On speeding-up modifier-adaptation schemes for real-time optimization

The real-time optimization scheme “modifier adaptation” (MA) has been developed to enforce steady-state plant optimality in the presence of model uncertainty. The key feature of MA is its ability to locally modify the model by adding bias and gradient correction terms to the cost and constraint functions or, alternatively, to the outputs. Since these correction terms are static in nature, their computation may require a significant amount of time, especially with slow processes. This paper presents two ways of speeding-up MA schemes for real-time optimization. The first approach proposes to estimate the modifiers from steady-state data via a tailored recursive least-squares scheme. The second approach investigates the estimation of static correction terms during transient operation. The idea is to first develop a calibration model to express the static plant-model mismatch as a function of inputs only. This calibration model can be generated via a single MA run that successively visits various steady states before reaching plant optimality. In addition, to account for process differences between calibration and subsequent operation, bias terms are estimated online from output measurements. Implementation and performance aspects are compared on two pedagogical examples, namely, an unconstrained nonlinear SISO plant and a constrained multivariable CSTR example.