccati equatiuon, a Lyapunov function of quadratic form of N order power state vector can be constracted, so a nonlinear regulator which has global stability can be obtained.
