Egerstedt standard problem
|Egerstedt standard problem|
|Discrete control functions:||3|
|Interior point equalities:||3|
The Egerstedt standard problem is the problem is of an academic nature and was proposed by Egerestedt to highlight the features of an Hybrid System algorithm in 2006 [Egerstedt2006]Author: M. Egerstedt; Y. Wardi; H. Axelsson
Journal: IEEE Transactions on Automatic Control
Title: Transition-time optimization for switched-mode dynamical systems
. It has been used since then in many MIOCP research studies (e.g. [Jung2013]Author: M. Jung; C. Kirches; S. Sager
Booktitle: Facets of Combinatorial Optimization -- Festschrift for Martin Gr\"otschel
Editor: M. J\"unger and G. Reinelt
Publisher: Springer Berlin Heidelberg
Title: On Perspective Functions and Vanishing Constraints in Mixed-Integer Nonlinear Optimal Control
) for benchmarking of MIOCP algorithms.
The mixed-integer optimal control problem after partial outer convexification is given by
If the problem is relaxed, i.e., we demand that be in the continuous interval instead of the binary choice , the optimal solution can be determined by using a direct method such as collocation or Bock's direct multiple shooting method.
The optimal objective value of the relaxed problem with is . The objective value of the binary controls obtained by Combinatorial Integral Approimation (CIA) is . The binary control solution was evaluated in the MIOCP by using a Merit function with additional Lagrange term .
Model description is available in
|[Egerstedt2006]||M. Egerstedt; Y. Wardi; H. Axelsson (2006): Transition-time optimization for switched-mode dynamical systems. IEEE Transactions on Automatic Control, 51, 110--115|
|[Jung2013]||M. Jung; C. Kirches; S. Sager (2013): On Perspective Functions and Vanishing Constraints in Mixed-Integer Nonlinear Optimal Control. Facets of Combinatorial Optimization -- Festschrift for Martin Gr\"otschel|
We present numerical results for a benchmark MIOCP from a previous study  with the addition of switching constraints. In its original form, the problem was:
After partial outer convexification with respect to the integer control v, the binary convexified counterpart problem reads