The disturbance decoupling problem for nonlinear control systems

Necessary and sufficient conditions are derived for the solution of the disturbance decoupling problem for general nonlinear control systems. Some conceptual algorithms needed are discussed.     

The finite-time almost disturbance decoupling for nonlinear systems

The finite-time almost disturbance decoupling problem is investigated for nonlinear systems in strict feedback form using backstepping. A recursive design algorithm is proposed to construct a continuous stabilising feedback controller so that the corresponding closed-loop system is finite-time stable when there is no external disturbances and the influence of the external disturbances on the output is attenuated to a given degree. This paper is the first to solve the finite-time almost disturbance decoupling problem. Two examples are given to show the feasibility of the proposed design method.     

The disturbance decoupling problem with stability for switching dynamical systems

The disturbance decoupling problem with stability is dealt with by means of the geometric approach for switching systems. The existence of feedbacks which decouple the disturbance and, at the same time, assure stability is difficult to characterize, since the action of the feedback couples with that of the switching law. Under suitable conditions, it is shown that the above requirement can be dealt with in separate ways and this allows us to state a checkable necessary condition and, on that basis, also a sufficient condition for solvability of the problem.     

Output feedback disturbance decoupling in nonlinear systems

The problem of disturbance decoupling by means of output feedback is addressed. The notion of conditioned invariance is reconsidered in a linear algebraic framework. Using this geometric notion, a necessary and sufficient condition (respectively, necessary condition) is obtained for solving the disturbance decoupling problem by quasi-static output feedback (respectively, the disturbance decoupling problem by dynamic output feedback (DDDPO)). The necessary conditions for DDDPO which are derived are weaker than the existing ones, a sufficient condition for the disturbance decoupling problem by static output feedback is given as well     

一类非线性切换系统输出与扰动的解耦

研究了一类单输入单输出非线性切换系统输出与扰动的完全解耦的可解性问题,提出了此类非线性切换系统输出与扰动的完全解耦的充要条件,并进一步给出了干扰可测并且能够用于反馈控制律的设计的情况下系统输出与扰动的完全解耦的条件.最后给出了仿真实例说明了本文结果的有效性.     

离散时间奇异系统的可测扰动解耦

为离散时间广义非线性控制系统的可测扰动提供一种反演算法．运用一类正则动态补偿器解决了系统的解耦问题，并且证明系统既可利用动态反馈进行解耦，也可利用拟表态反馈进行解耦．     

A note on the disturbance decoupling problem for retarded systems

The disturbance decoupling problem for linear control systems is to design a feedback control law in such a way that the disturbances do not influence these outputs which are to be regulated. In this note we present a very simple solution to this problem for a rather general class of retarded functional differential equations with delays in the state variables.     

模糊输出反馈实现动态不确定非线性系统的几乎干扰解耦

研究一类单输入单输出动态不确定非线性系统的几乎干扰解耦问题. 首先设计一类新型的模糊高增益观测器估计非线性系统的未知状态; 然后结合自适应模糊backstepping 控制、小增益定理和改变供能函数方法, 给出鲁棒自适应模糊控制器的设计. 所设计的控制器不仅可以保证整个闭环系统在输入到状态实际稳定意义下稳定, 同时抑制了干扰对输出的影响. 仿真结果表明了所提出控制方法的有效性.

     

Global almost disturbance decoupling with stability for non minimum-phase single-input single-output nonlinear systems

The so-called problem of almost disturbance decoupling with internal stability (ADDPS) is the following one. Given a system and an (arbitrarily small) number γ > 0, find a feedback law yielding a closed loop system which is stable and in which the gain (in the L₂ sense) between the exogenous input and the regulated output is less than or equal to γ. The complete solution of this problem has been known since a long time in the case of linear systems. In the case of nonlinear systems, the only global results available so far in the literature were about SISO systems having an asymptotically stable zero dynamics. In this paper, a new set of results are presented, dealing with nonlinear SISO systems having a possibly unstable zero dynamics, which include the (general) class of linear SISO systems as a special case.     

一类非线性不确定时滞系统时滞依赖鲁棒干扰抑制

针对一类范数有界非线性不确定状态时滞系统，讨论其时滞依赖鲁棒干扰抑制问题．非线性不确定性无需满足任何匹配条件，采用将非线性不确定性转换为线性不确定性的方法来完成上述设计．基于LMI技术设计的时滞依赖无记忆状态反馈控制律，可保证闭环系统的鲁棒稳定性且能优化二次型干扰抑制水平．计算机仿真算例表明了该方法的有效性．     

具有未知上界时滞状态扰动的非线性系统自适应鲁棒镇定

讨论了一类具有时滞状态扰动的非线性系统的自适应鲁棒镇定问题.时滞状态扰动的上界是未知的.在控制中通过自适应律估计上界的值,并且利用估计值设计鲁棒控制器.基于Lyapunov-Krasovskii函数,证明了闭环系统具有一致最终有界意义下的鲁棒稳定性.最后通过一个数值例子的仿真验证了结论的正确性.     

The disturbance decoupling problem in decentralized linear multi-variable systems by local dynamic feedback

Following the works of Hu and Zheng [7] on the problem of disturbance decoupling in decentralized systems with non-dynamic feedback (DDPP), this paper studies the problem of disturbance decoupling in decentralized linear multi-variable systems with one or two local dynamic feedbacks (abbreviated as DDDPDC1 or DDDPDC2 respectively). A counter-example is given to indicate that the main results of Cury [1] are incorrect. Developing the concepts such as structure subspace pair and structure subspace vector, the necessary and sufficient conditions of DDDPDC1 and DDDPDC2 using low order compensators is derived.     

Almost disturbance decoupling for single-input single-outputnonlinear systems

The almost disturbance decoupling problem for nonlinear single-input single-output systems is addressed by using singular perturbation methods and high-gain feedback. Sufficient conditions and the explicit high-gain nonlinear state feedback in solvable cases are given. They generalize both previous almost results for linear systems and exact ones for nonlinear systems. The necessity of the conditions is discussed; in particular, an example is given where the main structural condition is not satisfied and the high-gain control designed on the basis of linear approximations fails to achieve almost disturbance decoupling for the original system     

Almost disturbance decoupling of MIMO nonlinear systems and application to chemical processes

The problem of almost disturbance decoupling is considered for a class of nonlinear systems with unmeasurable time-varying disturbances. A structure, called nested lower triangular form, is introduced, which contains lower triangular form as a special case. The backstepping design technique is applied to construct an H_∞ feedback controller which achieves internal stability of the closed-loop system and renders a bounded L₂ gain from the disturbance input to the output. The application of the developed design method is illustrated through a two continuous stirred tank reactor example, which can be put into the nested lower triangular form.     

Controlled invariance for discrete-time nonlinear systems with an application to the disturbance decoupling problems

Invariant distributions are defined for discrete-time nonlinear control systems, and necessary and sufficient conditions are given for their controlled invariance. This extends to discrete-time systems the basic tool which has been so important in solving the various synthesis problems for continuous-time systems. To indicate their utility in the discrete-time setting, they are used to locally solve the disturbance decoupling problem.     

Backstepping design for time-delay nonlinear systems

The backstepping approach is adapted to the problem of globally uniformly asymptotically stabilizing nonlinear systems in feedback form with a delay arbitrarily large in the input. The strategy of design relies on the construction of a Lyapunov-Krasovskii functional. Continuously differentiable control laws are constructed.     

Dynamic decoupling for right-invertible nonlinear systems

It is shown that every system with more inputs than outputs that is right invertible, in the sense of [5], can be decoupled via a dynamic state feedback that can be computed using a given algorithm.This result generalizes the one of [2] and completes the results of [3].