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Control Barrier Functions (CBFs) have been widely utilized in the design of optimization-based controllers and filters for dynamical systems to ensure forward invariance of a given set of safe states. While CBF-based controllers offer…
Mixed-monotone systems are separable via a decomposition function into increasing and decreasing components, and this decomposition function allows for embedding the system dynamics in a higher-order monotone embedding system. Embedding the…
This work presents new tools for studying reachability and set invariance for continuous-time mixed-monotone dynamical systems subject to a disturbance input. The vector field of a mixed-monotone system is decomposable via a decomposition…
Robust model predictive control algorithms are essential for addressing unavoidable errors due to the uncertainty in predicting real-world systems. However, the formulation of such algorithms typically results in a trade-off between…
A new framework is developed for control of constrained nonlinear systems with structured parametric uncertainties. Forward invariance of a safe set is achieved through online parameter adaptation and data-driven model estimation. The new…
We present a robust data-driven control scheme for an unknown linear system model with bounded process and measurement noise. Instead of depending on a system model in traditional predictive control, a controller utilizing data-driven…
Zonotopes are widely used for over-approximating forward reachable sets of uncertain linear systems for verification purposes. In this paper, we use zonotopes to achieve more scalable algorithms that under-approximate backward reachable…
This paper addresses the conservatism in data-driven reachability analysis for discrete-time linear systems subject to bounded process noise, where the system matrices are unknown and only input--state trajectory data are available.…
The safety region of operation of a system is the subset of allowed outputs for which no undesirable outcome would occur. Knowing if a system would ever leave its safety regions of operation is important information for the planning and…
This paper over-approximates the reachable sets of a continuous-time uncertain system using the sensitivity of its trajectories with respect to initial conditions and uncertain parameters. We first prove the equivalence between an existing…
In this paper, we propose a computationally efficient framework for interval reachability of systems with neural network controllers. Our approach leverages inclusion functions for the open-loop system and the neural network controller to…
A constant-rate multi-mode system is a hybrid system that can switch freely among a finite set of modes, and whose dynamics is specified by a finite number of real-valued variables with mode-dependent constant rates. We introduce and study…
We present a scalable set-valued safety-preserving controller for constrained continuous-time linear time-invariant (LTI) systems subject to additive, unknown but bounded disturbance or uncertainty. The approach relies upon a conservative…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
We present a method to over-approximate reachable tubes over compact time-intervals, for linear continuous-time, time-varying control systems whose initial states and inputs are subject to compact convex uncertainty. The method uses…
Autonomous systems like aircraft and assistive robots often operate in scenarios where guaranteeing safety is critical. Methods like Hamilton-Jacobi reachability can provide guaranteed safe sets and controllers for such systems. However,…
The reachable sets of nonlinear control systems can in general only be numerically approximated, and are often very expensive to calculate. In this paper, we propose an algorithm that tracks only the boundaries of the reachable sets and…
Maintaining safety under adaptation has long been considered to be an important capability for autonomous systems. As these systems estimate and change the ego-model of the system dynamics, questions regarding how to develop safety…
Metric temporal logic (MTL) provides a formal framework for defining time-dependent mission requirements on autonomous vehicles. However, optimizing control decisions subject to these constraints is often computationally expensive. This…
Embedded systems are becoming more in demand to work in dynamic and uncertain environments, and being confined to the strong requirements of real-time. Conventional static scheduling models usually cannot cope with runtime modification in…