Collocation and Large-scale Nonlinear Programming for 
Dynamic Optimization in Chemical Engineering

Dedicated to Prof. H. G. Bock on his 60th Birthday

L. T. Biegler
Chemical Engineering Department
Carnegie Mellon University
Pittsburgh, PA 15213 USA

Dynamic optimization strategies based on collocation methods have been
applied over a wide number of engineering applications. They include
offline applications like optimal control, trajectory planning,
nonlinear parameter estimation and optimization of reactors and batch
processes, as well as on-line applications such as nonlinear model
predictive control, nonlinear state estimation and dynamic, real-time
optimization. Here we discuss recent advances for the simultaneous
collocation approach and emphasize the characteristics, benefits and
challenges related to these strategies. These relate to convergence
and stability properties, treatment of inequality constraints and
limiting performance behavior for challenging dynamic optimization
problems.  Moreover, we discuss the realization of these methods
through large-scale NLP strategies. Using full-space barrier methods,
these allow the efficient calculation of gradient and Hessian
information and the exploitation of sparsity. This leads to fast
solutions and sensitivity calculations. Finally, these developments
will be illustrated on several chemical engineering case studies.