Related papers: Control of Homodirectional and General Heterodirec…
In this paper, we study the homogenization of the third boundary value problem for semilinear parabolic PDEs with rapidly oscillating periodic coefficients in the weak sense. Our method is entirely probabilistic, and builds upon the work of…
This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary…
This paper addresses forward motion control for trajectory tracking and mobile formation coordination for a group of non-holonomic vehicles on SE(2). Firstly, by constructing an intermediate attitude variable which involves vehicles'…
We study the boundary control of solutions of the Helmholtz and Maxwell equations to enforce local non-zero constraints. These constraints may represent the local absence of nodal or critical points, or that certain functionals depending on…
Solving partial differential equations (PDEs) using neural networks has become a central focus in scientific machine learning. Training neural networks for singularly perturbed problems is particularly challenging due to certain parameters…
In this paper, we address the robustness of parabolic-elliptic systems under boundary control. A sliding mode control strategy is proposed to reject matched perturbations. The stability analysis establishes finite-time convergence of the…
This paper deals with the problem of string stability of interconnected systems with double-integrator open loop dynamics (e.g.~acceleration-controlled vehicles). We analyze an asymmetric bidirectional linear controller, where each vehicle…
An omnidirectional multirotor has the maneuverability of decoupled translational and rotational motions, superseding the traditional multirotors' motion capability. Such maneuverability is achieved due to the ability of the omnidirectional…
The present paper represents a continuation of our previous one. There, a continuous dependence result for the solution of an elliptic variational-hemivariational inequality was obtained and then used to prove the existence of optimal pairs…
Adiabatic protocols are employed across a variety of quantum technologies, from implementing state preparation and individual operations that are building blocks of larger devices, to higher-level protocols in quantum annealing and…
The positive impacts of platooning on travel time reliability, congestion, emissions, and energy consumption have been shown for homogeneous roadway segments. However, speed limit changes frequently throughout the transportation network,…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
Autonomous driving is achieved by controlling the coupled nonlinear longitudinal and lateral vehicle dynamics. Longitudinal control greatly affects lateral dynamics and must preserve lateral stability conditions, while lateral controllers…
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…
We develop a new variational formulation of the inverse Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundary. We employ optimal control framework,…
This paper presents a novel hybrid control protocol for de-conflicting multiple vehicles with constraints on control inputs. We consider turning rate and linear speed constraints to represent fixed-wing or car-like vehicles. A set of…
We prove controllability results for abstract systems of weakly coupled $N$ evolution equations in cascade by a reduced number of boundary or locally distributed controls ranging from a single up to $N-1$ controls. We give applications to…
In this article we study the minimal time for the exact controllability of one-dimensional first-order linear hyperbolic systems when all the controls are acting on the same side of the boundary. We establish an explicit and easy-to-compute…
For population systems modeled by age-structured hyperbolic partial differential equations (PDEs) that are bilinear in the input and evolve with a positive-valued infinite-dimensional state, global stabilization of constant yield set points…
The problem of robustly, asymptotically stabilizing a point (or a set) with two output-feedback hybrid controllers is considered. These control laws may have different objectives, e.g., the closed-loop systems resulting with each controller…