Related papers: Differential Dynamic Programming for the Optimal C…
An innovative numerical algorithm for solving infinite-horizon optimal control problems is introduced in this paper, using the IsoCost-HyperSurface (ICHS) concept. In the state space of an optimal control system, an ICHS is defined as a set…
Indirect trajectory optimization methods such as Differential Dynamic Programming (DDP) have found considerable success when only planning under dynamic feasibility constraints. Meanwhile, nonlinear programming (NLP) has been the…
Differential dynamic programming (DDP) is a widely used and powerful trajectory optimization technique, however, due to its internal structure, it is not exempt from local minima. In this paper, we present Differential Dynamic Programming…
We consider an elliptic optimal control problem where the objective functional contains evaluations of the state at a finite number of points. In particular, we use a fidelity term that encourages the state to take certain values at these…
In this paper, we propose two novel decentralized optimization frameworks for multi-agent nonlinear optimal control problems in robotics. The aim of this work is to suggest architectures that inherit the computational efficiency and…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…
We introduce Crocoddyl (Contact RObot COntrol by Differential DYnamic Library), an open-source framework tailored for efficient multi-contact optimal control. Crocoddyl efficiently computes the state trajectory and the control policy for a…
In order to autonomously learn to control unknown systems optimally w.r.t. an objective function, Adaptive Dynamic Programming (ADP) is well-suited to adapt controllers based on experience from interaction with the system. In recent years,…
This study is aimed at answering the famous question of how the approximation errors at each iteration of Approximate Dynamic Programming (ADP) affect the quality of the final results considering the fact that errors at each iteration…
We consider a general class of Dynamic Programming (DP) problems with non-separable objective functions. We show that for any problem in this class, there exists an augmented-state DP problem which satisfies the Principle of Optimality and…
Optimization problems emerging in most of the real-world applications are dynamic, where either the objective function or the constraints change continuously over time. This paper proposes projected primal-dual dynamical system approaches…
We analyze an optimal stopping problem with a constraint on the expected cost. When the reward function and cost function are Lipschitz continuous in state variable, we show that the value of such an optimal stopping problem is a continuous…
We consider the problem of stochastic optimal control, where the state-feedback control policies take the form of a probability distribution and where a penalty on the entropy is added. By viewing the cost function as a Kullback- Leibler…
Due to nonholonomic dynamics, the motion planning of nonholonomic robots is always a difficult problem. This letter presents a Discrete States-based Trajectory Planning(DSTP) algorithm for autonomous nonholonomic robots. The proposed…
Recent work [Ran22] formulated a class of optimal control problems involving positive linear systems, linear stage costs, and elementwise constraints on control. It was shown that the problem admits linear optimal cost and the associated…
The classical Dynamic Programming (DP) approach to optimal control problems is based on the characterization of the value function as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. The DP scheme for the numerical…
Optimal control problems can be solved via a one-shot (single) optimization or a sequence of optimization using dynamic programming (DP). However, the computation of their global optima often faces NP-hardness, and thus only locally optimal…
We formulate and study the infinite dimensional linear programming (LP) problem associated with the deterministic discrete time long-run average criterion optimal control problem. Along with its dual, this LP problem allows one to…
We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and…
Equipping approximate dynamic programming (ADP) with inputconstraints has a tremendous significance. This enables ADP to be applied tothe systems with actuator limitations, which is quite common for dynamicalsystems. In a conventional…