Switching cost aware rounding for relaxations of mixed-integer optimal control problems: the two-dimensional case

This article is concerned with a recently proposed switching cost aware rounding (SCARP) strategy in the combinatorial integral decomposition for mixed-integer optimal control problems (MIOCPs). We consider the case of a control variable that is discrete-valued and distributed on a two-dimensional domain. While the theoretical results from the one-dimensional case directly apply to the multidimensional … Read more

Mixed-Integer Optimal Control Problems with switching costs: A shortest path approach

We investigate an extension of Mixed-Integer Optimal Control Problems (MIOCPs) 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 … Read more

Efficient Derivative Evaluation for Rigid-body Dynamics based on Recursive Algorithms subject to Kinematic and Loop Constraints

Simulation, optimization and control of robotic and bio-mechanical systems depend on a mathematical model description, typically a rigid-body system connected by joints, for which efficient algorithms to compute the forward or inverse dynamics exist. Models that e.g.\ include spring-damper systems are subject to both kinematic and loop constraints. Gradient-based optimization and control methods require derivatives … Read more

A switching cost aware rounding method for relaxations of mixed-integer optimal control problems

This article investigates a class of Mixed-Integer Optimal Control Problems (MIOCPs) with switching costs. We introduce the problem class of Minimal-Switching-Cost Optimal Control Problems (MSCP) with an objective function that consists of two summands, a continuous term depending on the state vector and an encoding of the discrete switching costs. State vectors of Mixed-Integer Optimal … Read more

Improved Regularity Assumptions for Partial Outer Convexification of Mixed-Integer PDE-Constrained Optimization problems

Partial outer convexification is a relaxation technique for MIOCPs being constrained by time-dependent differential equations. Sum-Up-Rounding algorithms allow to approximate feasible points of the relaxed, convexified continuous problem with binary ones that are feasible up to an arbitrarily small $\delta > 0$. We show that this approximation property holds for ODEs and semilinear PDEs under … Read more

Approximation Properties of Sum-Up Rounding in the Presence of Vanishing Constraints

Approximation algorithms like sum-up rounding that allow to compute integer-valued approximations of the continuous controls in a weak$^*$ sense have attracted interest recently. They allow to approximate (optimal) feasible solutions of continuous relaxations of mixed-integer control problems (MIOCPs) with integer controls arbitrarily close. To this end, they use compactness properties of the underlying state equation, … Read more

Approximation Properties and Tight Bounds for Constrained Mixed-Integer Optimal Control

We extend recent work on mixed-integer 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. … Read more