"Deterministic Global Optimization of Dynamic Systems: State-of-the-Art and Opportunities"
Benoit Chachuat
Centre for Process Systems Engineering, Department of Chemical Engineering, Imperial College London
http://www3.imperial.ac.uk/people/b.chachuat Abstract
Many chemical processes are inherently dynamic, such as batch, semi-continuous and cyclic processes, while others are operated in an intentionally transient manner through frequent set-point changes. Optimizing such systems gives rise to dynamic optimization problems, which are often nonconvex and exhibit multiple suboptimal solutions. For those applications where a certificate of global optimality is essential, global optimization methods for dynamic systems are clearly warranted. In the first part of the presentation, I will give an overview of the developments in global dynamic optimization over the last 10+ years. The focus will be on deterministic approaches that can guarantee finite convergence to a global solution at an arbitrary precision. The ability to construct tight interval bounds or, better, convex/concave bounds on the dynamic trajectories is pivotal to the efficacy of these approaches. In the second part, I will present a new class of methods developed in my research group for the construction of convex/concave bounds for parametric nonlinear ODEs. These methods build upon verified solution techniques for ODEs and use a combination of Taylor models and McCormick relaxation to propagate the convex/concave bounds. Both theoretical and implementation issues will be discussed and illustrated through several case studies. I will close the presentation with a vision for future developments in global dynamic optimization.
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