A semidefinite programming approach for polynomial switched optimal control problems

2019 ◽  
Vol 40 (4) ◽  
pp. 626-646 ◽  
Author(s):  
Ramtin Davoudi ◽  
Seyed Mohammad Hosseini
Keyword(s):  
Optimal Control ◽  
Semidefinite Programming ◽  
Optimal Control Problems ◽  
Programming Approach ◽  
Control Problems

scholarly journals Mixed-integer optimal control problems with switching costs: a shortest path approach

2020 ◽  
Author(s):  
Felix Bestehorn ◽  
Christoph Hansknecht ◽  
Christian Kirches ◽  
Paul Manns
Keyword(s):  
Optimal Control ◽  
Shortest Path ◽  
Switching Costs ◽  
Optimal Control Problems ◽  
Directed Acyclic Graphs ◽  
Shortest Path Problem ◽  
Mixed Integer ◽  
Programming Approach ◽  
Control Problems ◽  
Decomposition Approach

Abstract We investigate an extension of Mixed-Integer Optimal Control Problems by adding switching costs, which enables the penalization of chattering and extends current modeling capabilities. The decomposition approach, consisting of solving a partial outer convexification to obtain a relaxed solution and using rounding schemes to obtain a discrete-valued control can still be applied, but the rounding turns out to be difficult in the presence of switching costs or switching constraints as the underlying problem is an Integer Program. We therefore reformulate the rounding problem into a shortest path problem on a parameterized family of directed acyclic graphs (DAGs). Solving the shortest path problem then allows to minimize switching costs and still maintain approximability with respect to the tunable DAG parameter $$\theta $$ θ . We provide a proof of a runtime bound on equidistant rounding grids, where the bound is linear in time discretization granularity and polynomial in $$\theta $$ θ . The efficacy of our approach is demonstrated by a comparison with an integer programming approach on a benchmark problem.

scholarly journals The linear programming approach to deterministic optimal control problems

1996 ◽  
Vol 24 (1) ◽  
pp. 17-33 ◽  
Author(s):  
Daniel Hernández-Hernández ◽  
Onésimo Hernández-Lerma ◽  
Michael Taksar
Keyword(s):  
Optimal Control ◽  
Linear Programming ◽  
Optimal Control Problems ◽  
Programming Approach ◽  
Control Problems ◽  
Linear Programming Approach
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