Simultaneous dynamic optimization strategies: Recent advances and challenges

Simultaneous dynamic optimization strategies, also known as direct transcription methods, have been applied in a wide number of domains. These include off-line 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 approach and emphasize the characteristics, benefits and challenges related to these strategies. In particular, we compare the properties of solutions generated by simultaneous approaches to those of classical variational methods, for a variety of problem classes. We next demonstrate why simultaneous strategies are especially beneficial for dynamic systems with unstable modes, with path constraints and for large-scale, structured problems. Finally, we outline a number of challenges and open research questions that will further improve the effectiveness of these methods on a wider range of applications.