Related papers: Optimal Configurations in Coverage Control with Po…

This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…

This paper focuses on finding approximate solutions to stochastic optimal control problems with control domains being not necessarily convex, where the state trajectory is subject to controlled stochastic differential equations. The…

Functional lifting methods provide a tool for approximating solutions of difficult non-convex problems by embedding them into a larger space. In this work, we investigate a mathematically rigorous formulation based on embedding into the…

This paper addresses the problem of longitudinal platooning control of homogeneous vehicles subject to external disturbances, such as wind gusts, road slopes, and parametric uncertainties. Our control objective is to maintain the relative…

The realization space of geometric constraint systems is given by the vanishing locus of polynomials corresponding to natural geometric constraints. Such geometric constraint systems arise in many real-world scenarios such as structural…

A simple and reliable algorithm for collision avoidance maneuvers (CAMs), capable of computing impulsive, multi-impulsive, and low-thrust maneuvers, is proposed. The probability of collision (PoC) is approximated by a polynomial of…

We consider the problem of planning the aggregate energy consumption for a set of thermostatically controlled loads for demand response, accounting price forecast trajectory and thermal comfort constraints. We address this as a…

We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…

In this paper, we study the optimal control of a mixed-autonomy platoon driving on a single lane to smooth traffic flow. The platoon consists of autonomous vehicles, whose acceleration is controlled, and human-driven vehicles, whose…

Intelligent transportation systems have recently emerged to address the growing interest for safer, more efficient, and sustainable transportation solutions. In this direction, this paper presents distributed algorithms for control and…

We introduce a simple, efficient and precise polynomial heuristic for a key NP complete problem, minimum vertex cover. Our method is iterative and operates in probability space. Once a stable probability solution is found we find the true…

For unconstrained control problems, a local convergence rate is established for an $hp$-method based on collocation at the Radau quadrature points in each mesh interval of the discretization. If the continuous problem has a sufficiently…

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

A decomposition-based coverage control scheme is proposed for multi-agent, persistent surveillance missions operating in a communication-constrained, dynamic environment. The proposed approach decouples high-level task assignment from…

We aim to solve a topology optimization problem where the distribution of material in the design domain is represented by a density function. To obtain candidates for local minima, we want to solve the first order optimality system via…

The solution space of any set of power flow equations may contain different number of real-valued solutions. The boundaries that separate these regions are referred to as power flow solution space boundaries. Knowledge of these boundaries…

This paper presents coordination algorithms for groups of mobile agents performing deployment and coverage tasks. As an important modeling constraint, we assume that each mobile agent has a limited sensing/communication radius. Based on the…

This paper concerns the numerical solution of a fully nonlinear parabolic double obstacle problem arising from a finite portfolio selection with proportional transaction costs. We consider the optimal allocation of wealth among multiple…

We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclidean distance cost, in any dimension larger than three.…

Direct collocation methods are powerful tools to solve trajectory optimization problems in robotics. While their resulting trajectories tend to be dynamically accurate, they may also present large kinematic errors in the case of constrained…