Evolution equation analysis and dynamic optimization of time-dependent industrial process systems

Abstract

Time-dependent industrial processes experience varying operating conditions, uncertainties in process parameters, disturbances and operational constraints. Traditional static and nominal optimization techniques may perform well under expected conditions; however, become susceptible to unfavorable parameter combinations. In this research, the problem of robust dynamic optimization for time-dependent industrial processes is considered. An evolution equation-based minimax dynamic optimization technique is formulated, which integrates time-dependent state evolution, control, parameter uncertainties and operational constraints into one model. The dynamic process is described using time-dependent operators and nonlinear state functions, while optimization involves the minimization of maximum objective over a feasible uncertainty set. Discretization is used to solve the dynamic state equations, generate worst-case realizations, update control trajectories and check the convergence of the proposed algorithm. The algorithm is compared with deterministic optimization, nominal dynamic optimization, robust optimization and stochastic optimization. The developed methodology had the worst objective of 12.86, which is better than the objectives obtained using the corresponding baseline methodologies: 17.92, 16.43, 14.21, and 13.87. The method satisfied all the constraints and had the minimum stability error of 0.029. The objective function was reduced from 18.72 to 12.86 over 50 iterations. Under uncertainties ranging between 5% and 25%, the objective function increased by just 10.10%, thus showing that the approach has better robustness against uncertain parameter changes. The ablation study revealed that the key components are minimax optimization, uncertainty modeling, time-varying parameters, and dynamic constraints.