Related papers: Data-driven optimal control via linear programming…
This survey is focused on certain sequential decision-making problems that involve optimizing over probability functions. We discuss the relevance of these problems for learning and control. The survey is organized around a framework that…
Research on control using models based on machine-learning methods has now shifted to the practical engineering stage. Achieving high performance and theoretically guaranteeing the safety of the system is critical for such applications. In…
Approximate linear programming (ALP) and its variants have been widely applied to Markov Decision Processes (MDPs) with a large number of states. A serious limitation of ALP is that it has an intractable number of constraints, as a result…
We present a novel approach to control design for nonlinear systems which leverages model-free policy optimization techniques to learn a linearizing controller for a physical plant with unknown dynamics. Feedback linearization is a…
Predictive control, which is based on a model of the system to compute the applied input optimizing the future system behavior, is by now widely used. If the nominal models are not given or are very uncertain, data-driven model predictive…
We consider the infinite dimensional linear programming (inf-LP) approach for solving stochastic control problems. The inf-LP corresponding to problems with uncountable state and input spaces is in general computationally intractable. By…
Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear…
The numerical realization of the dynamic programming principle for continuous-time optimal control leads to nonlinear Hamilton-Jacobi-Bellman equations which require the minimization of a nonlinear mapping over the set of admissible…
We consider the problem of tracking a target whose dynamics is modeled by a continuous It\=o semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds…
This document introduces a strategy to solve linear optimization problems. The strategy is based on the bounding condition each constraint produces on each one of the problem's dimension. The solution of a linear optimization problem is…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
This paper is devoted to a study of infinite horizon optimal control problems with time discounting and time averaging criteria in discrete time. It is known that these problems are related to certain infinite-dimensional linear programming…
Velocity Planning for self-driving vehicles in a complex environment is one of the most challenging tasks. It must satisfy the following three requirements: safety with regards to collisions; respect of the maximum velocity limits defined…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
This paper presents a novel hybrid approach that integrates linear programming (LP) within the loss function of an unsupervised machine learning model. By leveraging the strengths of both optimization techniques and machine learning, this…
In this paper, we explore the interplay between Predictive Control and closed-loop optimality, spanning from Model Predictive Control to Data-Driven Predictive Control. Predictive Control in general relies on some form of prediction scheme…
In this paper, we study the problem of optimizing a linear program whose variables are the answers to a conjunctive query. For this we propose the language LP(CQ) for specifying linear programs whose constraints and objective functions…
Constrained partially observable Markov decision processes (CPOMDPs) have been used to model various real-world phenomena. However, they are notoriously difficult to solve to optimality, and there exist only a few approximation methods for…
The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a…