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We introduce a new algorithm to solve constrained nonlinear optimal control problem, with an emphasis on low-thrust trajectory in highly nonlinear dynamics. The algorithm, dubbed Pontryagin-Bellman Differential Dynamic Programming (PDDP),…
We introduce a modeling framework for manipulation planning based on the formulation of the dynamics as a projected dynamical system. This method uses implicit signed distance functions and their gradients to formulate an equivalent…
Quadratic programmingis a class of constrained optimization problem with quadratic objective functions and linear constraints. It has applications in many areas and is also used to solve nonlinear optimization problems. This article focuses…
This paper presents a new fast and robust algorithm that provides fuel-optimal impulsive control input sequences that drive a linear time-variant system to a desired state at a specified time. This algorithm is applicable to a broad class…
This paper uncovers a critical yet overlooked phenomenon in multi-modal large language models (MLLMs): detrimental concept drift within chain-of-thought (CoT) reasoning during non-stationary reinforcement fine-tuning (RFT), where reasoning…
In this paper, we present a novel sufficient condition for the stability of discrete-time linear systems that can be represented as a set of piecewise linear constraints, which make them suitable for quadratic programming optimization…
We propose an adaptive optimization algorithm for solving unconstrained scaled gradient flow problems that achieves fast convergence by controlling the optimization trajectory shape and the discretization step sizes. Under a broad class of…
We study dynamical optimal transport of discrete time systems (dDOT) with Lagrangian cost. The problem is approached by combining optimal control and Kantorovich duality theory. Based on the derived solution, a first order splitting…
We develop novel integrated learning and optimization (ILO) methodologies to solve economic dispatch (ED) and DC optimal power flow (DCOPF) problems for better economic operation. The optimization problem for ED is formulated with load…
In this paper we discuss the use of implicit Runge-Kutta schemes for the time discretization of optimal control problems with evolution equations. The specialty of the considered discretizations is that the discretizations schemes for the…
This paper explores a method for solving constrained optimization problems when the derivatives of the objective function are unavailable, while the derivatives of the constraints are known. We allow the objective and constraint function to…
We propose an implicit neural formulation of optimal transport that eliminates adversarial min--max optimization and multi-network architectures commonly used in existing approaches. Our key idea is to parameterize a single potential in the…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
Learning-based control algorithms require data collection with abundant supervision for training. Safe exploration algorithms ensure the safety of this data collection process even when only partial knowledge is available. We present a new…
Interatomic potentials are essential to go beyond ab initio size limitations, but simulation results depend sensitively on potential parameters. Forward propagation of parameter variation is key for uncertainty quantification, whilst…
In this work, we propose the joint use of a mixed penalty-interior point method and direct search, for addressing nonlinearly constrained derivative-free optimization problems. A merit function is considered, wherein the set of nonlinear…
Quantum optimal control theory (QOCT) aims at finding an external field that drives a quantum system in such a way that optimally achieves some predefined target. In practice this normally means optimizing the value of some observable, a so…
This paper proposes an efficient numerical method based on second-order cone programming (SOCP) to solve dynamic optimal transport (DOT) problems with quadratic cost on staggered grid discretization. By properly reformulating discretized…
Model-based controllers on real robots require accurate knowledge of the system dynamics to perform optimally. For complex dynamics, first-principles modeling is not sufficiently precise, and data-driven approaches can be leveraged to learn…
We present a method for learning unknown parametric constraints from locally-optimal input-output trajectory data. We assume the data is generated by rollouts of stochastic nonlinear dynamics, under a single state or output feedback law and…