Related papers: Optimal Safe Controller Synthesis: A Density Funct…

Density function describes the density of states in the state space of a dynamic system or a Markov Decision Process (MDP). Its evolution follows the Liouville equation. We show that the density function is the dual of the value function in…

We introduce a novel approach for safe control design based on the density function. A control density function (CDF) is introduced to synthesize a safe controller for a nonlinear dynamic system. The CDF can be viewed as a dual to the…

This paper presents a novel approach for safe control synthesis using the dual formulation of the navigation problem. The main contribution of this paper is in the analytical construction of density functions for almost everywhere…

This paper presents a tractable framework for data-driven synthesis of robustly safe control laws. Given noisy experimental data and some priors about the structure of the system, the goal is to synthesize a state feedback law such that the…

We employ optimal control theory to study the problem of estimating the probability density function from a data set originating from an unknown probability distribution. The original variational problem is reformulated as a multi-stage…

Autonomous systems have witnessed a rapid increase in their capabilities, but it remains a challenge for them to perform tasks both effectively and safely. The fact that performance and safety can sometimes be competing objectives renders…

We consider the problem of navigating a nonlinear dynamical system from some initial set to some target set while avoiding collision with an unsafe set. We extend the concept of density function to control density function (CDF) for solving…

In this paper, we study a safe control design for dynamical systems in the presence of uncertainty in a dynamical environment. The worst-case error approach is considered to formulate robust Control Barrier Functions (CBFs) in an…

This work proposes an optimal safe controller minimizing an infinite horizon cost functional subject to control barrier functions (CBFs) safety conditions. The constrained optimal control problem is reformulated as a minimization problem of…

This letter addresses the constraint compatibility problem of control barrier functions (CBFs), which occurs when a safety-critical CBF requires a system to apply more control effort than it is capable of generating. This inevitably leads…

This paper considers the problem of designing a continuous-time dynamical system that solves a constrained nonlinear optimization problem and makes the feasible set forward invariant and asymptotically stable. The invariance of the feasible…

The control of complex systems faces a trade-off between high performance and safety guarantees, which in particular restricts the application of learning-based methods to safety-critical systems. A recently proposed framework to address…

Ensuring both performance and safety is critical for autonomous systems operating in real-world environments. While safety filters such as Control Barrier Functions (CBFs) enforce constraints by modifying nominal controllers in real time,…

In this paper, we design nonlinear state feedback controllers for discrete-time polynomial dynamical systems via the occupation measure approach. We propose the discrete-time controlled Liouville equation, and use it to formulate the…

We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are…

We present a closed-form optimal control that satisfies both safety constraints (i.e., state constraints) and input constraints (e.g., actuator limits) using a composition of multiple control barrier functions (CBFs). This main contribution…

For a broad class of nonlinear systems, we formulate the problem of guaranteeing safety with optimality under constraints. Specifically, we define controlled safety for differential inclusions with constraints on the states and the inputs.…

This letter presents a density function based safe control synthesis framework for the pursuit-evasion problem. We extend safety analysis to dynamic unsafe sets by formulating a reach-avoid type pursuit-evasion differential game as a robust…

State estimation uncertainty is prevalent in real-world applications, hindering the application of safety-critical control. Existing methods address this by strengthening a Control Barrier Function (CBF) condition either to handle actuation…

This paper considers safe control synthesis for dynamical systems with either probabilistic or worst-case uncertainty in both the dynamics model and the safety constraints. We formulate novel probabilistic and robust (worst-case) control…