Assumption 2 (Smoothness of the control problem) We assume that the function f : Rnx×nq 7→ Rx is sufficiently smooth. Note that Lipschitz continuity guarantees the unique existence of a solution x(·) of the differential equations for fixed q by virtue of the Picard-Lindelöf theorem. As we assume unique sensitivities in the following, also the partial derivative functions ∂f ∂x , ∂f ∂q , ∂f ∂x2 ...

We propose a sequential quadratic programming (SQP) method for the optimal control of large-scale dynamical systems. The method uses modified multiple shooting to discretize the dynamical constraints. When these systems have relatively few parameters, the computational complexity of the modified method is much less than that of standard multiple shooting. Moreover, the proposed method is demons...

In this paper, some results are provided for minimum time roll about velocity vector maneuvering with thrust-vectoring and aerodynamic control in effect. The mathematical model for attitude motions of the aircraft is developed. First order necessary conditions for optimality using Pontryagen principle is applied, and the existence of an extreme family of solutions for the maneuver is shown. Mul...

In this paper, some results are provided for minimum time roll about velocity vector maneuvering with thrust-vectoring and aerodynamic control in effect. The mathematical model for attitude motions of the aircraft is developed. First order necessary conditions for optimality using Pontryagen principle is applied, and the existence of an extreme family of solutions for the maneuver is shown. Mul...

We use the idea of the Direct Multiple Shooting Method (presented by H. G. Bock in Proceedings of the 9th IFAC world congress Budapest, Pergamon Press, 1984, for solving optimal control problems) to introduce an algorithm for solving some approximate shortest path problems in motion planning. The algorithm is based on a direct multiple shooting discretization that includes a collinear condition...

In this paper, we propose a numerical method to solve the classic $L^2$-optimal transport problem. Our algorithm is based on use of multiple shooting, in combination with continuation procedure, boundary value problem associated Based viewpoint Wasserstein Hamiltonian flow initial and target densities, our reflects structure underlying exploits it discretization. Several examples are presented ...

Chemical processes are modeled by large-scale, highly-nonlinear process models often governed by unstable dynamics. Dynamic optimization is required to exploit economical performance of these processes in their unstable regions. On the one hand, direct single shooting is able to solve large-scale dynamic optimization problems, but lacks the ability to cope properly with unstable dynamical syste...

In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems typically arise from the convexification of integer control decisions. We treat this problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using an SQP method. Concerning...