Dynamic Optimization Research Based On Tracking The Necessary Conditions Of Optimality

The optimization of dynamic processes has received growing attentions in recent years because of the need in reducing the production cost, improving product quality and satisfying safety requirements. However, due to the uncertainties stemming from model mismatch and process disturbance, the optimal solutions on the basis of nominal models are usually infeasible in practical applications. Hence, open-loop optimization is insufficient in the face of uncertainties.With the rapid development in measurements technology, a kind of measurement-based optimization method, which use the measurements to update the optimal solution basing on the necessary conditions of optimality (NCO), has shown great potential both in research and application area. This approach is referred as the NCO-tracking method and will be considered in this paper. In recent years, the theories studies on NCO-tracking theory have developed greatly. However, as a relatively new theory, there are many unsolved issues. The main innovative work of this paper is as follows.(1) The basic theories of the NCO-tracking which had proposed in the past ten years are systematic summarized. The related work such as the method of optimal profile structure detection are also described in detail.(2) The solution model, which is generated from the nominal optimal solution, is of great significance in NCO-tracking scheme. However, a systematic method for extracting the solution model is still remain to research. In this paper, a new approach for generating the optimal solution model is proposed. On the basis of structure detection and type analysis of optimal profile, it formulates sequential subspace optimization problems, which put the requirements from the follow-up control scheme into account. The simulation results demonstrate that a greatly simplified optimal solution model can be generated by solving sequential subspace optimization problem without human experience and physical insight. (3) In the NCO-tracking scheme, the switching structure of the solution model is supposed not to change with all kinds of uncertainties. However, there are known cases where this assumption is not valid and then the traditional NCO-tracking scheme has no way to deal with. Hence, the unreliability of the above assumption has become a great bottleneck of the traditional NCO-tracking scheme. In this paper, a two-level online identification-based NCO-tracking scheme is proposed. Estimates of states and model parameters are obtained by online identification approach, and the solution model will be updated repeatedly once the Parameter Variation Index shows the solution model has high probability of changing. The results demonstrate that in the cases where the assumption is not valid, the two-level online identification-based NCO-tracking scheme still works normally.