Recursive second-order approximation method for optimization and control of steady-state systems

Abstract

A recursive second-order approximation approach for the optimization and control of steady-state systems is proposed. The method constructs the hessian matrix of the real performance by using a modification of the Broyden, Fletcher, Goldfart, and Shanno (BFGS) formula which only uses first-order information of the real process. The iterative direction can be obtained by solving a second-order approximate optimization problem which is determined by a modification of the BFGS formula. To obtain a new iterative point, Newton step and one-dimensional search updating strategies are employed. Global convergence and optimality of the derived algorithms are thoroughly investigated. In particular, the R-superlinear properties of the new approach are verified under local conditions. Numerical results show that the new approach is superior to the sequence model approximation (SMA) method.