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With the increasing need for safe control in the domain of autonomous driving, model-based safety-critical control approaches are widely used, especially Control Barrier Function (CBF)-based approaches. Among them, Exponential CBF (eCBF) is…

Computing optimal feedback controls for nonlinear systems generally requires solving Hamilton-Jacobi-Bellman (HJB) equations, which are notoriously difficult when the state dimension is large. Existing strategies for high-dimensional…

This paper proposes a new framework to model control systems in which a dynamic friction occurs. The model consists in a controlled differential inclusion with a discontinuous right hand side, which still preserves existence and uniqueness…

In this paper, the safety-critical control problem for uncertain systems under multiple control barrier function (CBF) constraints and input constraints is investigated. A novel framework is proposed to generate a safety filter that…

This article introduces the Pareto Control Barrier Function (PCBF) algorithm to maximize the inner safe set of dynamical systems under input constraints. Traditional Control Barrier Functions (CBFs) ensure safety by maintaining system…

The framework of deep operator network (DeepONet) has been widely exploited thanks to its capability of solving high dimensional partial differential equations. In this paper, we incorporate DeepONet with a recently developed policy…

In this paper, we develop safe reinforcement-learning-based controllers for systems tasked with accomplishing complex missions that can be expressed as linear temporal logic specifications, similar to those required by search-and-rescue…

We consider a stochastic optimal control problem where the controller can anticipate the evolution of the driving noise over some dynamically changing time window. The controlled state dynamics are understood as a rough differential…

This paper proposes a safety controller for control-affine nonlinear systems with unmodelled dynamics and disturbances to improve closed-loop robustness. Uncertainty estimation-based control barrier functions (CBFs) are utilized to ensure…

This tutorial paper presents recent work of the authors that extends the theory of Control Barrier Functions (CBFs) to address practical challenges in the synthesis of safe controllers for autonomous systems and robots. We present novel…

Neural network approaches that parameterize value functions have succeeded in approximating high-dimensional optimal feedback controllers when the Hamiltonian admits explicit formulas. However, many practical problems, such as the space…

We address finding the semi-global solutions to optimal feedback control and the Hamilton--Jacobi--Bellman (HJB) equation. Using the solution of an HJB equation, a feedback optimal control law can be implemented in real-time with minimum…

Multi-agent navigation in unknown and cluttered environments has broad applications, yet remains fundamentally challenging. In particular, dense agent-agent and agent-obstacle reactive interactions can exacerbate the inherent competition…

Hamilton-Jacobi (HJ) reachability analysis is a widely used method for ensuring the safety of robotic systems. Traditional approaches compute reachable sets by numerically solving an HJ Partial Differential Equation (PDE) over a grid, which…

Modern nonlinear control theory seeks to endow systems with properties of stability and safety, and have been deployed successfully in multiple domains. Despite this success, model uncertainty remains a significant challenge in synthesizing…

In this paper, we study a stochastic recursive optimal control problem in which the system is governed by a functional forward-backward stochastic differential equation. Under standard assumptions, we establish the dynamic programming…

Reinforcement learning (RL) has demonstrated impressive performance in various areas such as video games and robotics. However, ensuring safety and stability, which are two critical properties from a control perspective, remains a…

Reach-avoid optimal control problems, in which the system must reach certain goal conditions while staying clear of unacceptable failure modes, are central to safety and liveness assurance for autonomous robotic systems, but their exact…

Continuous-time reinforcement learning offers an appealing formalism for describing control problems in which the passage of time is not naturally divided into discrete increments. Here we consider the problem of predicting the distribution…

This paper develops a robust fixed time optimization framework for constrained problems that guarantees exact constraint satisfaction and convergence to KKT points within fixed time , independent of initial conditions. The approach treats…