(745b) Improved Modifier-Adaptation Schemes Using Gaussian Processes for Real-Time Optimization

The business benefits of real-time optimization (RTO) are not disputed, but deployment, penetration and success have been relatively low, e.g. compared with long established advanced control techniques. The causes for this are many, but in particular, companies invariably need to employ highly-qualified process control engineers to design, install and continually maintain RTO applications to preserve benefits.

Modifier Adaptation [1,2] has its origins in the technique of Integrated System Optimization and Parameter Estimation [3], but differs in the fact that no parameter estimation is required. These RTO schemes have the ability to reach plant optimality upon convergence, despite the presence of structural plant-model mismatch. However, this comes at the cost of having to estimate gradient terms from process measurements.

This work investigates a new class of modifier-adaptation schemes [4,5], which embed a physical model in order to minimize risk during the exploration, in combination with machine learning techniques to capture the plant-model mismatch in a non-parametric way. In optimizing an uncertain process, a successful modifier-adaptation system must accommodate two conflicting objectives: First, it must optimize the system as well as possible; Second, it must ensure that enough information is known about the system to allow accurate and reliable gradient estimates. In essence, this problem is similar to the dual control problem [6], which has been studied extensively since the early 1960s. It has been well-known that the exact dual-control problem for nonlinear systems is computationally intractable. We present an RTO algorithm that uses Gaussian processes as workhorse, and that relies on trust-region ideas in order to expedite and robustify convergence [7]. The size of the trust region is adjusted based on the Gaussian processes’ ability to capture the plant-model mismatch in the cost and constraints. We furthermore exploit the variance term of the Gaussian processes to maintain sufficient excitation. Finally, we illustrate this new modifier-adaptation scheme on several benchmark problems and compare its performance to other RTO approaches.

References:

1. Chachuat B., Srinivasan B., Bonvin D. (2009) Adaptation strategies for real-time optimization. Comput. Chem. Eng. 33:1557-1567
2. Marchetti A.G., François G., Faulwasser T., Bonvin D. (2016) Modifier adaptation for real-time optimization—Methods and applications. Processes 4:55.
3. Roberts P.D., Williams T.W. (1981) On an algorithm for combined system optimisation and parameter estimation. Automatica 17:199-209.
4. E.A. del-Rio Chanona, J.E. Alves Graciano,E. Bradford, B.Chachuat. (2019) Modifier-Adaptation Schemes Employing Gaussian Processes and Trust Regions for Real-Time Optimization, in: 12th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems (DYCOPS 2019).
5. Ferreira T.A., Shukla H.A., Faulwasser T., Jones C.N., Bonvin D. (2018) Real-time optimization of uncertain process systems via modifier adaptation and Gaussian processes, in: European Control Conference (ECC’18).
6. B. Wittenmark, “Adaptive dual control methods: An overview,” in 5th IFAC Symposium on Adaptive Systems in Control and Signal Processing, 1995, pp. 67–72.
7. Conn A.R., Scheinberg K., Vicente L.N. (2009) Introduction to Derivative-Free Optimization, MPS-SIAM Book Series on Optimization, Philadelphia (PA).