  


Approximation Properties and Tight Bounds for Constrained MixedInteger Optimal Control
Christian Kirches(christian.kirchesiwr.uniheidelberg.de) Abstract: We extend recent work on mixedinteger nonlinear optimal control prob lems (MIOCPs) to the case of integer control functions subject to constraints. Promi nent examples of such systems include problems with restrictions on the number of switches permitted, or problems that minimize switch cost. We extend a theorem due to [Sager et al., Math. Prog. A, 133(12), 1–23 (2012)] to the case of MIOCPs with constraints on the integer control and show that the integrality gap is zero in function space event after adding constraints of this type. For the time discretized problem, we extend a sumup rounding (SUR) scheme due to [Sager et al., Math. Prog. A, 118(1), 109–149 (2009)] to the new problem class. Our scheme permits to constructively ob tain an εfeasible and εoptimal binary feasible control. We derive two tighter upper bounds on the integer control approximation error made by SUR. For unconstrained binary controls, we reduce the approximation error bound from O(Ω) to O(log Ω) asymptotically, where Ω is the number of binary controls. We further show that this new bound is tight. For constrained binary controls, we show that the approximation problem is more difficult, and we give a proof of an approximation error bound of complexity O(Ω). A numerical example compares our approach to a state of the art MINLP solver and illustrates the applicability of these results when solving MIOCPs using the direct and simultaneous approach. Keywords: Optimal Control · MixedInteger Optimization · Ordinary Differential Equations · Switched Dynamic Systems · Approximation Theory Category 1: Combinatorial Optimization (Approximation Algorithms ) Category 2: Complementarity and Variational Inequalities Category 3: Nonlinear Optimization (Systems governed by Differential Equations Optimization ) Citation: Submitted to Mathematical Programming. Download: [PDF] Entry Submitted: 04/12/2016 Modify/Update this entry  
Visitors  Authors  More about us  Links  
Subscribe, Unsubscribe Digest Archive Search, Browse the Repository

Submit Update Policies 
Coordinator's Board Classification Scheme Credits Give us feedback 
Optimization Journals, Sites, Societies  