A chain smoothing Newton method for heat and mass transfer control with discrete variability DAE models

Abstract

A multiple shooting based approach to an optimal control problem for highly nonlinear differential-algebraic systems (DAEs, differential-algebraic equations) is considered. The necessary optimality conditions being a consequence of the theory of variational inequalities are derived in the form of structured nonsmooth equations. A new indirect high accuracy optimization algorithm exploiting the chain structure of the mentioned equations is described. It uses the Chen-Harker-Kanzow-Smale smoothing function for the projection operator. A global superlinear (quadratic) convergence of the new algorithm is proven with using the theory of the smoothing Newton method specialized to the multiple shooting approach. The proposed algorithm is verified on the dynamic optimization of a highly nonlinear heat and mass exchange process. In general, the presented considerations have been motivated by the results of numerical simulations presented in the work Pandelidis et al., “Performance study of counter-flow indirect evaporative air coolers” Pandelidis et al. (2015).