Related papers: Robust Path-following for Keplerian Orbits
The hodograph of the Kepler-Coulomb problem, that is, the path traced by its velocity vector, is shown to be a circle and then it is used to investigate other properties of the motion. We obtain the configuration space orbits of the problem…
The orbital evolution and stability of planetary systems with interaction from the belts is studied using the standard phase-plane analysis. In addition to the fixed point which corresponds to the Keplerian orbit, there are other fixed…
Stabilization of a coupled system consisting of a parabolic partial differential equation and an elliptic partial differential equation is considered. Even in the situation when the parabolic equation is exponentially stable on its own, the…
Robust control problems have significant practical implications since external disturbances can significantly impact the performance of control methods. Existing robust control methods excel at control-affine systems but fail at neural…
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…
Starting from the second post-Keplerian (2PK) Hamiltonian describing the conservative part of the two-body dynamics in massless scalar-tensor (ST) theories, we build an effective-one-body (EOB) Hamiltonian which is a $\nu$-deformation…
We propose a hybrid feedback control law that guarantees both safety and asymptotic stability for a class of Lagrangian systems in environments with obstacles. Rather than performing trajectory planning and implementing a…
The stability of the orbital motion of two long cylindrical magnets interacting exclusively with magnetic forces is described. To carry out analytical studies a model of magnetically interacting symmetric tops [1] is used. The model was…
Path following and lateral stability are crucial issues for autonomous vehicles. Moreover, these problems increase in complexity when handling articulated heavy-duty vehicles due to their poor manoeuvrability, large sizes and mass…
This paper proposes a new indirect solution method for solving state-constrained optimal control problems by revisiting the well-established optimal control theory and addressing the long-standing issue of discontinuous control and costate…
The paper considers a motion control problem for kinematic models of nonholonomic wheeled systems. The class of maneuverable wheeled systems is defined consisting of systems that can follow any sufficiently smooth non-stop trajectory on the…
In this paper, we investigate collision orbits of two identical bodies placed on the surface of a two-dimensional sphere and interacting via an attracting potential of the form $V(q)=-\cot(q)$, where $q$ is the angle formed by the position…
Understanding the complex patterns in space-time exhibited by active systems has been the subject of much interest in recent times. Complementing this forward problem is the inverse problem of controlling active matter. Here we use optimal…
Many unmanned aerial vehicles (UAVs) can remain aerodynamically flyable after sustaining structural or control surface damage, yet insufficient robustness in conventional autopilots often leads to mission failure. This paper proposes a…
Closed-Form Kepler solutions in projective coordinates are used to define a corresponding set of eight orbit elements and obtain their governing equations for arbitrarily-perturbed two-body dynamics. The elements and their dynamics are…
This work addresses the problem of robust attitude control of quadcopters. First, the mathematical model of the quadcopter is derived considering factors such as nonlinearity, external disturbances, uncertain dynamics and strong coupling.…
To improve our understanding of orbital instabilities in compact planetary systems, we compare suites of $N$-body simulations against numerical integrations of simplified dynamical models. We show that, surprisingly, dynamical models that…
The high-multiplicity exoplanet systems are generally more tightly packed when compared to the solar system. Such compact multi-planet systems are often susceptible to dynamical instability. We investigate the impact of dynamical…
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is to optimize the stress field by controlling the displacement at prescribed parts of…
We numerically investigate the dynamics of orbits in 3D circumbinary phase-space as a function of binary eccentricity and mass fraction. We find that inclined circumbinary orbits in the elliptically-restricted three-body problem display a…