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     

基于LMI的大型互联线性系统的分散有限时间镇定

借助于有限时间稳定性的定义,针对大型互联线性系统,引入了分散有限时间镇定的概念.对一类大型互联线性系统进行分散状态反馈和分散动态输出反馈控制器设计,利用线性矩阵不等式(LMI)的方法提出一个充分条件,当反馈控制律作用于该系统时,闭环系统是有限时间稳定的.仿真算例说明了所得结论的可行性和有效性.     

一类扩展结构大系统的分散有限时间鲁棒关联镇定

研究一类扩展结构大系统分散有限时间鲁棒关联镇定问题. 扩展结构大系统是在原结构系统上增加新子系统而构成的, 在原系统分散控制律确定不变的情况下, 设计新加入子系统的鲁棒分散控制律, 使扩展后的系统仍能保持有限时间关联稳定. 利用LMI 方法推导此类系统基于状态反馈和输出反馈的分散有限时间关联镇定的充分条件, 并给出扩展子系统的相应控制器的设计方法. 最后通过仿真实验表明了所提出方法的可行性和有效性.

     

具有干扰输入的大型互联线性系统的分散有限时间镇定

借助于大型互联线性系统有限时间稳定性的定义,对具有干扰输入的大型互联线性系统引入了分散有限时间镇定的概念,并对一类具有干扰输入的大型互联不确定线性系统进行了分散状态反馈和分散动态输出反馈控制器设计,利用线性矩阵不等式（LMI）方法,提出了一个充分条件.当反馈控制律作用于该系统时,闭环系统是有限时间稳定的.     

Global uniform input-to-state stabilization of large-scale interconnections of MIMO generalized triangular form switched systems

We solve the problem of global uniform input-to-state stabilization with respect to external disturbance signals for a class of large-scale interconnected nonlinear switched systems. The overall system is composed of switched subsystems each of which has the nonlinear MIMO generalized triangular form, which (in contrast to strict-feedback form) has non-invertible input–output maps. The switching signal is an arbitrary unknown piecewise constant function and the feedback constructed does not depend on the switching signal.     

Finite-time output feedback stabilisation for a class of feedforward nonlinear systems with input saturation

This paper considers the problem of global finite-time stabilisation by output feedback for a class of feedforward (upper triangular) nonlinear systems with input saturation. Based on the finite-time stability theorem, and by skillfully using the homogeneous domination approach and the nested saturation technique, a saturated output feedback controller is successfully constructed, which renders the origin of the closed-loop system globally finite-time stable. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme. Moreover, the design strategy is successfully applied to solve the saturated finite-time control problem for vertical wheel on rotating table.     

Decentralized adaptive control of a class of large-scaleinterconnected nonlinear systems

Decentralized adaptive control design for a class of large-scale interconnected nonlinear systems with unknown interconnections is considered. The motivation behind this work is to develop decentralized control for a class of large-scale systems which do not satisfy the matching condition requirement. To this end, large-scale nonlinear systems transformable to the decentralized strict feedback form are considered. Coordinate-free geometric conditions under which any general interconnected nonlinear system can be transformed to this form are obtained. The interconnections are assumed to be bounded by polynomial-type nonlinearities. Global stability and asymptotic regulation are established using classical Lyapunov techniques. The controller is shown to maintain robustness for a wide class of systems obtained by perturbation in the dynamics of the original system. Furthermore, appending additional subsystems does not require controller redesign for the original subsystems. Finally, the scheme is extended to the model reference tracking problem when global uniform boundedness of the tracking error to a compact set is established     

不确定广义大系统有限时间鲁棒分散控制

研究不确定连续广义大系统的有限时间鲁棒分散控制问题,设计系统的有限时间鲁棒分散状态反馈控制器.首先应用广义Lyapunov 函数法,给出不确定广义大系统有限时间鲁棒稳定的充分条件;其次,给出不确定广义大系统应用分散状态反馈控制器鲁棒镇定的充分条件和有限时间鲁棒分散控制器的设计方法;最后,通过仿真例子验证所提出方法的有效性.     

Input–output finite-time stability of discrete-time systems under finite-time boundedness

This paper deals with the input–output finite-time stability of discrete time-varying linear systems in the presence of finite-time boundedness. The state boundedness and output stability of this system are concerned simultaneously to avoid the large unacceptable values during certain transients. For two different classes of norm-bounded input signals, the sufficient conditions for the system satisfying both the state finite-time boundedness (FTB) and input–output finite-time stability (IO-FTS) are developed. Based on a set of linear matrix inequalities (LMIs), the controller design method via state feedback for the discrete-time system satisfying both FTB and IO-FTS is presented for the two classes of external norm-bounded input. The conditions proposed can simultaneously guarantee the state and output of closed-loop system do not exceed the boundary during the specified finite-time interval. Two examples are employed to verify the effectiveness of the proposed method.     

不确定相似组合系统的分散自适应输出反馈控制

本文讨论了不确定组合大系统的分散自适应输 出反馈控制问题,不确定项满足通常的匹配条件．针对不确定项界未知的情形,通过设计自 适应输出反馈控制器,使系统渐近稳定．仿真结果表明本文的设计方法是有效的．     

Decentralized global disturbance attenuation for a class of large-scale uncertain nonlinear systems

This paper studies the problem of global robust disturbance attenuation via decentralized state feedback for a class of large-scale nonlinear systems with parameter and interconnection uncertainties. The parameter uncertainty is from a compact set and the uncertain interconnections are bounded by higher-order polynomials of state variables. The problem that we address is to design a robust decentralized controller such that the closed-loop large-scale nonlinear system is input-to-state stable and the L₂ gain from the disturbance input to the controlled output is below a prescribed value for all admissible uncertain parameters and interconnections. A Lyapunov-based recursive design approach is developed to construct the decentralized controller explicitly. As a special case, the problem of almost disturbance decoupling via decentralized state feedback is also solved.     

IMPLICIT TRIANGULAR OBSERVER FORM DEDICATED TO A SLIDING MODE OBSERVER FOR SYSTEMS WITH UNKNOWN INPUTS

It has been presented in previous works that every uniformly observable single‐output system can be put on a triangular observation form. For this structure a special kind of sliding mode observer has been designed by authors, which ensures a finite‐time state reconstruction using a step by step observation algorithm. In this paper, we show that the multi‐output case is more delicate to study especially when the system has some unknown inputs. Thus, in order to generalizes the triangular observer form, from single to multi‐output case, we define an Implicit Triangular Observer (ITO) form. For such a form, two results are given. Firstly, we design a finite time converging observer for all values of the unknown inputs. Secondly, we give the necessary and sufficient condition, including a matching condition, for the existence of a coordinate change to put the system into this form. It is also shown that this class of systems is a subset of the uniform observable class of systems.     

一类MIMO非线性大系统基于H∞ 跟踪的分散自适应输出反馈模糊控制

针对一类状态不可测的MIMO不确定非线性大系统,提出一种基于H∞跟踪的分散自适应输出反馈模糊控制器.主要工作有:1)通过对观测误差向量进行滤波来确保严格正实条件成立,使得提出的反馈与自适应机制可以执行;2)利用模糊系统提出一种适用于一般非线性大系统基于H∞跟踪的分散自适应模糊控制方案;3)在统一的框架下处理了控制器奇异性.闭环大系统被证明足稳定的,且输出误差具有H∞跟踪性能.仿真结果验证了控制器设计的有效性.     

Semi-global observer for multi-output nonlinear systems

We present an explicit form of nonlinear observers for a class of multi-input multi-output systems. Observer construction for multi-output nonlinear systems is not a trivial extension of single output case, especially when the global error convergence is of interest. In this paper, we consider a class of systems in which the subsystem for each output has a triangular dependence on the states of that subsystem itself, and the overall system has a block triangular form for each subsystem. Hence, the contribution is to extend the results existing in the literature in that interconnections between the subsystems are allowed. The construction is based on the saturation of some estimates, which is originated by Khalil and Esfandiari for the use of semi-global output feedback control.     

一类非线性大系统分散自适应预设性能有限时间跟踪控制

研究一类非线性互联大系统的分散自适应预设性能有限时间跟踪控制问题.结合神经网络自适应技术、实际有限时间控制理论和预设性能控制方法,提出一种新的预设性能控制设计方法,以解决传统预设性能方法难以实现分散控制的问题.所设计的控制器能够保证大系统中各个子系统的跟踪误差被有限时间性能函数约束,在任意给定的停息时间内收敛到平衡点的一个给定的邻域内,且该闭环大系统的所有信号是实际有限时间稳定的.特别地,该停息时间与系统初始状态无关.两个仿真例子验证了所提出控制方法的有效性和优越性.     

具有输入饱和的非线性系统的分散输出控制

考虑了一类具有输入饱和的非线性组合大系统的镇定问题。利用李雅普诺夫稳定理论和矩阵理论研究了这类非线性组合大系统的分散输出镇定问题,并给出了一种分散输出镇定控制器的设计。考虑了另一类具有输入饱和的非线性相似组合大系统,由于相似组合系统的结构特点,给出了简洁的分散输出镇定的条件。     

Finite-time coordination in multiagent systems using sliding mode control approach

Finite-time stability in dynamical systems theory involves systems whose trajectories converge to an equilibrium state in finite time. In this paper, we use the notion of finite-time stability to apply it to the problem of coordinated motion in multiagent systems. Specifically, we consider a group of agents described by fully actuated Euler–Lagrange dynamics along with a leader agent with an objective to reach and maintain a desired formation characterized by steady-state distances between the neighboring agents in finite time. We use graph theoretic notions to characterize communication topology in the network determined by the information flow directions and captured by the graph Laplacian matrix. Furthermore, using sliding mode control approach, we design decentralized control inputs for individual agents that use only data from the neighboring agents which directly communicate their state information to the current agent in order to drive the current agent to the desired steady state. Sliding mode control is known to drive the system states to the sliding surface in finite time. The key feature of our approach is in the design of non-smooth sliding surfaces such that, while on the sliding surface, the error states converge to the origin in finite time, thus ensuring finite-time coordination among the agents in the network. In addition, we discuss the case of switching communication topologies in multiagent systems. Finally, we show the efficacy of our theoretical results using an example of a multiagent system involving planar double integrator agents.     

Decentralized adaptive output feedback design for large-scalenonlinear systems

In this paper, we present a global, decentralized adaptive design procedure for a class of large-scale nonlinear systems, which utilizes only local output feedback. The advocated scheme guarantees robustness to parametric and dynamic uncertainties in the interconnections and also rejects any bounded disturbances entering the system. The systems belonging to this class are those which can be transformed using a global diffeomorphism to the output feedback canonical form, where the interconnections are a function of subsystem outputs only. The uncertainties are assumed to be bounded by an unknown pth-order polynomial in the outputs. The resulting controller maintains global robustness and disturbance rejection properties. The output tracking error is shown to be bounded within a compact set, the size of which can be made arbitrarily small by appropriate choice of the control gains. For the case where the objective is regulation, global asymptotic regulation of all the states of the closed-loop system is achieved