Global H infinty control and almost disturbance decoupling for a class of interconnected non-linear systems

This paper is concerned with a global H infinity control problem for a class of interconnected non-linear systems. We first consider a fairly general clas of large-scale non-linear systems with strong non-linear interconnections. It is shown that the decentralized H infinity control problem for the system can be converted into the centralized control problems associated with a set of auxiliary systems. The solutions to the latter problems in general rely on solutions of their associated Hamilton-Jacobi-Isaacs (HJI) inequalities. Realizing that finding a global solution of the HJI inequality is usually impossible, we then consider a global decentralized almost disturbance decoupling problem (DADDP) and a global decentralized inverse H infinity control problem (DIHCP) for a class of interconnected systems with lower triangular structure. The DADDP is concerned with the design of decentralized control laws that achieve an arbitrarily small disturbance input to the controlled output. The DIHCP involves seeking not only control laws but also state-dependent weights of the control inputs such that the associated global decentralized control problem is solvable. It is shown that the solutions to both the DADDP and DIHCP can be obtained via a recursive design technique. L2-gain from the     

Robust stabilization of uncertain systems with persistent disturbance and a class of non-linear actuators

Linear uncertain systems perturbed by persistent disturbances and driven by actuators subject to band-bounded nonlinearities are considered. A set of linear matrix inequality based sufficient conditions are derived for designing state feedback controllers which assure ultimate boundedness of closed-loop state trajectories. The effect of the non-linear actuators is identified to that of the considered persistent disturbances. The control purpose is to minimize the ultimate boundedness region to which the state trajectories are eventually confined, while tolerating disturbances of given or the largest magnitudes. Finally, an experimental system, an inverted pendulum on a Stewart platform making translational movement, is arranged to demonstrate the feasibility and effectiveness of the derived results.     

Global stabilization and disturbance suppression of a class of nonlinear systems with uncertain internal model

This paper deals with global stabilization and disturbance suppression of a class of nonlinear systems using output feedback. The disturbances generated from a unknown linear exosystem are completely compensated. The order of the exosystem is assumed known and the eigenvalues are distinct. No other assumptions are needed in the control design. This means that the proposed control design is able to completely compensate the disturbances without knowing their amplitudes, frequencies and phases, as long as the number of different frequency components in the disturbances is known. A new formulation of state estimation is introduced to ensure the global stabilization and complete disturbance suppression. Adaptive control technique is used to design an adaptive internal model based on a recently introduced formulation of unknown exosystems and the parameters in the adaptive internal model converge to the actual values, from which the unknown disturbance frequencies can be calculated. In the proposed control design, a number of control coefficients are made adaptive so that the result is global with respect to unknown frequencies in the disturbances.     

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.     

Global finite-time stabilization of a class of uncertain nonlinear systems

This paper studies the problem of finite-time stabilization for nonlinear systems. We prove that global finite-time stabilizability of uncertain nonlinear systems that are dominated by a lower-triangular system can be achieved by Hölder continuous state feedback. The proof is based on the finite-time Lyapunov stability theorem and the nonsmooth feedback design method developed recently for the control of inherently nonlinear systems that cannot be dealt with by any smooth feedback. A recursive design algorithm is developed for the construction of a Hölder continuous, global finite-time stabilizer as well as a C¹ positive definite and proper Lyapunov function that guarantees finite-time stability.     

Global output-feedback stabilization for a class of uncertain time-varying nonlinear systems

This paper investigates the global output-feedback stabilization for a class of uncertain time-varying nonlinear systems. The remarkable structure of the systems is the presence of uncertain control coefficients and unmeasured states dependent growth whose rate is inherently time-varying and of unknown polynomial-of-output, and consequently the systems have heavy nonlinearities, serious uncertainties/unknowns and serious time-variations. This forces us to explore a time-varying plus adaptive methodology to realize the task of output-feedback stabilization, rather than a purely adaptive one. Detailedly, based on a time-varying observer and transformation, an output-feedback controller is designed by skillfully combining adaptive technique, time-varying technique and well-known backstepping method. It is shown that, with the appropriate choice of the design parameters/functions, all the signals of the closed-loop system are bounded, and furthermore, the original system states globally converge to zero. It is worth mentioning that, the heavy nonlinearities are compensated by an updating law, while the serious unknowns and time-variations are compensated by a time-varying function. The designed controller is still valid when the system has an additive input disturbance which, essentially different from those studied previously, may not be periodic or bounded by any known constant.     

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.     

输出反馈实现一类带不确定输入动态非线性系统的鲁棒几乎干扰解耦

研究一类带不确定输入动态非线性系统的输出反馈干扰抑制问题并基于观测器给出了输出反馈控制器 构造性的设计方法.所设计的控制器具有对可允许不确定动态的鲁棒性.不仅在L₂增益意义上抑制了干扰对输出 的影响,同时在ISS镇定意义上抑制了干扰对状态的影响.     

Nonlinear almost disturbance decoupling

The L₂-gain almost disturbance decoupling problem for SISO nonlinear systems is formulated. Sufficient conditions are identified for the existence of a parametrized state feedback controller such that the L₂-gain from disturbances to output can be made arbitrarily small by increasing its gain. The controller is explicity constructed using a Lyapunov-based recursive scheme. Sufficient conditions for the solvability of the almost disturbance decoupling problem and the explicit construction of teh controller are given for a more restrictive class of nonlinear systems.     

一类不确定非线性系统的全局鲁棒有限时间镇定

对一类不确定非线性系统提出了一种连续的全局鲁棒有限时间控制律．首先,针对标称系统设计出了一种状态反馈控制律,应用Lyapunov直接稳定性理论和Lasalle不变性原理证明了闭环标称系统的全局渐近稳定性,同时具有负的齐次度;其次,引入辅助变量和采用有限时间收敛的二阶滑模Super—twisting算法,设计出了对不确定性和干扰进行抑制的补偿控制项,并根据有限时间Lyapunov函数给出了补偿控制项参数的取值范围;最后,综合得到一种连续的使实际闭环系统有限时间收敛到平衡点的鲁棒镇定控制律．仿真结果表明了所提控制律的有效性．     

General approach to stability and stabilization for a class of uncertain discrete non-linear systems

This paper presents a general and unified approach to the problem of stability and stabilization for uncertain discrete-time systems which may be both non-linear and time-varying. General stability conditions based on the principle of contraction mapping are recalled and used to formulate unified stability conditions and stabilization problem for the uncertain system under consideration. For two typical cases (additive uncertainty and multiplicative uncertainty) and three forms of uncertainties, a set of sufficient stability conditions is presented. Some of them are compared with the related conditions described in the literature.     

Global exponential stabilization for a class of uncertain nonlinearsystems with control constraint

In this paper, the global exponential stabilization for a class of uncertain nonlinear systems with control constraint is investigated. A bounded and continuous feedback control is constructed, under which the global exponential convergence for such systems can be guaranteed. A numerical example is also provided to illustrate the use of our main result     

Practical stabilization of a class of uncertain nonlinear systems

In this paper the problem of robust control of a class of nonlinear systems with internal and input channel uncertainties is addressed. The proposed control algorithm reflects the two-level structure of the plant and guarantees the system uniform asymptotic stability with respect to an arbitrary neighbourhood of the nominal system stability point.     

Asymptotic stabilization of a class of uncertain composite systems

A class of stabilizing, generalized feedback controls is presented for a class of uncertain dynamical systems. The uncertain systems are based on a composite prototype system consisting of two nonlinearly coupled subsystems, with a non-asymptotically-stabilizable linearization. To encompass all possible realizations of uncertainty, a problem formulation based on differential inclusions is adopted. The generalized feedback controls, described in terms of set-valued maps, have practical analogues in the form of discontinuous feedback controls. An intrinsic element of the control strategy is designed to render a prescribed nonlinear manifold, containing the state origin, invariant and globally finite-time attractive. For each uncertain system, the generalized feedback controls guarantee global asymptotic stability of the zero state.     

一类参数不确定系统的鲁棒镇定

给出了一类参数不确定性系统的鲁棒镇定方法,首先对这类系统给出了一般描述,即这种系统的系统阵、输入阵都包含不确定参数,其非线性扰动项满足一定的约束条件.其次讨论了上述系统的基于代数黎卡提方程的正定解的鲁棒镇定方法.在应用方面,以包含静止同步补偿器(STATCOM)的电力系统为例,通过直接反馈线性化将上述系统转换为所讨论的线性系统.仿真结果验证了所提方法的控制效果.     

Global stabilization for nonlinear uncertain systems with unmodeledactuator dynamics

Second-order sliding-mode control (2-SMC) algorithms are analyzed to assess their global convergence properties. While standard first-order sliding-mode control (1-SMC) algorithms derive their effectiveness from the global solution of the well known "reaching condition" ss˙⩽-k²|s| (s=0 being the actual sliding manifold), 2-SMC is based on more complex differential inequalities, for which a global solution could not exist. The approach presented introduces a suitable commutation logic (based on an online simple predictor) that prevents an uncontrollable growth of the uncertainties. Due to this new commutation logic, the global convergence of the state trajectory to the designed sliding manifold is ensured     

Direct approach to almost disturbance and almost input-output decoupling

A direct solution to the almost input-output and disturbance decoupling problem is given. The approach is based on a new canonical form for linear systems—which is obtained in a fully constructive way—together with some elementary approximation results. The solution is given in the form of an explicit feedback law, parameterized by a scalar ε. By letting ε go to zero, the accuracy of the resulting approximate solution can be improved to any desired degree.     

带扰动和未知参数混沌系统变量函数向量同步

研究了带有扰动和未知参数的混沌系统状态变量函数向量同步问题。分别针对驱动系统和响应系统设计出状态变量函数向量,利用自适应反馈原理和Lyapunov定理,构造出控制器,可以保证两状态变量函数向量同步。仿真结果表明该方法的有效性。