Approximate H∞ end-point optimization for nonlinear dynamic processes

An approach to obtaining performance robustness in an H_∞ sense for end-point optimization of nonlinear dynamic systems is presented. Classically, end-point optimization is performed only for the nominal process model using optimal control methods, and the question of performance robustness to disturbances and model-plant mismatch remains unaddressed. The present contribution solves the endpoint optimization problem for nonlinear affine systems with fixed final time through series expansion of the Hamilton-Jacobi PDE, yielding an arbitrarily fine approximation to the optimal robust end-point controller. As model-plant mismatch is particularly common with chemical batch processes, the suitability of the robust optimizing feedback is demonstrated on a semi-batch reactor simulation example, where robustness to several realistic mismatches is investigated and the results are compared against those for the optimal open-loop policy and the optimal feedback designed for the nominal model