Jihao Luo

Control of underactuated spacecraft with bounded inputs

Bounded feedback control laws are designed for stabilization and tracking of underactuated spacecraft. The flat outputs of the system are computed and are used to generate reference trajectories for the tracking problem.

Exponentially convergent control laws for nonholonomic systems in power form

Abstract This paper introduces a method for constructing exponentially convergent control laws for n -dimensional nonholonomic systems in power form. The methodology is based on the construction of a series of nested invariant manifolds for the closed-loop system under a linear control law. A recursive algorithm is presented which uses these manifolds to construct a three-dimensional system in power form. It is shown that the feedback controller for the original system is the one for this three-dimensional system with a proper choice of the gains.

Control design for chained-form systems with bounded inputs

Discontinuous, time-invariant controllers have been recently proposed in the literature as an alternative method to stabilize nonholonomic systems. These control laws are not continuous at the origin and although they provide exponential rates of convergence, they may use significant amount of control effort, especially if the initial conditions are close to an equilibrium manifold. We seek to remedy this situation by constructing bounded controllers (with exponential convergence rates) for nonholonomic systems in chained form.

Reduced Effort Control Laws for Underactuated Rigid Spacecraft

A nonsmooth, time-invariant feedback control law can be used to rotate an axisymmetric rigid spacecraft to the zero equilibriumusingonly twocontroltorques.Thismethod,however, may requireasignie cantamountofcontrol effort, especially for initial conditions close to an equilibrium manifold corresponding to rotations about the unactuated principal axis.Acontrollawisproposedin thiswork thatreducesthecontroleffortrequired toperformrestto-restmaneuversforinitialconditionsclosetothisequilibrium manifold.Specie cally,thephasespaceofthesystem is divided into two parts, one corresponding to initial conditions producing large control effort (the “ bad” region ) and theothercorresponding to initialconditionsproducing small control signals (the“ good” region ). Theproposed control lawthen rendersthisundesirableequilibrium manifold unstable, driving the trajectoriesof theclosed-loop system into the good region, where the original control law is subsequently used. Numerical simulations indicate reduction of the control magnitude on theorder of 80 ‐90% for initial conditions close to theequilibrium manifold.

Control design for systems in chained form with bounded inputs

Discontinuous, time-invariant controllers have been recently proposed in the literature as an alternative method to stabilize nonholonomic systems. These control laws are not Lipschitz continuous at the origin and hence they may use significant amount of control effort, especially if the initial conditions are close to an equilibrium manifold. We seek to remedy this situation by constructing bounded convergent controllers (with exponential convergence rates) for nonholonomic systems in chained form.

Stabilization and Tracking of Underactuated Axisymmetric Spacecraft with Bounded Control

Abstract We provide stabilizing and tracking feedback control laws for the kinematic system of an underactuated axisymmetric spacecraft subject to input constraints. As a special case we also provide a feedback control to track a specified direction in inertial space. All proposed control laws achieve asymptotic stability with exponential convergence. One of the novelties of the proposed control design is the use of a new, non-standard description of the attitude motion, which allows the decomposition of the general motion into two rotations. This attitude description is especially useful for analyzing axisymmetric bodies, where the motion of the symmetry axis maybe of prime importance.

Exponentially convergent controllers for n-dimensional nonholonomic systems in power form

Introduces a method for constructing exponentially convergent control laws for n-dimensional nonholonomic systems in power form. The methodology is based on the construction of a series of invariant manifolds for the closed-loop system under a linear control law. A recursive algorithm is presented to derive a feedback controller which drives the system exponentially to the origin. A numerical example illustrates the proposed theoretical developments.

A reduced-effort control law for underactuated rigid bodies

Previous results show that a nonsmooth, time-invariant feedback control law can be used to stabilize an axisymmetric rigid body using only two control torques to the zero equilibrium. This method, however, may require a significant amount of control effort, especially for initial conditions close to an equilibrium manifold. In this paper we propose a modification of the previous control law which reduces the control effort required. A rigid spacecraft is considered.

LFT REPRESENTATIONS FOR NONLINEAR MECHANICAL SYSTEMS

Abstract In this paper, we present a systematic methodology for constructing LFT representations for general mechanical systems derived via Lagranges equations. The LFT representation allows for any nonlinear matrix second-order mechanical system to be transformed into an interconnection of an LTI system with a diagonal “uncertainty” block. This uncertainty block is, in fact, state-dependent. Sufficient conditions that ensure well-posedness of the LFT interconnection are given. Using such LFT representations, the stability properties of the system can then be analyzed using Linear Matrix Inequalities (LMIs).