Global optimal control with the direct multiple shooting method
نویسندگان
چکیده
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 , ∂f ∂q2 , ∂f ∂x∂q are assumed to be Lipschitz continuous. Furthermore, we assume that there exists at least one feasible q∗ ∈ Q for (1).
منابع مشابه
Direct Multiple Shooting Method for Finding Approximate Shortest Paths in Polygonal Environments
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...
متن کاملFast Direct Multiple Shooting Algorithms for Optimal Robot Control
In this overview paper, we first survey numerical approaches to solve nonlinear optimal control problems, and second, we present our most recent algorithmic developments for real-time optimization in nonlinear model predictive control. In the survey part, we discuss three direct optimal control approaches in detail: (i) single shooting, (ii) collocation, and (iii) multiple shooting, and we spec...
متن کاملDistributed Multiple Shooting for Optimal Control of Large Interconnected Systems
Large interconnected systems consist of a multitude of subsystems with their own dynamics, but coupled with each other via input-output connections. Each subsystem is typically modelled by ordinary differential equations or differential-algebraic equations. Simulation and optimal control of such systems pose a challenge both with respect to CPU time and memory requirements. We address optimal c...
متن کاملBlock-structured quadratic programming for the direct multiple shooting method for optimal control
In this contribution we address the efficient solution of optimal control problems of dynamic processes with many controls. Such problems arise, e.g., from the outer convexification of integer control decisions. We treat this optimal control problem class using the direct multiple shooting method to discretize the optimal control problem. The resulting nonlinear problems are solved using sequen...
متن کاملComplementary Condensing for the Direct Multiple Shooting Method
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...
متن کامل