Real-time Optimization with Estimation of Experimental Gradients

For good performance in practice, real-time optimization schemes need to be able to deal with the inevitable plant-model mismatch problem. Unlike the two-step schemes combining parameter estimation and optimization, the modifier-adaptation approach uses experimental gradient information and does not require the model parameters to be estimated on-line. The dual modifier-adaptation approach presented in this paper drives the process towards optimality, while paying attention to the accuracy of the estimated gradients. The gradients are estimated from successive operating points generated by the optimization algorithm. The novelty lies in the development of an upper bound on the norm of the gradient errors, which is used as a constraint when determining the next operating point. The proposed approach is demonstrated in simulation via the real-time optimization of a continuous reactor.