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.     

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．     

Non-singular terminal sliding mode control of rigid manipulators

This paper presents a global non-singular terminal sliding mode controller for rigid manipulators. A new terminal sliding mode manifold is first proposed for the second-order system to enable the elimination of the singularity problem associated with conventional terminal sliding mode control. The time taken to reach the equilibrium point from any initial state is guaranteed to be finite time. The proposed terminal sliding mode controller is then applied to the control of n-link rigid manipulators. Simulation results are presented to validate the analysis.     

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.     

A robust reinforcement learning using the concept of sliding mode control

In this article, we propose a new control method using reinforcement learning (RL) with the concept of sliding mode control (SMC). Some remarkable characteristics of the SMC method are good robustness and stability for deviations from control conditions. On the other hand, RL may be applicable to complex systems that are difficult to model. However, applying reinforcement learning to a real system has a serious problem, i.e., many trials are required for learning. We intend to develop a new control method with good characteristics for both these methods. To realize it, we employ the actor-critic method, a kind of RL, to unite with the SMC. We are able to verify the effectiveness of the proposed control method through a computer simulation of inverted pendulum control without the use of inverted pendulum dynamics. In particular, it is shown that the proposed method enables the RL to learn in fewer trials than the reinforcement learning method. This work was presented in part at the 13th International Symposium on Artificial Life and Robotics, Oita, Japan, January 31–February 2, 2008     

Finite time convergent control using terminal sliding mode

A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. The proposed method, different from many existing terminal sliding model control design methods, is studied, and then feedback laws are designed for a class of nonlinear systems, along with illustrative 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.     

Nonsmooth finite-time control of uncertain second-order nonlinear systems

Nonsmooth finite-time stabilizing control laws have been developed for the double integrator system. The objective of this paper is to further explore the finite-time tracking control problem of a general form of uncertain second-order affine nonlinear system with the new forms of terminal sliding mode (TSM). Discontinuous and continuous finite-time controllers are also developed respectively without the singularity problem. Complete robustness can be acquired with the former, and enhanced robustness compared with the conventional boundary layer method can be expressed as explicit bounded function with the latter. Simulation results on the stabilizing and tracking problems are presented to demonstrate the effectiveness of the control algorithms.     

On the second-order sliding mode control of nonlinear systems with uncertain control direction

This note deals with the implementation of a second-order sliding mode control algorithm for a class of nonlinear systems in which the sign of the high-frequency gain, though constant, is unknown. A specific second-order sliding mode control algorithm, the “Suboptimal” algorithm, is properly modified in order to face the uncertainty in the control direction. It is shown that after a finite time the uncertain sign is identified and the standard finite time convergence takes place from that time on. Simulation results are provided.     

Terminal sliding mode observers for a class of nonlinear systems

This paper proposes a terminal sliding mode observer for a class of nonlinear systems to achieve finite time convergence for all error states. Compared to standard sliding mode observers which only enable finite time convergence of the output error, the observer in this paper makes use of fractional powers to reduce other non-output errors to zero in finite time. A 2-degree-of-freedom robotic manipulator is used to demonstrate the effectiveness of the proposed observer.     

Design of sliding mode control for a class of uncertain switched systems

This paper considers the problem of sliding mode control for a class of uncertain switched systems with parameter uncertainties and external disturbances. A key feature of the controlled system is that each subsystem is not required to share the same input channel, which was usually assumed in some existing works. By means of a weighted sum of the input matrix, a common sliding surface is designed in this work. It is shown that the reachability of the sliding surface can be ensured by the present sliding mode controller. Moreover, the sliding motion on the specified sliding surface is asymptotically stable under the proposed switching signal dependent on the state and time. Additionally, the above results are further extended to the case that the system states are unavailable. Both the sliding surface and sliding mode controller are designed by utilising state-observer. Finally, numerical simulation examples are given to illustrate the effectiveness of the present 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.     

A new terminal sliding mode control for robotic manipulators

In this study, a new terminal sliding mode control approach is developed for robotic manipulators based on finite-time stability theory and differential inequality principle. The corresponding stability analysis is presented to lay a foundation for theoretical understanding to the underlying design issue as well as safe operation for real system. An illustrative example of a two-link rigid robotic manipulator is presented to validate effectiveness of the proposed approach.     

Event-triggered sliding mode control for a class of nonlinear systems

ABSTRACT

Event-triggering strategy is one of the real-time control implementation techniques which aims at achieving minimum resource utilisation while ensuring the satisfactory performance of the closed-loop system. In this paper, we address the problem of robust stabilisation for a class of nonlinear systems subject to external disturbances using sliding mode control (SMC) by event-triggering scheme. An event-triggering scheme is developed for SMC to ensure the sliding trajectory remains confined in the vicinity of sliding manifold. The event-triggered SMC brings the sliding mode in the system and thus the steady-state trajectories of the system also remain bounded within a predesigned region in the presence of disturbances. The design of event parameters is also given considering the practical constraints on control execution. We show that the next triggering instant is larger than its immediate past triggering instant by a given positive constant. The analysis is also presented with taking delay into account in the control updates. An upper bound for delay is calculated to ensure stability of the system. It is shown that with delay steady-state bound of the system is increased than that of the case without delay. However, the system trajectories remain bounded in the case of delay, so stability is ensured. The performance of this event-triggered SMC is demonstrated through a numerical simulation.     

Robust tracking and model following of uncertain dynamic systems via discrete-time integral sliding mode control

A discrete-time integral sliding mode control scheme is proposed to realize the problem of robust tracking and modeling following for a class of uncertain linear systems. It will be shown that the proposed scheme guarantees the stability of closed-loop system and achieves zero-tracking error in the presence of parameter uncertainties and external disturbances. The selection of switching surface and the existence of sliding mode are two important issues, which have been addressed. This scheme assures robustness against system uncertainties and disturbances. Chattering phenomenon and reaching phase are eliminated. Moreover, the knowledge of upper bound of uncertainties is not required. Both the theoretical analysis and illustrative example demonstrate the validity of the proposed scheme. 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.     

Adaptive sliding mode control of nonlinear robotic systems with time-varying parameters

In this paper an adaptive sliding mode control scheme is presented for nonlinear robotic systems with bounded time-varying parameters. The control scheme developed is very simple and computationally efficient since it does not require a knowledge of either The mathematical model or the parameter values of the robotic dynamics. It is shown that the controller is globally stable in the presence of a class of state-dependent uncertainties and that the size of the tracking error can be made arbitrarily small.     

Robust integral sliding mode control for uncertain stochastic systems with time-varying delay

This paper is concerned with sliding mode control for uncertain stochastic systems with time-varying delay. Both time-varying parameter uncertainties and an unknown nonlinear function may appear in the controlled system. An integral sliding surface is first constructed. Then, by means of linear matrix inequalities (LMIs), a sufficient condition is derived to guarantee the global stochastic stability of the stochastic dynamics in the specified switching surface for all admissible uncertainties. The synthesized sliding mode controller guarantees the reachability of the specified sliding surface. Finally, a simulation example is presented to illustrate the proposed method.     

Time-varying sliding mode control for a class of uncertain MIMO nonlinear system subject to control input constraint

To solve the regulator problem of a class of uncertain MIMO nonlinear systems subject to control input constraint, three types of time-varying sliding mode control laws are proposed. The sliding surfaces pass the initial value of the system at the initial time, and are shifted/rotated towards the predetermined ones. The controller parameters are optimized by genetic algorithm (GA). Lyapunov method is adopted to prove the stability and robustness to the parameter uncertainties and external disturbance. By me...     

Continuous finite-time control for robotic manipulators with terminal sliding mode

A continuous finite-time control scheme for rigid robotic manipulators is proposed using a new form of terminal sliding modes. The robustness of the controller is established using the Lyapunov stability theory. Theoretical analysis and simulation results show that faster and high-precision tracking performance is obtained compared with the conventional continuous sliding mode control method.