Related papers: Geometric control theory of vertical rolling disc …
Geometric optimal control utilizes tools from differential geometry to analyze the structure of a problem to determine the control and state trajectories to reach a desired outcome while minimizing some cost function. For a controlled…
In this article, we survey the primary research on polyhedral computing methods for constrained linear control systems. Our focus is on the modeling power of convex optimization, featured to design set-based robust and optimal controllers.…
We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set $\Omega$. The considered problems are well studied for the case when $\Omega$ is a unit disc, but barely studied for…
In this paper we study the problem of designing periodic orbits for a special class of hybrid systems, namely mechanical systems with underactuated continuous dynamics and impulse events. We approach the problem by means of optimal control.…
Optimal control problems are formulated and efficient computational procedures are proposed for combined orbital and rotational maneuvers of a rigid body in three dimensions. The rigid body is assumed to act under the influence of forces…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
Necessary conditions for existence of normal extremals in optimal control of systems subject to nonholonomic constraints are derived as solutions of a constrained second order variational problems. In this work, a geometric interpretation…
We show an example providing a significance in geometric control theory of the existence of the dependence locus of a system of vector fields in particular, the generic appearance of non-trivial singular trajectories embedded in the…
We develop a differential geometric framework for parallel transport over path spaces and a corresponding discrete theory, an integrated version of the continuum theory, using a category-theoretic framework.
In this thesis, we provide new insights into the theory of cascade feedback linearization of control systems. In particular, we present a new explicit class of cascade feedback linearizable control systems, as well as a new obstruction to…
This paper explores the role of symmetries and reduction in nonlinear control and optimal control systems. The focus of the paper is to give a geometric framework of symmetry reduction of optimal control systems as well as to show how to…
The goal of quantum tracking control is to identify shaped fields to steer observable expectation values along designated time-dependent tracks. The fields are determined via an iteration-free procedure, which is based on inverting the…
This note proposes a general control approach, called vector-field guided constraint-following control, to solve the dynamics control problem of geometric path-following for a class of uncertain mechanical systems. More specifically, it…
In this paper, we demonstrate an approach to quantum robust control based on the tools of geometric optimal control. The central objects of interest are the sensitivity functions defined as the coefficients in the Taylor expansion of the…
In this paper we exploit some interesting properties of a class of bipedal robots which have an inertial disc. One of this properties is the ability to control every position and speed except for the disc position. The proposed control is…
In this paper, we propose a framework for designing sliding mode controllers for a class of mechanical systems with symmetry, both unconstrained and constrained, that evolve on principal fiber bundles. Control laws are developed based on…
This paper presents an experimental study of a path-tracking framework for autonomous vehicles in which the lateral control command is applied to a dynamic control point along the wheelbase. Instead of enforcing a fixed reference at either…
The symmetric product of vector fields on a manifold arises when one studies the controllability of certain classes of mechanical control systems. A geometric description of the symmetric product is provided using parallel transport, along…
This paper addresses the time-optimal control problem for a class of control systems which includes controlled mechanical systems with possible dissipation terms. The Lie algebras associated with such mechanical systems enjoy certain…
Recent developments in extreme value statistics have established the so-called geometric approach as a powerful modelling tool for multivariate extremes. We tailor these methods to the case of spatial modelling and examine their efficacy at…