Dynamic optimization with control vector parameterization using different trial functions: a comparative case study

Solution of Dynamic Optimization Problem (DOP) is a computationally expensive task especially for chemical processes, which are usually highly nonlinear and complex in nature. Hence, there is a need of computational efficient dynamic optimization problem solver. In this work we present a comparative study on different trial functions based control vector parameterization (CVP) approach for solving a dynamic optimization problem. While 0th and 1st order polynomial trial functions are very popular, it is rare to find an application of a higher order polynomial trial function in CVP. There are two major problems in selecting a higher order interpolation technique, namely ill conditioned linear algebraic system to be solved for interpolation and poor interpolation between two data points. Cubic spline interpolation is well known to overcome both of these problems. We, in this work have implemented cubic spline trial function and compared DOP solutions with that using 0th and 1st order trial functions. The proposed cubic spline trial function based CVP approach resulted in two fold benefits compare to the other two trial functions: (1) lesser computational effort to solve the DOP and (2) smaller objective function value for the minimization problem. compare to the other trial functions, namely 0th and 1st order ones. A hypothetical fermentation process was used as an application to illustrate the comparative study for solving the dynamic optimization problem. The objective function in this application is to maximize the product concentration at the end of fedbatch time by optimizing the temporal trajectories of substrate flowrates during fedbatch time. Apart from the two issues mentioned above with the DOP solver, namely computational efforts and better objective function value, there is no free DOP software available to the best knowledge of the authors. The dynamic optimization software developed in this work will shortly be available in the author's webpage for its use by research community.by Nitin Padhiyar and K Shandily