Welcome to Optimal Control!

These web pages provide general information on optimal control problems, software, and applications. The download section gives access to software packages developed by Prof. Dr. Matthias Gerdts for registered users subject to an academic user license agreement. Suggestions and contributions are welcome!

What is optimal control about?

Basically, an optimal control problem aims to find control and state functions such that a performance criterion is optimized. To this end, a common optimal control problem consists of

  • state variables which describe the state of a dynamic process
  • control variables which allow to influence the dynamic behavior of the process
  • ordinary/partial/stochastic differential equations (ODEs/PDEs/SDEs) or differential-algebraic equations (DAEs) which define a model of the dynamic behavior of the process
  • control or state constraints which need to be obeyed
  • performance criterion (cost function/objective function) which has to be minimized or maximized.


Optimal control problems arise in many exciting applications in science, economy, and engineering. Examples are trajectory optimization in robotics, aerospace engineering (ascent/descent/emergency trajectories, orbit transfers,...), vehicle simulation (avoidance trajectories, virtual testdriving, chassis control,...), controller design (LQR, model-predictive control, ...), process engineering (chemical processes, ...), fishing strategies, etc.


docking maneuver for
space debris removal

virtual testdrives and
driver assistance systems

model-predictive control of cars 
in road traffic scenario