Symmetric algorithmic differentiation based exact Hessian SQP method and software for Economic MPC

Economic Model Predictive Control (EMPC) is an advanced receding horizon based control technique which optimizes an economic objective subject to potentially nonlinear dynamic equations as well as control and state constraints. The main contribution of this paper is an algorithmic differentiation (AD) based real-time EMPC algorithm including a software implementation in ACADO Code Generation. The scheme is based on a novel memory efficient, symmetric AD approach for real-time propagation of second order derivatives. This is used inside a tailored multiple-shooting based SQP method, which employs a mirrored version of the exact Hessian. The performance of the proposed auto-generated EMPC algorithm is demonstrated for the optimal control of a nonlinear biochemical reactor benchmark case-study. A speedup of a factor more than 2 can be shown in the CPU time for integration and Hessian computation of this example.