Hybrid quantum-inspired evolutionary algorithm-based parameter estimation for chaotic systems
基于混合量子进化计算的混沌系统参数估计

Parameter estimation of chaotic systems is essentially a multidimensional optimization problem. To estimate the unknown parameters of chaotic systems precisely, we present an effective hybrid quantum-inspired evolutionary algorithm (HQEA), in which the real-valued quantum angle is used to express the Q-bits of chromosome, and the probability of each Q-bit is considered the position information of the chromosome. Combining the quantum differential evolutionary algorithm (QDE) which uses differential evolution to update the state of Q-bits with the real-coded quantum evolutionary algorithm (RQEA) which employs quantum rotation gate to update the state of Q-bits, we make a balance between the global exploration and the local exploitation. In addition, the HQEA performs the quantum non-gate operation in which the Q-bits selected from the current best chromosome with a certain probability are transformed to get rid of the premature local optimum. The experimental results of benchmark function tests show that the HQEA algorithm greatly improves the global optimization performance as well as the reliability performance. Numerical simulation results of the Lorenz system also demonstrate its effectiveness.