Research On Nonsmooth Control Theory With Application To Spacecraft Systems

Nonsmooth controller not only can improve the convergence rate and the distur-bance rejection ability of the closed-loop systems, but also can be applied to more wide class of systems. The analysis and synthesis issues of nonsmooth control systems have attracted more and more attention in recent years. However, there are still many open problems need to be investigated in this branch. This dissertation mainly discusses the universal finite-time observer (UFTO) problem design for nonlinear systems, global de-centralized stabilization problem of uncertain large-scale upper-triangular systems, the output feedback finite-time stabilization problem of lower-triangular nonlinear stochastic systems, finite-time soft landing control problem of an asteroid probe, finite-time control of 6 degree-of-freedom (6DOF) spacecraft formation flying systems and finite-time atti-tude tracking control problem of spacecraft systems. The main results and contributions of this dissertation can be summarized as follows:(1) For a class of uncertain nonlinear systems that may be subject to disturbances and uncertain parameters, an UFTO design method is proposed. The original system is extended to a new system firstly based on the assumptions that the disturbances and uncertain parameters are satisfied. Then, by using appropriate coordinate transforma-tion, homogeneous system theory and nonsmooth control analysis technique, an UFTO is proposed such that the unmeasured states, unknown parameters, disturbance and its derivatives can be estimated in finite time under a unified framework. Finally, the pro-posed UFTO is employed to estimate the unmeasured states, unknown parameters and disturbances of a hydraulic turbine system. Furthermore, based on the proposed UFTO and the nonsmooth control design method, the finite-time output feedback regulation problem of the hydraulic turbine system is solved.(2) For a class of uncertain large-scale upper-triangular nonlinear systems with non-Lipschitz nonlinear terms, a global decentralized controller design method is proposed. First, the adding a power integrator method is utilised to design nonsmooth controller for the nominal system of every subsystems, such that every nominal subsystem can be globally asymptotically stabilized. And it can be shown that under the proposed nonsmooth decentralized controller the whole large-scale system is locally asymptotical-ly stable. Then, a series of nested saturation functions are imposed on the proposed nonsmooth decentralized controller, a saturated decentralized controller is obtained. Fi-nally, from bottom to top, it is proved that by adjusting the saturation levels, under the obtained saturated nonsmooth decentralized controller the whole closed-loop system is globally asymptotically stable.(3) For a class of p-norm form lower-triangular nonlinear stochastic systems, a global finite-time output feedback control method is proposed. First of all, based on adding a power integrator method and homogeneous system theory, a homogeneous reduced order observer and controller are constructed in a recursive manner. Then, homogeneous domination approach is used to deal with the nonlinearities in the drift and diffusion terms. It is shown that the proposed output feedback controller can render that the closed-loop systems is globally finite time stable in probability. Numerical simulation examples demonstrate the effectiveness and rationality of the proposed control approach.(4) For a class of asteroid centered probe landing system described by two di-mensional dynamic equations, a finite-time control scheme for soft landing based on line-of-sight angle is proposed. Firstly, as the system has the characteristics of multi-variable, nonlinear and strong coupled, the landing error dynamics of asteroid probe is divided into two subsystems, including a position error subsystem and a line-of-sight angle error subsystem. Secondly, homogenous system theory is used to design controller for line-of-sight angle error subsystem, such that the states of line-of-sight angle error subsystem will converge to the origin in finite time. Finally, homogenous system theory is used again to design finite-time controller for the reduced position error subsystem. Strict analysis shows that the proposed control method can guarantee the whole system is finite time stable.(5) For a class of 6DOF spacecraft formation flying system, three different finite-time controller design methods are proposed. First of all, based on nonsingular terminal sliding mode method, a local finite-time controller is constructed. Secondly, UFTO is used to estimate the disturbances, and then a composite finite-time controller which is composed by a nonsingular terminal sliding mode controller and a feedforward compen-sation term based on UFTO technique is proposed. The merit of the proposed method is that chattering is significantly reduced. Finally, based on switching control method, continuous nonsingular terminal sliding mode and UFTO technique, a global finite-time controller is developed for 6DOF spacecraft formation flying system.(6) For a class of spacecraft attitude system, a continuous finite-time attitude track-ing controller is proposed based on a continuous finite-time disturbance observer. First of all, based on homogeneous system theory and saturation technique, a continuous finite-time disturbance observer is constructed for a dynamic system subject to high or-der nonlinear disturbances. Theoretical analysis demonstrates that both the disturbance and its derivatives can be estimated precisely under the proposed continuous finite-time disturbance observer. Then, based on the proposed continuous finite-time disturbance technique, a continuous finite-time controller is developed such that the spacecraft can track the desired attitude precisely. Numerical simulation results illustrate the feasibility of the proposed control scheme.