Mixed-integer optimal control problems arise in many practical applications combining nonlinear, dynamic, and combinatorial features. To cope with the resulting complexity, several approaches have been suggested in the past. Some of them rely on solving a reformulated and relaxed control problem, referred to as partial outer convexification. Inspired by an efficient algorithm for switching time … Read more
Objective: A promising treatment for congestive heart failure is the implementation of a left ventricular assist device (LVAD) that works as a mechanical pump. Modern LVADs work with adjustable constant rotor speed and provide therefore continuous blood flow; however, recently undertaken efforts try to mimic pulsatile blood flow by oscillating the pump speed. This work … Read more
Time transformation is a ubiquitous tool in theoretical sciences, especially in physics. It can also be used to transform switched optimal con trol problems into control problems with a fixed switching order and purely continuous decisions. This approach is known either as enhanced time transformation, time-scaling, or switching time optimization (STO) for mixed-integer optimal control. … Read more
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
We introduce the concept of sos-convex Lyapunov functions for stability analysis of both linear and nonlinear difference inclusions (also known as discrete-time switched systems). These are polynomial Lyapunov functions that have an algebraic certificate of convexity and that can be efficiently found via semidefinite programming. We prove that sos-convex Lyapunov functions are universal (i.e., necessary … Read more