Suboptimal Control Strategies for Finite-Time Nonlinear Processes with Input Constraints

Novel techniques for the optimization and control of finite-timeprocesses in real-time are pursued. These are developed in the frameworkof the Hamiltonian optimal control. Two methods are designed. The firstone constructs the reference control trajectory as an approximation of theoptimal control via the Riccati equations in an adaptive fashion basedon the solutions of a set of partial differential equations called the α andβ matrices. These allow calculating the Riccati gain for a range of theduration of the process T and the final penalization S. The second methodintroduces input constraints to the general optimization formulation. Thenotions of linear matrix inequalities allow us to recuperate the Riccati gainas in the first method, but using an infinite horizon optimization method. Finally, the performance of the proposed strategies is illustrated throughnumerical simulations applied to a batch reactor and a penicillin fed-batchreactor