Single-integration mode scheduling for linear time-varying switched systems

This paper considers the problem of optimizing the schedule of modes in a linear time-varying switched system subject to a quadratic cost functional. The switched system optimization is formulated as an infinite-dimensional optimal control problem where a projection-based technique handles an integer constraint. In the proposed implementation, only a single set of differential equations needs to be solved off-line, with no additional simulation required during the optimization. Robustness to numerical errors is enhanced as these differential equations are as smooth as the system´s vector fields, despite the optimization itself being non-smooth. An example demonstrates the optimization algorithm steps and verifies feasibility and convergence.