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

Novel techniques for the optimization and control of finite-time processes in real-time are pursued. These are developed in the framework of the Hamiltonian optimal control. Two methods are designed. The first one constructs the reference control trajectory as an approximation of the optimal control via the Riccati equations in an adaptive fashion based on the solutions of a set of partial differential equations called the and matrices. These allow calculating the Riccati gain for a range of the duration of the process and the final penalization . The second method introduces input constraints to the general optimization formulation. The notions of linear matrix inequalities allow us to recuperate the Riccati gain as in the first method, but using an infinite horizon optimization method. Finally, the performance of the proposed strategies is illustrated through numerical simulations applied to a batch reactor and a penicillin fed-batch reactor. 1. Introduction Batch processes have received much attention during the past two decades due to developing chemical and pharmaceutical products, new polymers, and recent biotechnological applications. Usually, the engineers state that a batch process has three operative stages: start-up, batch run, and shutdown. While these three stages are widely studied by the engineers for each particular batch process, it is important to note that in a wide number of cases, the batch run stage is far from an optimal operation, supported only with the experience of operators and engineers. Control techniques have been made inroad in the industry in order to improve the performance of the process. In batch context, interesting ideas such as controllability, observability, and stability have been introduced despite the duration of batch processes. Numerous control techniques have been adapted to the peculiarities of these kinds of systems. One example is the model predictive control (MPC). This method is essentially numerical, usually implemented on-line. Most successful industrial applications of MPC reported so far are in refining and petrochemical plants (see for instance [1, 2]), where processes are run near optimal steady-states and model linearizations are reliable approximations. In spite of its many advantages, some undesired disadvantages (such as the high computational cost) have caused a major problem: only a few of the available commercial software packages are cautiously suggested for truly nonlinear batch processes as it is reported in [3]. Here, the optimal control paradigm is tackled, where the Hamiltonian