Simultaneous design and control under uncertainty: A back-off approach using power series expansions

- A methodology for simultaneous design and control under uncertainty is developed.
- Back-off approach is used to move progressively to a new feasible operating point.
- PSE approximation is used to obtain analytical expressions for optimal design.
- PSE coefficients were calculated both numerically and analytically.
- Large-scale and highly nonlinear systems can be addressed with the proposed method.

A methodology for simultaneous design and control for dynamic systems under uncertainty has been developed. The algorithm moves away (back-off) from the optimal steady-state design (which is often found to be dynamically infeasible) to a new feasible operating point under process dynamics and parameter uncertainty by solving a set of optimization problems in an iterative manner. Power Series Expansions (PSE) are employed to represent the cost function and constraints in the optimization problems. The challenge in this method is to calculate in a systematic fashion the amount of back-off needed to accommodate the transient operation of the process. The method has been tested on an isothermal storage tank and a waste water treatment plant and the results compared with the formal integration. The results have shown that this method has the potential to address the simultaneous design and control of dynamic systems under uncertainty at lower computational costs.