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Designing controllers that achieve task objectives while ensuring safety is a key challenge in control systems. This work introduces Opt-ODENet, a Neural ODE framework with a differentiable Quadratic Programming (QP) optimization layer to…
The paper provides results for a non-standard, hyperbolic, 1-D, nonlinear traffic flow model on a bounded domain. The model consists of two first-order PDEs with a dynamic boundary condition that involves the time derivative of the…
Control Barrier Functions (CBFs) have emerged as a powerful tool in the design of safety-critical controllers for nonlinear systems. In modern applications, complex systems often involve the feedback interconnection of subsystems evolving…
Motivated by engineering applications of subsea installation by deepwater construction vessels in oil drilling, and of aid delivery by unmanned aerial vehicles in disaster relief, we develop output-feedback boundary control of…
We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…
This paper proposes a safety-critical controller for dynamic and uncertain environments, leveraging a robust environment control barrier function (ECBF) to enhance the robustness against the measurement and prediction uncertainties…
The safety-critical nature of adaptive cruise control (ACC) systems calls for systematic design procedures, e.g., based on formal methods or control barrier functions (CBFs), to provide strong guarantees of safety and performance under all…
Control barrier function (CBF)-based methods provide the minimum modification necessary to formally guarantee safety in the context of quadratic programming, and strict safety guarantee for safety critical systems. However, most CBF-related…
This paper presents a safe stabilization of the Stefan PDE model with a moving boundary governed by a high-order dynamics. We consider a parabolic PDE with a time-varying domain governed by a second-order response with respect to the…
Bringing dynamic robots into the wild requires a tenuous balance between performance and safety. Yet controllers designed to provide robust safety guarantees often result in conservative behavior, and tuning these controllers to find the…
Ensuring reliable performance in situations outside the Operational Design Domain (ODD) remains a primary challenge in devising resilient autonomous systems. We explore this challenge by introducing an approach for adapting probabilistic…
In this paper, a nonsmooth semilinear parabolic partial differential equation (PDE) is considered. For a reduced basis (RB) approach, a space-time formulation is used to develop a certified a-posteriori error estimator. This error estimator…
This paper investigates the stabilization of a coupled system comprising a parabolic PDE and an elliptic PDE with nonlinear terms. A rigorous backstepping design provides an explicit boundary control law and exponentially convergent…
This paper develops a new control design for guaranteeing a vehicle's safety during lane change maneuvers in a complex traffic environment. The proposed method uses a finite state machine (FSM), where a quadratic program based optimization…
This paper presents an algorithm to apply nonlinear control design approaches in the case of stochastic systems with partial state observation. Deterministic nonlinear control approaches are formulated under the assumption of full state…
We propose a new paradigm for designing efficient p-adaptive arbitrary high order methods. We consider arbitrary high order iterative schemes that gain one order of accuracy at each iteration and we modify them in order to match the…
In this paper, we consider controlling a class of single-input-single-output (SISO) commensurate fractional-order nonlinear systems with parametric uncertainty and external disturbance. Based on backstepping approach, an adaptive controller…
Modern autonomous systems, such as flying, legged, and wheeled robots, are generally characterized by high-dimensional nonlinear dynamics, which presents challenges for model-based safety-critical control design. Motivated by the success of…
In this work, we propose to efficiently solve time dependent parametrized optimal control problems governed by parabolic partial differential equations through the certified reduced basis method. In particular, we will exploit an error…
In this work, we propose a cascaded scheme of linear Model prediction Control (MPC) based on Control Barrier Functions (CBF) with Dynamic Feedback Linearization (DFL) for Vertical Take-off and Landing (VTOL) Unmanned Aerial Vehicles (UAVs).…