Robust control for a class of time-delay uncertain nonlinear systems based on sliding mode observer

In this paper, a robust control scheme is proposed for a class of time-delay uncertain nonlinear systems with unknown input using the sliding mode observer. The sliding mode state observer is given with radial basis function neural networks, and then the robust control scheme is presented based on the designed sliding mode observer. The developed observer-based control scheme consists of two parts. One term is a linear controller and the other term is a neural network controller. Using the Lyapunov method, a criterion for bounded stability of the closed-loop system is developed in terms of linear matrix inequalities. Finally, a simulation example is used to illustrate the effectiveness of the proposed robust control scheme.     

Dynamic integral sliding mode for MIMO uncertain nonlinear systems

In this paper the authors propose a novel sliding mode control methodology for Multi-Input and Multi-Output (MIMO) uncertain nonlinear systems. The proposed approach synthesizes dynamic sliding mode and integral sliding mode control strategies into dynamic integral sliding mode. The new control laws establish sliding mode without reaching phase with the use of an integral sliding manifold. Consequently, robustness against uncertainties increases from the very beginning of the process. Furthermore, the control laws considerably alleviate chattering along the switching manifold. In addition, the performance of the controller boost up in the presence of uncertainties. A comprehensive comparative analysis carried out with dynamic sliding mode control and integral sliding mode control demonstrates superiority of the newly designed control law. A chatter free regulation control of two uncertain nonlinear systems with improved performance in the presence of uncertainties ensures the robustness of the proposed dynamic integral sliding mode controller.     

Adaptive RCMAC sliding mode control for uncertain nonlinear systems

An adaptive recurrent cerebellar-model-articulation-controller (RCMAC) sliding-mode control (SMC) system is developed for the uncertain nonlinear systems. This adaptive RCMAC sliding-model control (ARCSMC) system is composed of two systems. One is an adaptive RCMAC system utilized as the main controller, in which an RCMAC is designed to identify the system models. Another is a robust controller utilized to achieve system’s robust characteristics, in which an uncertainty bound estimator is developed to estimate the uncertainty bound so that the chattering phenomenon of control effort can be eliminated. The on-line adaptive laws of the ARCSMC system are derived in the sense of Lyapunov so that the system stability can be guaranteed. Finally, a comparison between SMC and ARCSMC for a chaotic system and a car-following system are presented to illustrate the effectiveness of the proposed ARCSMC system. Simulation results demonstrate that the proposed control scheme can achieve favorable control performances for the chaotic system and car-following systems without the knowledge of system dynamic functions.     

不确定非线性时滞系统的自适应滑模控制

针对一类不确定非线性时滞系统的鲁棒滑模控制器设计问题,提出了一种自适应滑模控制方法,该方法能够有效地削弱系统的输入抖动.基于自适应滑模控制技术和Lyapunov稳定方法,克服了系统不确定性和时滞特性影响,不但保证系统状态可以在有限的时间内到达滑模面,而且还保证了系统的渐近稳定特性.最后给出的仿真结果验证了该控制方案的有效性.     

Robust sliding mode control of uncertain nonlinear systems

A dynamic sliding mode controller design method is proposed for multiple input-output systems with additive uncertainties. A previous result on the stability of triangular systems is generalised to the case of uniform ultimate boundedness of controlled triangular systems. This is used to prove the stability of the overall closed-loop system. The uncertain system with appropriately chosen sliding mode control is shown to be ultimately bounded if the zero dynamics of the nominal system are uniformly asymptotically (exponentially) stable. The design method is demonstrated with two examples.     

Observer-based adaptive sliding mode control for nonlinear uncertain state-delayed systems

This paper presents a methodological approach to design observer-based adaptive sliding mode control for a class of nonlinear uncertain state-delayed systems with immeasurable states. A novel switching surface is proposed and a state observer is employed to reconstruct the sliding mode control action. The proposed method does not need a priori knowledge of upper bounds on the norm of the uncertainties, but estimates them by using the adaptation technique so that the reaching condition can be satisfied. Based on Lyapunov stability theorem and linear matrix inequality (LMI) technique, the stability of the overall closed-loop nonlinear uncertain state-delayed system is guaranteed for the proposed control scheme under certain conditions. Furthermore, the state observer and control law can be constructed from the positive-definite solutions of two LMIs, and the design technique is simple and efficient. The validity of the proposed control methodology is demonstrated by simulation results. Recommended by Editorial Board member Ju Hyun Park under the direction of Editor Young IL Lee. Ming-Chang Pai received the M.S. and Ph.D. degrees in mechanical engineering in 1994 and 1998 from Pennsylvania State University, State College, P.A.. He is currently an Associate Professor in the Department of Automation Engineering at Nan Kai University of Technology. His research interests are in mechatronics, robots, robust control and nonlinear control.     

A novel dynamic terminal sliding mode control of uncertain nonlinear systems

A new dynamic terminal sliding mode control （DTSMC） technique is proposed for a class of single-input and single-output （SISO） uncertain nonlinear systems. The dynamic terminal sliding mode controller is formulated based on Lyapunov theory such that the existence of the sliding phase of the closed-loop control system can be guaranteed, chattering phenomenon caused by the switching control action can be eliminated, and high precision performance is realized. Moreover, by designing terminal equation, the output tracking error converges to zero in finite time, the reaching phase of DSMC is eliminated and global robustness is obtained. The simulation results for an inverted pendulum are given to demonstrate the properties of the proposed method.     

Decentralized sliding mode adaptive controller design based on fuzzy neural networks for interconnected uncertain nonlinear systems

A new type controller, fuzzy neural networks sliding mode controller (FNNSMC), is developed for a class of large-scale systems with unknown bounds of high-order interconnections and disturbances. Although sliding mode control is simple and insensitive to uncertainties and disturbances, there are two main problems in the sliding mode controller (SMC): control input chattering and the assumption of known bounds of uncertainties and disturbances. The FNNSMC, which incorporates the fuzzy neural networks (FNNs) and the SMC, can eliminate the chattering by using the continuous output of the FNN to replace the "discontinuous" sign term in the SMC. The bounds of uncertainties and disturbances are also not required in the FNNSMC design. Two examples are presented to support the validity of the new controller. The simulation results show that the FNNSMC is more robust than the SMC.     

Switching observer design for uncertain nonlinear systems

The problem of designing a switching observer for a finite or infinite set of nonlinear time-varying systems with unknown parameters and/or varying structure is studied in this paper. Under a compactness condition and a Lyapunov detectability assumption, it is shown that a switching observer with asymptotically stable error dynamics can be constructed. Different from the variable structure control method, only a finite number of switches occur before the asymptotic stability is achieved. The Lyapunov direct method is used to construct both the switching gain and the switching index. The special case where the error dynamics becomes exponentially convergent with quadratic Lyapunov detectability is also examined to illustrate the proposed observer design procedure     

Linear extended state observer based sliding mode disturbance decoupling control for nonlinear multivariable systems with uncertainty

In this paper, the sliding mode dynamic disturbance decoupling tracking control method based on the linear extended state observer (LESO) is proposed for a class of square multivariable nonlinear uncertain system. The model plant contains the known linear dynamics, the unknown nonlinear dynamics and the internal and external disturbances, and the various input-output pairs are interacted. The system states are not available for measurement. An improved LESO is developed. The leading feature which is different from the typical ESO lies in that its extended state does not contain the known linear dynamics. The improved LESO can guarantee the error variables to be uniformly ultimately bounded with respect to a ball whose radius is a function of design parameters. So this ball radius can be arbitrarily as small as desired by tuning design parameters. And we give a simple method by which the gain parameters of LESO can be computed easily. This estimation to the total disturbance of the original system is introduced into the sliding mode control design to complete disturbance rejection and decoupling. Rigorous stability analysis shows that the system output can track the desired signal closely. Finally, a class of mass–spring–damper system is taken to make the numerical simulation analysis to illustrate the effectiveness of the proposed control method.     

一类非线性不确定系统的非奇异Terminal滑模控制

针对一类二阶非线性系统提出新的Terminal滑模控制面以克服传统的Terminal滑模控制的奇异问题，同时确保系统从任何初始状态能在有限时间内收敛至平衡点．进一步考虑系统参数摄动和外界扰动等不确定性因素上界的未知性，用Lyapunov稳定性方法给出了一个带有未知性上界参数估计的自适应非奇异Terminal滑模控制（NTSM）控制．最后通过实例比较三种滑模控制方法，仿真结果验证了非奇异Terminal滑模控制能克服传统的Terminal滑模控制的奇异问题，并说明了自适应非奇异Terminal滑模控制的有效性和可行性．     

一类不确定非线性系统的改进积分型滑模控制

针对一类不确定非线性系统的传统滑模控制,推导了滑模误差和稳态误差的范围．为了减小系统的稳态误差,同时防止积分饱和,设计了一种改进积分型滑模面．在边界层外,通过调节因子对积分项进行削弱,以防止在初始误差较大的条件下积分饱和引起的超调较大和调节时间较长的问题;在边界层内,采用传统积分以减小系统稳态误差．理论分析和仿真研究表明了所提改进积分型滑模控制方法的有效性．     

A singular system approach to robust sliding mode control for uncertain Markov jump systems

The robust sliding mode control for Markov jump systems with parameter uncertainties and an unknown nonlinear function is discussed. Based on a singular system approach and linear matrix inequality (LMI), a sufficient condition which guarantees the existence of linear switching surface and the stochastic stability of sliding mode dynamics is given. A sliding mode controller is designed such that the closed-loop system is convergent to the switching surface in finite time. A numerical example is given to show the effectiveness of the proposed method.     

Simplex sliding mode methods for the chattering reduction control of multi-input nonlinear uncertain systems

The simplex sliding mode control method is further developed by considering uncertain control systems non-affine in the control law. In order to reduce chattering effects, a set of integrators is added in the input channels. The augmented system is then controlled by a switching logic based on the simplex control method. As a result, the original control vector turns out to be continuous. A second order sliding mode observer is used when the sliding output is not available. Explicit conditions are identified about systems uncertainties and the simplex geometry in order to guarantee the convergence of the proposed methodology.     

State observer based robust adaptive fuzzy controller for nonlinear uncertain and perturbed systems

A robust adaptive fuzzy controller, based on a state observer, for a nonlinear uncertain and perturbed system is presented. The state observer is introduced to resolve the problem of the unavailability of the state variables. Two control signals are added to a basic state feedback control law, deduced from a nominal model, to guarantee the tracking performance in the presence of structural uncertainties and external disturbances. The first control signal is computed from an adaptive fuzzy system and eliminates the effect of structural uncertainties and estimation errors. Updating the adjustable parameters is ensured by a PID law to obtain a fast convergence. Robustness of the closed-loop system is guaranteed by an H infinity supervisor computed from a Riccati type equation. Simulation example is presented to show the efficiency of the proposed method.     

Terminal sliding mode control design for uncertain dynamic systems

A terminal sliding mode control design scheme for uncertain dynamic systems in the pure-feedback form is presented in this paper. This design employs a recursive procedure which utilizes a set of switching manifolds to realize finite time convergence. To avoid a singularity problem, the scheme uses two-phase control: one phase is a preterminal sliding mode control that transfers the trajectory to a specified open region in which the terminal sliding mode control is not singular. Inside the region, the other phase – the terminal sliding mode control takes place bringing the state to the origin in finite time.     

Robust observer design for nonlinear uncertain systems with LQ regulators

For a class of uncertain systems with linear nominal dynamics and nonlinear uncertainties, it has been shown (Katayama and Sasaki 1987) that linear quadratic (LQ) state feedback regulators can be used to provide robust asymptotic stability. In this paper, we study the combined observer-controller design problem, based on the linear state feedback regulator proposed by Katayama and Sasaki (1987), so that only output feedback is needed. Both full-order and reduced-order observers are considered. For the full-order observer, we propose an algorithm to synthesize the robust observer gain matrix. It is shown that with the observer it is still possible to achieve robust asymptotic stability. For the reduced-order observer, some conditions are derived to guarantee the robust asymptotic stabilizability of the uncertain systems. The trade-off between the magnitudes of controller and observer gains is clear in our approach. An example is used to illustrate the design process of the robust controller with full-order as well as reduced-order observers.