(733b) Computationally Efficient Economic Model Predictive Control: Stability, Performance, Convergence

Traditionally, in the operation of chemical processes, economic optimization and process control are carried out in two different layers in a hierarchical system. Economic optimization is performed in the upper real-time optimization (RTO) layer based on steady-state process models according to certain economic metrics reflecting operation profits or costs. The outputs of the RTO layer are optimal operating points of the process which are sent to a lower layer -- the advanced process control layer. Model predictive control (MPC) is often used in the advanced process control layer. This hierarchical approach has been successful and has been widely used. However, in many processes (for example, the oilsand separation process), the dynamic performance is crucial and the optimization-control separation is either inefficient or inappropriate. Economic model predictive control (EMPC) removes the separation between optimization and control and addresses both in one single layer in the framework of model predictive control. 

Motivated by the lack of an easy-to-implement approach for the construction of terminal cost for EMPC, in our previous work [1], we developed an approach to construct the terminal cost for EMPC and proposed two EMPC algorithms for both infinite-time and finite-time operations. In the approach for the terminal cost construction, an auxiliary nonlinear controller which renders the desired optimal steady state asymptotically stable is taken advantage of. The idea is to take the auxiliary nonlinear controller as a benchmark control system and to design EMPC algorithms that gives better economic performance than the auxiliary nonlinear controller. Two EMPC algorithms for infinite-time and finite-time operations were designed. The two EMPC algorithms give provable (practically) improved economic performance. Because of the terminal cost, there is no requirement on the length of the prediction horizon of the EMPC which means that the developed EMPC algorithms could be very computationally efficient.

In this work, we focus on the rigorous analysis of the stability, performance and convergence properties of the computationally efficient EMPC. We show that for strictly dissipative systems, the proposed economic MPC scheme achieves practical stability and near optimal asymptotic performance. Moreover, we show that exponential stability of the optimal steady state can be achieved if the auxiliary controller is exponentially stabilizing in a strong sense. This condition can be relaxed if the storage function satisfies further assumptions. Achievable performance under exponential stability is also characterized. These results will be demonstrated via numerical examples.

[1] Liu, S.; Zhang, J. & Liu, J. Economic MPC with Terminal Cost and Application to an Oilsand Primary Separation Vessel, Chemical Engineering Science, 2015.