Decentralized robust output feedback control for control affine nonlinear interconnected systems

In this paper, a scheme for decentralized robust control for control affine nonlinear interconnected systems using linear matrix inequalities (LMIs) is presented. Based on the Lyapunov theory, sufficient conditions for closed-loop stability of a nonlinear system, reference input tracking, and disturbance attenuation over its operating-range are obtained. Then, achieving these sufficient conditions are formulated as local LMI optimization problems. By solving the appropriately defined local problems, provided the obtained sufficient conditions are satisfied, the closed-loop stability, input tracking, and disturbance attenuation over the operating-range of the system are guaranteed. The designed controller is linear whose implementation is straightforward. An example is given to illustrate the proposed methodology.     

Sliding mode control design for mismatched uncertain systems using output feedback

International Journal of Control, Automation and Systems - This paper develops an output feedback sliding mode control law for linear MIMO systems having mismatched parameter uncertainties along...     

Decentralised robust sliding mode control for a class of nonlinear interconnected systems by static output feedback

In this paper, a class of nonlinear interconnected systems with nonlinear nominal subsystems is considered. Matched and mismatched uncertainties are both dealt with. Based on sliding mode techniques, a decentralised robust control scheme, using only output information, is presented to stabilise the system locally, but under certain circumstances, global results can be obtained. The approach allows a more general structure for the interconnections and uncertainty bounds than other literature in this area. The conservatism in the results is reduced by fully using system output information and the uncertainty bounds. A numerical example is used to demonstrate the efficacy of the method.     

Adaptive multiple-surface sliding control for non-autonomous systems with mismatched uncertainties

In this paper, we propose a sliding mode-based controller for a class of single-input single-output nonlinear systems with mismatched uncertainties whose variation bounds are not given. The concept of multiple-surface sliding control is used to cope with the uncertainty mismatch problem, and the function approximation technique is introduced to transform the uncertainties into a finite combination of orthonormal basis functions. An adaptive controller can thus be designed using the Lyapunov approach to achieve output error convergence and boundedness of all signals. Simulation results of a benchmark problem have verified the performance and feasibility of the proposed control strategy.     

Fuzzy sliding mode control for an under-actuated system with mismatched uncertainties

This article presents a robust fuzzy sliding mode controller. The methodology of sliding mode control provides an easy way to control under-actuated nonlinear systems with uncertainties. The structure of the sliding surface is designed as follows. First, decouple the entire system into second-order systems so that each subsystem has a separate control target expressed in terms of a sliding surface. Second, from the sliding surface of subsystems, organize the main sliding surface system. Third, generate a control input for the main sliding surface to make whole subsystems move toward their sliding surface. A fuzzy controller is used to obtain a smooth boundary layer to the sliding surface. Finally, the fuzzy sliding mode controller presented is used to control an under-actuated nonlinear system, and confirms the validity of the proposed approach and its robustness to uncertainties.     

Discrete sliding mode control of systems with unmatched uncertainty using multirate output feedback

Systems with uncertainties and disturbances are common in practice. In some cases, these disturbances are unmatched. Moreover, in most cases the entire state information is also not available for control purpose. This note proposes a control algorithm for achieving quasi-sliding mode in discrete-time linear time-invariant (LTI) systems with bounded unmatched uncertainties. A multirate output feedback based strategy is used for this purpose. The proposed algorithm is illustrated through an example.     

Decentralized dynamic output feedback for robust stabilization of a class of nonlinear interconnected systems

The objective of this paper is to propose an approach to robust stabilization of systems which are composed of linear subsystems coupled by nonlinear time-varying interconnections satisfying quadratic constraints. The proposed algorithms, which are formulated within the convex optimization framework, employ linear dynamic feedback structure involving local Luenberger-type observers. It is also shown how the new methodology can produce improved results if interconnections have linear parts that are known a priori. Examples of output stabilization of inverted pendulums and decentralized control of a platoon of vehicles are used to illustrate the applicability of the design method.     

Applying output feedback integral sliding mode controller to uncertain time-delay systems with mismatched disturbances

For time-delay systems with mismatched disturbances and uncertainties, this paper develops an integral sliding mode control algorithm using output information only to stabilize the systems. An integral sliding surface is comprised of output signals and an auxiliary full-order compensator. The proposed output feedback sliding mode controller can satisfy the reaching and sliding condition and maintain the system on the sliding surface from the initial moment. When two specific algebraic Riccati inequalities have solutions, our method can guarantee the stability of the closed-loop system and satisfy the property of robust disturbance attenuation. Moreover, the design parameters of controller and compensator can be simultaneously determined by solutions to the algebraic Riccati inequalities. Finally, two numerical examples illustrate the applicability of the proposed scheme.     

Robust dynamic output feedback second-order sliding mode controller for uncertain systems

This paper addresses the problem of designing a dynamic output feedback sliding mode control algorithm to stabilize a linear MIMO uncertain system having relative degree two. Introducing a suitable dynamic compensator into the sliding variable, the additional degree of freedom can be used to robustly guarantee the closed-loop system stability once the system is in the sliding mode. A modified asymptotically stable second-order sliding mode control is analyzed and the proposed controller can obtain the real second-order sliding mode. Finally, the feasibility of the proposed method is illustrated by a numerical example.     

Adaptive fuzzy sliding mode controller for linear systems with mismatched time-varying uncertainties

A new design approach for an adaptive fuzzy sliding mode controller (AFSMC) for linear systems with mismatched time-varying uncertainties is presented. The coefficient matrix of the sliding function can be designed to satisfy a sliding coefficient matching condition provided time-varying uncertainties are bounded. With the sliding coefficient matching condition satisfied, an AFSMC is proposed to stabilize the uncertain system. The parameters of output fuzzy sets in the fuzzy mechanism are on-line adapted to improve the performance of the fuzzy sliding mode control system. The bounds of uncertainties are not required to be known in advance for the AFSMC. Stability of the fuzzy control system is guaranteed and the system is shown to be invariant on the sliding surface. Moreover, chattering around the sliding surface in sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed AFSMC.     

On the design of sliding mode output feedback controllers

The development of sliding mode controllers for uncertain linear systems using only a subset of the state information is considered. The case of static output feedback is first reviewed. The use of low order dynamical compensators (which do not possess observer interpretations) is explored. It will be shown that the constraint of global sliding surface reachability which is usually employed in the state feedback case is unnecessarily restrictive when developing controllers based on output measurements only. A case study involving steer-by-wire of a passenger vehicle is employed throughout the paper to illustrate the theoretical results.     

Decentralized robust control for a class of large-scale interconnected systems with uncertainties

The design problem of decentralized robust controllers is considered for a class of large-scale systems. The system considered in this paper is composed of interconnected subsystems with time-varying uncertainties. For such large-scale uncertain systems, we give a simple und new method whereby we can derive the sufficient conditions for asymptotically stabilizing the overall system using decentralized feedback robust controllers. An illustrative example is given to demonstrate the design procedure of the decentralized feedback robust controllers, in the light of the method developed in this paper.     

Decentralized output feedback robust stabilization for a class ofnonlinear interconnected systems with similarity

In this paper, the problem of decentralized output feedback stabilization for a class of nonlinear uncertain interconnected systems with similar subsystems is considered, and a type of controller with holographic structure is developed. It is shown that both the analyses of systems and the design of controllers are simplified by a similar structure. Finally, an example is presented to illustrate the results given in this paper and an estimation of the associated stabilized domain. Simulation shows that our method is very effective     

Adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties

A new design approach of an adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties is presented in this paper. A fuzzy terminal sliding mode controller is designed to retain the advantages of the terminal sliding mode controller and to reduce the chattering occurred with the terminal sliding mode controller. The sufficient condition is provided for the uncertain system to be invariant on the sliding surface. The parameters of the output fuzzy sets in the fuzzy mechanism are adapted on-line to improve the performance of the fuzzy sliding mode control system. The bounds of the uncertainties are not required to be known in advance for the presented adaptive fuzzy sliding mode controller. The stability of the fuzzy control system is also guaranteed. Moreover, the chattering around the sliding surface in the sliding mode control can be reduced by the proposed design approach. Simulation results are included to illustrate the effectiveness of the proposed adaptive fuzzy terminal sliding mode controller.     

Backstepping sliding mode control with FWNN for strict output feedback non-smooth nonlinear dynamic system

An output feedback backstepping sliding mode control scheme was developed for precision positioning of a strict single-input and single-output (SISO) non-smooth nonlinear dynamic system that could compensate for deadzone, dynamic friction, uncertainty and estimations of immeasurable states. An adaptive fuzzy wavelet neural networks (FWNNs) technique was used to provide improved approximation ability to the system uncertainty. The adaptive laws were derived for application to estimate the deadzone and friction parameters using recursive backstepping controller design procedures. In addition, the sliding mode control method was also combined to enforce the robustness of the output feedback backstepping controller against disturbance. The Lyapunov stability theorem was used to prove stability of the proposed control system. The usefulness of the proposed control system was verified by simulations and experiments on a robot manipulator in the presence of a deadzone and friction in the actuator.     

Design of sliding mode controllers for bilinear systems with time varying uncertainties.

Sliding mode controllers for the bilinear systems with time varying uncertainties are developed in this paper. The bilinear coefficient matching condition which is similar to the traditional matching condition for linear system is defined for the homogeneous bilinear systems. It can be seen that the bilinear coefficient matching condition is very limited and is not generally applicable to the nonhomogeneous bilinear system. Thus, the sliding coefficient matching condition is also considered for the bilinear systems with time varying uncertainties. Then, the sufficient conditions are provided for the reaching mode of the time varying uncertain bilinear systems to be guaranteed by the designed sliding mode controllers. Moreover, the stability of the uncertain bilinear systems with the sliding mode controller is discussed. Simulation results are included to illustrate the effectiveness of the proposed sliding mode controllers.     

Finite-time output feedback control of uncertain switched systems via sliding mode design

The problem of sliding mode control (SMC) is investigated for a class of uncertain switched systems subject to unmeasurable state and assigned finite (possible short) time constraint. A key issue is how to ensure the finite-time boundedness (FTB) of system state during reaching phase and sliding motion phase. To this end, a state observer is constructed to estimate the unmeasured states. And then, a state estimate-based SMC law is designed such that the state trajectories can be driven onto the specified integral sliding surface during the assigned finite time interval. By means of partitioning strategy, the corresponding FTB over reaching phase and sliding motion phase are guaranteed and the sufficient conditions are derived via average dwell time technique. Finally, an illustrative example is given to illustrate the proposed method.     

基于快速输出采样反馈的网络控制系统滑模控制

针对网络控制系统的网络诱导时延问题,提出了一种新的滑模控制方法。通过快速采样被控对象输出,建立了具有线性时不变被控对象的网络控制系统的离散模型。在此基础上,用极点配置法给出了滑模切换面参数,设计了输出反馈离散滑模控制器。仿真结果验证了该控制方法的有效性。