Related papers: Expanding the Class of Quadratic Control-Lyapunov …
Approximating the action of a matrix function $f(\mathbf{A})$ on a vector $\mathbf{b}$ is an increasingly important primitive in machine learning, data science, and statistics, with applications such as sampling high dimensional Gaussians,…
We present a novel way of generating Lyapunov functions for proving linear convergence rates of first-order optimization methods. Our approach provably obtains the fastest linear convergence rate that can be verified by a quadratic Lyapunov…
Reinforcement learning (RL) exhibits impressive performance when managing complicated control tasks for robots. However, its wide application to physical robots is limited by the absence of strong safety guarantees. To overcome this…
This paper proposes a novel Taylor-Lagrange Control (TLC) method for nonlinear control systems to ensure the safety and stability through Taylor's theorem with Lagrange remainder. To achieve this, we expand a safety or stability function…
This paper presents a novel method for directly incorporating user-defined control input saturations into the calculation of a control Lyapunov function (CLF)-based walking controller for a biped robot. Previous work by the authors has…
Many control policies used in various applications determine the input or action by solving a convex optimization problem that depends on the current state and some parameters. Common examples of such convex optimization control policies…
This paper considers the problem of decentralized goal assignment and trajectory generation for multi-robot networks when only local communication is available, and proposes an approach based on methods related to switched systems and set…
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 a method for control synthesis under spatio-temporal constraints. First, we consider the problem of reaching a set $S$ in a user-defined or prescribed time $T$. We define a new class of control Lyapunov functions, called…
The lack of stability guarantee restricts the practical use of learning-based methods in core control problems in robotics. We develop new methods for learning neural control policies and neural Lyapunov critic functions in the model-free…
This paper introduces a framework for learning a minimum-norm stabilizing controller for a system with unknown dynamics using model-free policy optimization methods. The approach begins by first designing a Control Lyapunov Function (CLF)…
This paper presents a methodology for the construction of simple Control Lyapunov Functionals (CLFs) for boundary controlled parabolic Partial Differential Equations (PDEs). The proposed methodology provides functionals that contain only…
This paper introduces new solvers for the computation of low-rank approximate solutions to large-scale linear problems, with a particular focus on the regularization of linear inverse problems. Although Krylov methods incorporating explicit…
In this paper, we develop a systematic method for constructing a generalized discrete-time control Lyapunov function for the flexible-step Model Predictive Control (MPC) scheme, recently introduced in [2], when restricted to the class of…
This article presents a unified approach to quadratic optimal control for both linear and nonlinear discrete-time systems, with a focus on trajectory tracking. The control strategy is based on minimizing a quadratic cost function that…
Foundation models have achieved tremendous success in different domains. However, their huge computation and storage complexity make these models difficult to fine-tune and also less applicable in practice. Recent study shows training in…
We introduce a new approach to evaluate the largest Lyapunov exponent of a family of nonnegative matrices. The method is based on using special positive homogeneous functionals on $R^{d}_+,$ which gives iterative lower and upper bounds for…
In this study, we propose a novel method that integrates Nonlinear Model Predictive Contour Control (NMPCC) with an Exponentially Stabilizing Control Lyapunov Function (ES-CLF) and Exponential Higher-Order Control Barrier Functions to…
Reinforcement learning (RL) has proven to be particularly effective in solving complex decision-making problems for a wide range of applications. Safe reinforcement learning refers to a class of constrained problems where the constraint…
In this paper, we present the combined learning-and-control (CLC) approach, which is a new way to solve optimal control problems with unknown dynamics by unifying model-based control and data-driven learning. The key idea is simple: we…