Victor Zavala, a computational mathematician in Argonne’s MCS Division, delivered a keynote speech at the International Symposium on Advanced Control of Chemical Processes (ADCHEM) June 9, 2015, in British Columbia, Canada. ADCHEM is a triennial meeting of the International Federation of Automatic Control that brings together researchers and practitioners to discuss recent developments in the control of chemical, biochemical, and related process systems.
Zavala’s lecture was titled “A Multiobjective Optimization Perspective on the Stability of Economic MPC.” Model predictive control (MPC) is a powerful technique to control dynamical systems that relies on real-time solutions of optimization problems over a rolling horizon. MPC was formulated in the late 1970s to enable practitioners in the chemical industry to optimize different objective functions, satisfy physical constraints and coordinate control loops in a systematic way.
“Before MPC, control loops had to be tuned in an ad hoc manner to achieve these goals—a major impediment since an industrial system can have hundreds to thousands of loops,” said Zavala. MPC has been adopted by myriad industries including aerospace, robotics, buildings, and manufacturing and has generated billions of dollars in savings and much safer operations.
Despite its great practical success, however, MPC is inherently unstable. And while constraints can be imposed to avoid this instability, they severely restrict the type of cost function that can be used – which contradicts one of the basic reasons industry invented MPC in the first place.
In his keynote Zavala presented a multiobjective optimization technique that quantifies how much stability can be sacrificed to optimize economics. Using this technique, he has designed a stabilizing constraint for an MPC controller that optimizes economic performance. Moreover, he has proved that the constraint can always be satisfied and that the economic MPC controller is always stable.
Multiobjective optimization theory also enables Zavala to prove that when stability and economics are conflicting, the dual variable of the stabilizing constraint can be interpreted as a “price of stability.” In his keynote Zavala explains why this approach is important:
“Stability is typically enforced very strictly by practitioners because they do not know exactly how much flexibility they have. In some cases, economics and stability conflict very strongly; but in some cases they are not conflicting at all – and we do not know that! The price of stability can be used to detect situations like this one.”
The multiobjective optimization setting also has enabled Zavala to integrate different economic MPC controllers. In particular, researchers have proposed to weight economic and tracking objectives or to extend the economic MPC formulation by using a decay constraint. Zavala has proved that both these strategies are special cases of his formulation and hence can be incorporated into his unified framework.
For a copy of Zavala’s paper, see http://www.mcs.anl.gov/papers/P5283-0115.pdf.
For information about the conference, see the website http://adchem2015.org.