Related papers: Global Adaptive Dynamic Programming for Continuous…
A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and…
This paper build on our recent work where we presented a dual stochastic optimal control formulation of the nonlinear filtering problem [1]. The constraint for the dual problem is a backward stochastic differential equations (BSDE). The…
In this paper, we propose a generalized alternating direction method of multipliers (ADMM) with semi-proximal terms for solving a class of convex composite conic optimization problems, of which some are high-dimensional, to moderate…
We are interested in high-order linear multistep schemes for time discretization of adjoint equations arising within optimal control problems. First we consider optimal control problems for ordinary differential equations and show loss of…
We propose a parallel algorithm for the numerical solution of a class of second order semi-linear equations coming from stochastic optimal control problems, by means of a dynamic domain decomposition technique. The new method is an…
This paper is about operator-theoretic methods for solving nonlinear stochastic optimal control problems to global optimality. These methods leverage on the convex duality between optimally controlled diffusion processes and…
Many modern computer vision and machine learning applications rely on solving difficult optimization problems that involve non-differentiable objective functions and constraints. The alternating direction method of multipliers (ADMM) is a…
We propose new methods to speed up convergence of the Alternating Direction Method of Multipliers (ADMM), a common optimization tool in the context of large scale and distributed learning. The proposed method accelerates the speed of…
For continuous systems modeled by dynamical equations such as ODEs and SDEs, Bellman's Principle of Optimality takes the form of the Hamilton-Jacobi-Bellman (HJB) equation, which provides the theoretical target of reinforcement learning…
Trajectory optimization is an efficient approach for solving optimal control problems for complex robotic systems. It relies on two key components: first the transcription into a sparse nonlinear program, and second the corresponding solver…
In this paper we introduce an iterative Jacobi algorithm for solving distributed model predictive control (DMPC) problems, with linear coupled dynamics and convex coupled constraints. The algorithm guarantees stability and persistent…
Many optimal control problems are formulated as two point boundary value problems (TPBVPs) with conditions of optimality derived from the Hamilton-Jacobi-Bellman (HJB) equations. In most cases, it is challenging to solve HJBs due to the…
In this paper we propose and analyze a method based on the Riccati transformation for solving the evolutionary Hamilton-Jacobi-Bellman equation arising from the stochastic dynamic optimal allocation problem. We show how the fully nonlinear…
Safe operation of systems such as robots requires them to plan and execute trajectories subject to safety constraints. When those systems are subject to uncertainties in their dynamics, it is challenging to ensure that the constraints are…
We develop a new Approximate Dynamic Programming (ADP) method for infinite horizon discounted reward Markov Decision Processes (MDP) based on projection onto a subsemimodule. We approximate the value function in terms of a $(\min,+)$ linear…
This paper develops a method for obtaining guaranteed outer approximations for global attractors of continuous and discrete time nonlinear dynamical systems. The method is based on a hierarchy of semidefinite programming problems of…
We develop dynamical programming methods for the purpose of optimal control of quantum states with convex constraints and concave cost and bequest functions of the quantum state. We consider both open loop and feedback control schemes,…
While globally optimal solutions to many convex programs can be computed efficiently in polynomial time, this is, in general, not possible for nonconvex optimization problems. Therefore, locally optimal approaches or other efficient…
This paper studies the optimal control problem for discrete-time nonlinear systems and an approximate dynamic programming-based Model Predictive Control (MPC) scheme is proposed for minimizing a quadratic performance measure. In the…
To ensure the system stability of the $\bf{\mathcal{H}_{2}}$-guaranteed cost optimal decentralized control problem (ODC), an approximate semidefinite programming (SDP) problem is formulated based on the sparsity of the gain matrix of the…