Conjugate gradient based Cholesky CMA-ES estimation algorithms for Hammerstein systems

This paper studies the parameter estimation problems of nonlinear systems with colored noise using the covariance matrix adaptation evolution strategy (CMA-ES), which is one of the most competitive evolutionary algorithms available and has been applied in the area of reinforcement learning and process control. However, a major limitation that impedes the application of the CMA-ES is the high computational complexity caused by matrix decomposition. To alleviate this problem, an efficient Cholesky CMA-ES is proposed, which uses the Cholesky factor instead of the covariance matrix to reduce the computational complexity, and updates the search direction and distribution mean based on the conjugate gradient method to further improve the search accuracy. In virtue of the auxiliary model identification idea, the Cholesky CMA-ES can be applied to solve the parameter estimation problems of the Hammerstein nonlinear systems with colored noise. A simulation example is provided to demonstrate its effectiveness.