Related papers: Constrained Differential Dynamic Programming: A pr…
Differential Dynamic Programming (DDP) has become a well established method for unconstrained trajectory optimization. Despite its several applications in robotics and controls however, a widely successful constrained version of the…
Trajectory optimization considers the problem of deciding how to control a dynamical system to move along a trajectory which minimizes some cost function. Differential Dynamic Programming (DDP) is an optimal control method which utilizes a…
We present FilterDDP, a differential dynamic programming algorithm for solving discrete-time, optimal control problems (OCPs) with nonlinear equality constraints. Unlike prior methods based on merit functions or the augmented Lagrangian…
Matrix Lie groups are an important class of manifolds commonly used in control and robotics, and optimizing control policies on these manifolds is a fundamental problem. In this work, we propose a novel computationally efficient approach…
In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…
We introduce a new algorithm to solve constrained nonlinear optimal control problem, with an emphasis on low-thrust trajectory in highly nonlinear dynamics. The algorithm, dubbed Pontryagin-Bellman Differential Dynamic Programming (PDDP),…
Motivated by robotic trajectory optimization problems we consider the Augmented Lagrangian approach to constrained optimization. We first propose an alternative augmentation of the Lagrangian to handle the inequality case (not based on…
Distributed optimization algorithms are used in a wide variety of problems involving complex network systems where the goal is for a set of agents in the network to solve a network-wide optimization problem via distributed update rules. In…
By exploiting double-penalty terms for the primal subproblem, we develop a novel relaxed augmented Lagrangian method for solving a family of convex optimization problems subject to equality or inequality constraints. The method is then…
Trajectory following is one of the complicated control problems when its dynamics are nonlinear, stochastic and include a large number of parameters. The problem has significant difficulties including a large number of trials required for…
In complex engineered systems, completing an objective is sometimes not enough. The system must be able to reach a set performance characteristic, such as an unmanned aerial vehicle flying from point A to point B, \textit{under 10 seconds}.…
Differential Dynamic Programming (DDP) is an efficient trajectory optimization algorithm relying on second-order approximations of a system's dynamics and cost function, and has recently been applied to optimize systems with time-invariant…
The continuous nonlinear resource allocation problem (CONRAP) has broad applications in economics, engineering, production and inventory management, and often serves as a subproblem in complex programming. Without relying on monotonicity…
This paper develops a primal-dual dynamical system where the coefficients are designed in closed-loop way for solving a convex optimization problem with linear equality constraints. We first introduce a ``second-order primal" +…
We study a class of optimization problems in which the objective function is given by the sum of a differentiable but possibly nonconvex component and a nondifferentiable convex regularization term. We introduce an auxiliary variable to…
Differential Dynamic Programming (DDP) is one of the indirect methods for solving an optimal control problem. Several extensions to DDP have been proposed to add stagewise state and control constraints, which can mainly be classified as…
We study deterministic and stochastic primal-dual sub-gradient algorithms for distributed optimization of a separable objective function with global inequality constraints. In both algorithms, the norm of the Lagrangian multipliers are…
Differential Dynamic Programming is an optimal control technique often used for trajectory generation. Many variations of this algorithm have been developed in the literature, including algorithms for stochastic dynamics or state and input…
This paper provides an overview, analysis, and comparison of second-order dynamic optimization algorithms, i.e., constrained Differential Dynamic Programming (DDP) and Sequential Quadratic Programming (SQP). Although a variety of these…
This paper is devoted to the theoretical and numerical investigation of an augmented Lagrangian method for the solution of optimization problems with geometric constraints. Specifically, we study situations where parts of the constraints…