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We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…
This paper addresses the inverse optimal control problem of finding the state weighting function that leads to a quadratic value function when the cost on the input is fixed to be quadratic. The paper focuses on a class of infinite horizon…
This paper presents and analyzes a reconfigurable intelligent surface (RIS)-based high-altitude platform (HAP) network. Stochastic geometry is used to model the arbitrary locations of the HAPs and RISs as a homogenous Poisson point process.…
We propose two novel algorithms for constructing convex collision-free polytopes in robot configuration space. Finding these polytopes enables the application of stronger motion-planning frameworks such as trajectory optimization with…
We study the problem of computing isochrones in road networks, where the objective is to identify the region that is reachable from a given source within a certain amount of time. While there is a wide range of practical applications for…
This work presents an efficient method to solve a class of continuous-time, continuous-space stochastic optimal control problems of robot motion in a cluttered environment. The method builds upon a path integral representation of the…
A classical approach for solving discrete time nonlinear control on a finite horizon consists in repeatedly minimizing linear quadratic approximations of the original problem around current candidate solutions. While widely popular in many…
This paper investigates the performance of Newton's method, iterative Linear Quadratic Regulator (iLQR), and Differential Dynamic Programming (DDP) in solving discrete-time optimal control problems. We offer a unified perspective on these…
We present a novel linear program for the approximation of the dynamic programming cost-to-go function in high-dimensional stochastic control problems. LP approaches to approximate DP have typically relied on a natural `projection' of a…
Optimal control problems with a very large time horizon can be tackled with the Receding Horizon Control (RHC) method, which consists in solving a sequence of optimal control problems with small prediction horizon. The main result of this…
This paper describes the structure of optimal policies for discounted periodic-review single-commodity total-cost inventory control problems with fixed ordering costs for finite and infinite horizons. There are known conditions in the…
Collisions are common in many dynamical systems with real applications. They can be formulated as hybrid dynamical systems with discontinuities automatically triggered when states transverse certain manifolds. We present an algorithm for…
In this paper we provide optimal bounds for fully discrete approximations to finite horizon problems via dynamic programming. We adapt the error analysis in \cite{nos} for the infinite horizon case to the finite horizon case. We prove an a…
This paper presents a novel non-stationary dynamic pricing algorithm design, where pricing agents face incomplete demand information and market environment shifts. The agents run price experiments to learn about each product's demand curve…
Semidefinite programs (SDPs) are convex optimization programs with vast applications in control theory, quantum information, combinatorial optimization and operational research. Noisy intermediate-scale quantum (NISQ) algorithms aim to make…
Inverse kinematics (IK) is central to robot control and motion planning, yet its nonlinear kinematic mapping makes it inherently nonconvex and particularly challenging under complex constraints. We present IKSPARK (Inverse Kinematics using…
This study describes the development of a novel numerical optimization framework to maximize the endurance of unmanned aerial vehicles (UAVs). We address the problem of numerically determining the optimal thrust and cruise angle of attack…
We consider stochastic impulse control problems when the impulses cost functions are arbitrary. We use the dynamic programming principle and viscosity solutions approach to show that the value function is a unique viscosity solution for the…
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…
This paper proposes a new simultaneous terahertz (THz) information and power transfer (STIPT) system, which is assisted by reconfigurable intelligent surface (RIS) for both the information data and power transmission. We aim to maximize the…