An LMI-based variable structure control for a class of uncertain singular Markov switched systems

An H-infinifty variable structure control is presented for singular Markov switched systems with mismatched norm-bounded uncertainties and mismatched norm-bounded external disturbances. It is shown that the sliding mode dynamics on the given switching surface is regular, impulse-free, and stochastically stable and satisfies H-infinity performance. A variable structure controller is designed to guarantee that the system trajectory converges to the linear switching surface in some finite time. Finally, a numerical example is solved to show the effectiveness and validness of the theoretical results.     

Output feedback variable structure control for a class of uncertain switched systems

This paper considers the output feedback variable structure control problem for a class of uncertain switched systems. A single sliding surface is constructed using only output information. Robust stability of the sliding motion restricted to the sliding surface is achieved and complete invariance to the matched and the mismatched uncertainties is guaranteed via a hysteresis switching law based on a reduced order observer. Output feedback variable structure controllers are given to guarantee that the redefined sliding surface is reached in finite time. A numerical example illustrates the effectiveness of the proposed design method. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一类非匹配不确定性系统的变结构控制

研究一类非匹配不确定性系统的变结构控制问题. 引入适当的状态变换, 将非匹配不确定系统描述成具有分级形式的两个子系统. 在保证第一个子系统二次渐近稳定的条件下, 利用线性矩阵不等式方法得到第二个状态变量的期望值, 并由第二个状态变量与其期望值之差构造滑动模, 并利用滑模运动的到达条件, 得到变结构控制律.     

Decentralized variable structure control for mismatched uncertain large-scale systems: a new approach

In this paper, a decentralized variable structure controller for a class of large-scale systems with mismatched uncertainties is proposed. In every subsystem, two sets of switching surfaces is introduced. New invariance conditions are derived such that the system in the new sliding mode is completely invariant to both matched and mismatched uncertainties. To demonstrate the effectiveness of the proposed scheme, a decentralized variable structure controller is synthesized to perform the new sliding mode. Moreover, the stability analysis of the overall system is also provided.     

Design of decentralised variable structure observer for mismatched nonlinear uncertain large-scale systems

Although the state feedback approach is quite popular in control engineering, it cannot be used while the system states cannot be measured. The state observer approach may be used to overcome such a shortcoming. Also, most control systems have become larger and more complicated; therefore, based on the variable structure control theory, a new decentralised variable structure observer (DVSO) for a class of nonlinear large-scale systems with mismatched uncertainties will be considered in this article. The switching surface function is determined such that the equivalent system will have the desired behaviour once the system reaches the switching surface. And then a new DVSO is designed such that the estimated states will approach the system states. Using the Lyapunov stability theory and using the generalised matrix inverse concept, the uncertain nonlinear error system trajectories can be driven onto the sliding manifold and then the existence of a sliding mode and the attractiveness to the sliding surface is ensured. With the proposed DVSO, the estimation errors asymptotically tend to zero if the matching condition is satisfied, and the effects of the mismatched parts can be uniformly ultimately bounded if the matching condition is not satisfied. Finally, a numerical example with a succession of computer simulations is given to demonstrate the effectiveness of the proposed approach.     

离散变结构控制基于扰动动态补偿的理想趋近律

研究了带有系统内部参数摄动和外部干扰的离散时间系统变结构控制综合问题。给出了非匹配不确定离散时间系统带有扰动动态补偿的理想趋近律,消除了常规变结构控制中不确定项必须有界和满足匹配条件的限制。所设计的变结构控制器在有限时间内可达切换面,有效地削弱了系统抖振,减小了切换带带宽,改善了系统动态品质。仿真结果验证了该方法的可行性和有效性。     

Adaptive controller design for uncertain fuzzy systems using variable structure control approach

Based on the variable structure control (VSC) theory, we develop an adaptive fuzzy control system design method for uncertain Takagi-Sugeno fuzzy models with norm-bounded uncertainties. We relax the restrictive assumptions that each nominal local system model shares the same input channel and the norm bound of the uncertainty is known, which are usually invoked in the traditional VSC-based fuzzy control design methods. As the local controller we use a VSC law with a switching feedback control term and an adaptation law to account for the norm-bounded uncertainties. In terms of LMIs, we derive a sufficient condition for the existence of linear sliding surfaces guaranteeing the asymptotic stability. We present an LMI characterization of such sliding surfaces. We also give an LMI-based design algorithm, together with a numerical design example.     

Robust fault-tolerant control of a class of non-minimum phase nonlinear processes

This article concerns with the regulation and fault-tolerant control of non-minimum phase nonlinear processes with mismatched uncertainties. A variable structure controller, switching between a first-order sliding mode control and a second-order sliding mode control, is proposed to regulate the output and to stabilize the unstable zero dynamics with mismatched uncertainties. Once detected, the fault is estimated on-line by an approximator of radial basis function network; the control law is reconfigured to compensate the fault with closed-loop system asymptotically stable. The application of the proposed algorithm to a non-minimum phase continuously stirred tank reactor (CSTR) is illustrated in the presence of matched and mismatched uncertainties and component fault.     

An LMI-based switching surface design method for a class of mismatched uncertain systems

In this note, we consider the problem of designing linear sliding surfaces for multivariable uncertain systems with mismatched uncertainties in the state matrix. In terms of linear matrix inequalities, we give a new invariance condition guaranteeing the existence of a linear switching surface such that the reduced-order equivalent sliding mode dynamics restricted to the switching surface is not only stable but completely invariant to mismatched uncertainties. We also give an explicit formula of such linear switching surfaces, together with a design example.     

坦克稳定器滑动模态变结构控制

该文介绍了用滑动模态变结构控制对坦克水平向稳定器进行设计。滑动模态变结构控制主要由两部分组成：求取切换函数及变结构控制。文章采用最优化方法设计切换函数，保证滑动模态稳定；用幂次趋近律确定变结构控制，使切换面以外的相轨线于有限时间到达切换面。在此基础上又进行了仿真实验。仿真结果显示系统单位阶跃响应快速无超调，稳态误差为零，斜坡输入下能平稳跟踪。该设计方法优于传统设计方法，满足各项技术指标要求，能够有效提高坦克稳定器性能，为稳定器设计提供了一种切实可行的方法。     

Design of two-layer switching rule for stabilization of switched linear systems with mismatched switching

A two-layer switching architecture and a two-layer switching rule for stabilization of switched linear control systems are proposed, under which the mismatched switching between switched systems and their candidate hybrid controllers can be allowed. In the low layer, a state-dependent switching rule with a dwell time constraint to exponentially stabilize switched linear systems is given; in the high layer, supervisory conditions on the mismatched switching frequency and the mismatched switching ratio are presented, under which the closed-loop switched system is still exponentially stable in case of the candidate controller switches delay with respect to the subsystems. Different from the traditional switching rule, the two-layer switching architecture and switching rule have robustness, which in some extend permit mismatched switching between switched subsystems and their candidate controllers.     

一类奇异非线性变结构控制系统的跟踪问题

首次利用变结构控制方法研究了一类奇异非线性系统的模型跟踪问题，在不同情况下，通过引入动态补偿器的概念，设计了奇异模型跟踪系统的切换函数，得到了在切换面上实现跟踪的条件，然后利用趋近律方法设计了变结构控制，以保证在切换面外的运动在有限时间到达切换面，通过滑动运动实现跟踪，最后讨论了参数模型为正常系统的线性定常奇异系统的跟踪问题。     

Output feedback variable structure control for linear systems with uncertainties and disturbances

This paper proposes a dynamic output feedback variable structure controller for linear MIMO systems with mismatched and matched norm-bounded uncertainties and matched nonlinear disturbances. The proposed controller consists of nonlinear and linear parts, similar to the unit vector type of controller. The nonlinear part of the new controller takes care only of matched uncertainties and disturbances and, on the other hand, the linear part with full dynamics completely handles mismatched uncertainties. Designing such a linear part leads to use a Lyapunov function associated with the full states, which achieves the global stability against the mismatched uncertainties. The resulting criteria are, furthermore, converted into solvable ones, by using the so-called cone complementary linearization algorithm for bi-convex problems.     

Variable structure output feedback control design for a class of uncertain dynamic systems

In this paper, we consider the problem of designing a variable structure output feedback control (VSOFC) law for a class of uncertain systems with mismatched uncertainty in the state matrix. We derive existence conditions of linear sliding surfaces in terms of constrained linear matrix inequalities (LMIs), and we give VSOFC strategies. We also give a simple design procedure and parameterizations of the linear switching surfaces, together with solvability conditions for the given constrained LMIs. Finally, we give a design example in order to show the effectiveness of our method.     

含有不灵敏区有界不确定非线性系统的鲁棒跟踪控制

针对具有控制输入不灵敏区及有界不确定性的非线性系统,研究其鲁棒跟踪问题.利用变结构控制方法和自适应参数估计方法,在同时存在的参数、结构及干扰的不确定性和未知控制输入不灵敏区的情形下,提出了鲁棒控制律设计方法,并提出克服控制信号抖动的改进算法.所提出的控制律可以保证闭环系统的一致终结有界,并且算法比较简单,便于实现.用数字仿真方法验证了所得控制律设计方法的有效性.     

Robust control guaranteeing uniform ultimate boundedness for a class of mismatched uncertain parabolic distributed parameter systems

The robust control problem for a class of mismatched uncertain parabolic distributed parameter systems is studied under conditions of the uncertain terms being norm-bounded. The proposed robust controller can guarantee the system states to be the uniform ultimate boundedness, and their bound can be arbitrarily small. And, the proposed control method is successfully applied to a typical diffusion-reaction process with uncertain terms.     

A new method of switching surface design for multivariable variablestructure systems

In this paper, we discuss the problem of the switching surface for a multivariable variable structure system. We first propose a new switching surface by which robustness of the controlled system to disturbances is provided. Based on the switching surface, we develop control input to drive the system to track the desired trajectory. This control input does not produce the chattering that normally occurs when a conventional control input is used. We apply the proposed method to a multivariable linear system and discuss the simulation results to show the computational procedure and its effectiveness     

Fault-tolerant control for uncertain linear systems via adaptive and LMI approaches

This paper proposes a fault-tolerant control scheme for linear systems with mismatched uncertainties which are assumed to be norm-bounded, affine and polytopic, respectively. The linear fractional transformation (LFT) and linear matrix inequality (LMI) techniques are introduced to handle the mismatched uncertainties, and the adaptive techniques are used to compensate actuator faults. By using the cone complementary linearisation algorithm, the resulting stability criteria are converted into solvable ones. Then, on the basis of Lyapunov stability theory, it is shown that the solutions to the closed-loop system and error system are uniformly bounded, especially, the states converge asymptotically to zero. Finally, simulations are given to illustrate the effectiveness and advantages of the proposed theoretical results.     

Quadratic stabilization of switched systems

We consider quadratic stabilization of uncertain switched systems when a switching rule is imposed on state feedback controllers of subsystems. A method is proposed to constructively design switching rules for continuous and discrete-time switched systems with norm-bounded time-varying uncertainties. The switching rules designed via this method do not rely on uncertainties, and the switched system is quadratically stabilizable via switched state feedback for all uncertainties.     

Dynamic Output Integral Sliding-Mode Control With Disturbance Attenuation

This technical note proposes a dynamic output feedback sliding-mode control algorithm for linear MIMO systems with mismatched norm-bounded uncertainties along with disturbances and matched nonlinear perturbations. A control law is first designed to ensure that the system behavior can satisfy the reaching and sliding condition. A scheme designed to combine the output-dependent integral sliding surface with a full-order compensator is then proposed. Through utilizing $H _{infty} $ control analytical technique, once the system is in the sliding mode, the proposed algorithm can guarantee robust stabilization and sustain the nature of performing disturbance attenuation when the solutions to two algebraic Riccati inequalities can be found. Finally, the feasibility of our proposed algorithm is illustrated using a numerical example.