MPDopt: A versatile toolbox for adjoint-based model predictive control of smooth and switched nonlinear dynamic systems

Over the years, adjoint-based model predictive control (MPC) has proven to be a viable and effective tool for both offline and online optimization of control sequences for dynamic systems governed by differentiable nonlinear equations. This paper extends this versatile method to a class of nonsmooth systems in which the dynamical equation governing the physical system experiences sudden "switches" when the system changes operational modes. This extension involves only minimal alteration of the basic adjoint-based MPC algorithm. We then further improve this algorithm by introducing control trajectory smoothing via state augmentation. Finally, we present a new Matlab toolbox we have developed, MPDopt, that incorporates all of these developments while being user friendly, easily extensible, and capable of offline trajectory planning for wide range of smooth and switched systems of the present class.