Related papers: Periodic trajectory tracking for control-affine dr…
Efficient real-time trajectory planning and control for fixed-wing unmanned aerial vehicles is challenging due to their non-holonomic nature, complex dynamics, and the additional uncertainties introduced by unknown aerodynamic effects. In…
We study control systems invariant under a Lie group with application to the problem of nonlinear trajectory planning. A theory of symmetry reduction of exterior differential systems is employed to demonstrate how symmetry reduction and…
This paper addresses the trajectory-tracking problem for discrete-time linear time-invariant systems with bounded parametric uncertainty, subject to hard constraints on system states, control inputs, and input rates. Unlike existing…
In this article, the continuous time random walk on the circle is studied. We derive the corresponding generalized master equation and discuss the effects of topology, especially important when Levy flights are allowed. Then, we work out…
For a product of i.i.d. random maps or a memoryless stochastic flow on a compact space $X$, we find conditions under which the presence of locally asymptotically stable trajectories (e.g. as given by negative Lyapunov exponents) implies…
We consider the problem of transporting \nota{one probability measure into another through} the flow of a given driftless control-affine system. Under suitable regularity conditions, the controllability of the system by means of open-loop…
We study nonautonomous discrete dynamical systems with randomly perturbed trajectories. We suppose that such a system is generated by a sequence of continuous maps which converges uniformly to a map $f$. We give conditions, under which a…
Tracking the solution of time-varying variational inequalities is an important problem with applications in game theory, optimization, and machine learning. Existing work considers time-varying games or time-varying optimization problems.…
This paper presents a generalization of conventional sliding mode control designs for systems in Euclidean spaces to fully actuated simple mechanical systems whose configuration space is a Lie group for the trajectory-tracking problem. A…
This paper presents a control method and trajectory planner for vehicles with first-order nonholonomic constraints that guarantee asymptotic convergence to a time-indexed trajectory. To overcome the nonholonomic constraint, a fixed point in…
We consider a periodic problem for the motion of a charged particle in a magnetic field. Introducing a notion of Ricci curvature for such Lagrangian systems and using the methods of the calculus of variations in the large, we prove the…
Periodic solutions of the three body problem are very important for understanding its dynamics either in a theoretical framework or in various applications in celestial mechanics. In this paper we discuss the computation and continuation of…
We investigate the convergence towards periodic orbits in discrete dynamical systems. We examine the probability that a randomly chosen point converges to a particular neighborhood of a periodic orbit in a fixed number of iterations, and we…
Periodic and quasi-periodic orbits of the $n$-body problem are critical points of the action functional constrained to the Sobolev space of symmetric loops. Variational methods yield collisionless orbits provided the group of symmetries…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of a new iterative scheme and an effective technique for selecting initial points. The iterative…
A topological approach and understanding to the detection of unstable periodic orbits based on a recently proposed method (PRL 78, 4733 (1997)) is developed. This approach provides a classification of the set of transformations necessary…
In this work, we address the design of tracking controllers that drive a mechanical system's state asymptotically towards a reference trajectory. Motivated by aerospace and robotics applications, we consider fully-actuated systems evolving…
We study a driftless system on a three-dimensional manifold driven by two scalar controls. We assume that each scalar control has an independent bound on its modulus and we prove that, locally around every point where the controlled vector…
In the circular restricted three-body problem, low energy transit orbits are revealed by linearizing the governing differential equations about the collinear Lagrange points. This procedure fails when time-periodic perturbations are…