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We prove a concise and easily verifiable criterion on the existence and global stability of stationary solutions for random dynamical systems (RDSs). As a consequence, we can show that the $\omega$-limit sets of all pullback trajectories of…
Safety-critical perception systems require both reliable uncertainty quantification and principled abstention mechanisms to maintain safety under diverse operational conditions. We present a novel dual-threshold conformalization framework…
Soft landing on small celestial bodies (SCBs) poses unique challenges, as gravitational models poorly characterize the higher-order gravitational effects of SCBs. Existing control approaches lack guarantees for safety under gravitational…
This paper investigates the problem of pose synchronization for multiple rigid body systems evolving on the matrix Lie group $\SE(3)$. We propose a distributed hybrid feedback control scheme with global asymptotic stability guarantees using…
The gravitational three-body problem is a fundamental problem in physics and has significant applications to astronomy. Three-body configurations are often considered stable as long the system is hierarchical; that is, the two orbital…
This paper is concerned with the design of optimal control for finite-dimensional control-affine nonlinear dynamical systems. We introduce an optimal control problem that specifically optimizes nonlinear observability in addition to…
This paper presents a control framework designed to enhance the stability and robustness of legged robots in the presence of uncertainties, including model uncertainties, external disturbances, and faults. The framework enables the…
Digital controller design for nonlinear systems may be complicated by the fact that an exact discrete-time plant model is not known. One existing approach employs approximate discrete-time models for stability analysis and control design,…
This paper proposes a control strategy consisting of a robust controller and an Echo State Network (ESN) based control law for stabilizing a class of uncertain nonlinear discrete-time systems subject to persistent disturbances. Firstly, the…
We investigate input-to-state stability (ISS) of infinite-dimensional collocated control systems subject to saturated feedback. Here, the unsaturated closed loop is dissipative and uniformly globally asymptotically stable. Under an…
In the real-world, self-driving vehicles are required to achieve steering maneuvers in both uncontrolled and uncertain environments while maintaining high levels of safety and passengers' comfort. Ignoring these requirements would…
We present a theoretical and numerical framework to compute bifurcations of equilibria and stability of slender elastic rods. The 3D kinematics of the rod is treated in a geometrically exact way by parameterizing the position of the…
The attitude tracking problem for a full-actuated rigid body in 3D is studied using a impulsive system model based on Lie algebra so(3). A nonlinear homogeneous controller is designed to globally track a smooth attitude trajectory in a…
A coupled oscillator system displays enhanced sensitivity of its saturated steady-state (SS) oscillation frequency to small parameter perturbations near an exceptional point degeneracy (EPD), a property that can be used to realize EPD-based…
This paper is devoted to the development of adaptive control schemes for uncertain discrete-time systems, which guarantee robust, global, exponential convergence to the desired equilibrium point of the system. The proposed control scheme…
This paper presents a constraint-enforcing control framework for a class of discrete-time strict-feedback nonlinear systems. The objective is to guarantee closed-loop stability while ensuring forward invariance of a prescribed safe set…
This paper presents a deterministic hybrid observer for the attitude dynamics of a rigid body that guarantees global asymptotical stability. Any smooth attitude observer suffers from the inherent topological restriction that it is…
This paper presents a novel extremum seeking control (ESC) approach for the vibrational stabilization of a class of mechanical systems (e.g., systems characterized by equations of motion resulting from Newton second law or Euler-Lagrange…
Bipedal robots are a prime example of systems which exhibit highly nonlinear dynamics, underactuation, and undergo complex dissipative impacts. This paper discusses methods used to overcome a wide variety of uncertainties, with the end…
This paper investigates the problem of continuous attitude estimation on $SO(3)$ using continuous angular velocity and linear acceleration measurements as well as intermittent linear velocity and inertial vector measurements. First, we…