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This paper presents a novel method of global adaptive dynamic programming (ADP) for the adaptive optimal control of nonlinear polynomial systems. The strategy consists of relaxing the problem of solving the Hamilton-Jacobi-Bellman (HJB)…
Quadratically constrained quadratic programs (QCQPs) are ubiquitous in optimization: Such problems arise in applications from operations research, power systems, signal processing, chemical engineering, and portfolio theory, among others.…
Public transit systems are the backbone of urban mobility systems in the era of urbanization. The design of transit schedules is important for the efficient and sustainable operation of public transit. However, previous studies usually…
This paper investigates the central role played by the Hamiltonian in continuous-time nonlinear optimal control problems. We show that the strict convexity of the Hamiltonian in the control variable is a sufficient condition for the…
In this paper, we consider the problem of deploying a robot from a specification given as a temporal logic statement about some properties satisfied by the regions of a large, partitioned environment. We assume that the robot has noisy…
This paper presents a spatial-based trajectory planning method for automated vehicles under actuator, obstacle avoidance, and vehicle dimension constraints. Starting from a nonlinear kinematic bicycle model, vehicle dynamics are transformed…
This study investigates formal-method-based trajectory optimization (TO) for bipedal locomotion, focusing on scenarios where the robot encounters external perturbations at unforeseen times. Our key research question centers around the…
This paper studies the approximation of optimal control policies by quantized (discretized) policies for a very general class of Markov decision processes (MDPs). The problem is motivated by applications in networked control systems,…
Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO) are among the most successful policy gradient approaches in deep reinforcement learning (RL). While these methods achieve state-of-the-art performance across a…
In recent years, the increasing need for high-performance controllers in applications like autonomous driving has motivated the development of optimization routines tailored to specific control problems. In this paper, we propose an…
We propose FlexQP, an always-feasible convex quadratic programming (QP) solver based on an $\ell_1$ elastic relaxation of the QP constraints. If the original constraints are feasible, FlexQP provably recovers the optimal solution. If the…
This paper examines the question of finding feasible points to discrete-time optimal control problems. The optimization problem of finding a feasible trajectory is transcribed to an unconstrained optimal control problem. An efficient…
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
We consider the problem of adaptive stabilization for discrete-time, multi-dimensional linear systems with bounded control input constraints and unbounded stochastic disturbances, where the parameters of the true system are unknown. To…
As the number of uncontrollable objects in low earth orbit is rising, the thread of collisions and thus the breakdown of working satellites becomes worth analyzing. Consequently, projects on removing objects from the important orbits are…
Combinatorial optimization serves as an essential part in many modern industrial applications. A great number of the problems are offline setting due to safety and/or cost issues. While simulation-based approaches appear difficult to…
We propose a model-based approach to design feedback policies for dexterous robotic manipulation. The manipulation problem is formulated as reaching the target region from an initial state for some non-smooth nonlinear system. First, we use…
In this work, we explore how probabilistic programs can be used to represent policies in sequential decision problems. In this formulation, a probabilistic program is a black-box stochastic simulator for both the problem domain and the…
Scalable multi-robot transition is essential for ubiquitous adoption of robots. As a step towards it, a computationally efficient decentralized algorithm for continuous-time trajectory optimization in multi-robot scenarios based upon model…
This work studies the planning problem for robotic systems under both quantifiable and unquantifiable uncertainty. The objective is to enable the robotic systems to optimally fulfill high-level tasks specified by Linear Temporal Logic (LTL)…