Adaptive fuzzy sliding mode control with GA-based reaching laws

doi:10.1016/S0165-0114(99)00107-4

Fuzzy Sets and Systems

Volume 120, Issue 1, 16 May 2001, Pages 145-158

https://doi.org/10.1016/S0165-0114(99)00107-4 Get rights and content

Abstract

Based on fuzzy approximators of nonlinear functions, a stable $σ$ -adaptive fuzzy sliding mode continuous control with a fixed continuous reaching law is proposed in this paper for a class of nonlinear plants. In a comparison with most existing adaptive fuzzy sliding mode control schemes where the parameter projection algorithm is often involved in the adaptive laws to prevent the estimated value of the input gain function from evolving into zero, the proposed control law has shown its success and simplicity in tackling the case when the value of the estimated input gain function becomes zero during on-line operations. Moreover, based on the genetic algorithm (GA) approach to the optimal design of parameters of the reaching law, the reaching dynamics can be significantly improved during the reaching phase. The bounding parameters of the model approximation error and the external disturbance are all regarded as unknown constants in this paper, and adaptive laws for them are devised for tracking purpose. Based on Lyapunov's stability theory the proposed controller has been shown to render the tracking error to an arbitrarily small neighborhood of zero. This can be illustrated by the simulation results for an inverted pendulum system.

References (20)

J. Baker, Reducing bias and inefficiency in the selection algorithm, in: J. Grefenstette (Ed.), Proc. of the 1st...
S. Fabri et al.
Dynamic structure neural networks for stable adaptive control of nonlinear systems
IEEE Trans. Neural Networks
(1996)
W. Gao et al.
Variable structure control of nonlinear systems: a new approach
IEEE Trans. Ind. Electron.
(1993)
M. Gen et al.
Genetic Algorithms & Engineering Design
(1997)
D.E. Goldberg
Genetic Algorithms in Search, Optimization and Machine Learning
(1989)
P.A. Ioannou et al.
Robust Adaptive Control
(1996)
A. Isidori
Nonlinear Control Systems
(1989)
S. Jeoung, J. Han, K. Im, W. Ham, B. Yoo, Adaptive fuzzy sliding mode control of nonlinear system: the second control...
S. Jeoung, K. Im, B. Yoo, Adaptive sliding mode control based on FLS, Proc. of the 5th IEEE International Fuzzy...
H.K. Khalil, Nonlinear Systems, 2nd ed., Prentice-Hall, Englewood Cliffs, NJ,...

There are more references available in the full text version of this article.

Cited by (39)

Adaptive robust finite-time tracking control for quadrotor subject to disturbances
2023, Advances in Space Research
Quadrotors are extremely agile UAVs with many unknowns regarding their moment of inertia, drag coefficients, and mass. Aside from aerodynamic turbulence, the quadrotor has a high level of nonlinearity due to its underactuated mechanical system. These last two factors cause issues that necessitate adaptive and robust control. A hybrid robust nonlinear control approach for a quadrotor is described in this research paper. To address the quadrotor trajectory tracking problem, a combination of backstepping and sliding-mode approaches based on proportional integral derivative (PID) surfaces is developed, with the Lyapunov method used to evaluate the control system’s stability. The adaptive technique, in conjunction with sliding-mode and super-twisting algorithm, is then investigated in order to reduce the chattering impact of sliding mode control and estimate the various controller parameters. Super-twisting adaptive backstepping PID sliding mode approach for the quadrotor rotational and translational subsystems is presented to reduce error convergence time and improve speed tracking performance. The simulation results under various scenarios (parameters uncertainties under Gaussian random disturbances, constant and time-varying external disturbance) are given to demonstrate the efficacy and practicability of the proposed control. A comparative analysis is performed with different developed controllers using the performance of the integral of absolute error and the integral of the absolute value of the derivative of the control inputs to demonstrate the superiority and effectiveness of the designed control technique.
Variance and passivity constrained sliding mode fuzzy control for continuous stochastic non-linear systems
2016, Neurocomputing
Citation Excerpt :
However, the idea of sliding model fuzzy control [4–10] is to combine sliding mode control and fuzzy control in such a way that the advantages of both techniques can be realized. Extending the sliding mode fuzzy control approach, some control techniques are also included in the controller design problems for non-linear systems, e.g., adaptive control [11–14] and genetic algorithm control [14,15]. By using the sliding mode fuzzy control technique, the motivation of this paper is to design sliding mode fuzzy controllers for the non-linear stochastic systems such that the stability constraint, individual state variance constraint and passivity constraint are all achieved.
A multiple performance constrained sliding mode fuzzy control problem is investigated in this paper for continuous-time stochastic non-linear systems. The stability constraint, passivity constraint and individual state variance constraint are simultaneously considered in this paper. By combining sliding mode control, variance constrained control and model-based fuzzy control, a novel performance constrained fuzzy control approach is developed. Applying Lyapunov function, some sufficient conditions are derived in term of linear matrix inequalities that can be solved by convex optimal programming algorithm. The main contribution of this paper is to develop a parallel distributed compensation based sliding mode fuzzy controller such that closed-loop system can achieve multiple performance constraints. At last, a numerical example for the control of translational oscillations with a rotational actuator system is given to demonstrate the validity and effectiveness of proposed sliding mode fuzzy control method.
Variable structure control optimized by differential evolution approach applied to continuous stirred tank reactor
2015, Chemical Engineering Research and Design
Citation Excerpt :
The need for automatic design methods has always existed but only recently has its development and use increased due to improved computing power (McGookin and Murray-Smith, 2006). Recently, as an alternative to the conventional mathematical approaches, modern heuristic optimization techniques such as evolutionary algorithms (Huang et al., 2003; Efe et al., 2002; You et al., 2004; Lin and Chou, 2003; Su and Chen, 2001; Moin et al., 1995; Lin and Chen, 1997; Coelho and Krohling, 2003), simulated annealing (Utkin, 1992; McGookin et al., 1996), and particle swarm optimization (Yu and Hu, 2006) have been given much attention by many researchers due to their ability to find VSC designs that perform satisfactorily for a given task. This paper presents a discrete VSC design using an improved differential evolution optimization (IDE) approach.
This paper considers the control design based on self-tuning discrete variable structure control (VSC) technique. A novel and systematic VSC design methodology is proposed, which integrates an estimator based on recursive least-squares algorithm, a discrete quasi-sliding surface, and an optimization method. Contrary to the trial and error tuning of the variable structure feedback gains reported in the literature, the controller parameters selection in this paper is done using an improved differential evolution (IDE) optimization approach. This paper introduces an improvement to the original differential evolution (DE) to enhance the convergence rate during the optimization cycle. Our IDE algorithm utilizes a population diversity measure to tune the mutation factor. The proposed IDE has been assessed to VSC design in order to control a continuous stirred tank reactor with nonlinear dynamic behavior. Simulation results reveal that the IDE is applicable and promising for the VSC design. Moreover, when compared to classical DE, IDE performed better in the task of VSC tuning in terms of the speed of convergence and solution quality.
A decentralized adaptive fuzzy robust strategy for control of upright standing posture in paraplegia using functional electrical stimulation
2012, Medical Engineering and Physics
Citation Excerpt :
However, all these works replaced the discontinuous term k · sign(s) in the sliding mode control law with a continuous term to reduce the chattering. This violates the η-reachability condition which insures finite-time convergence to sliding surface [25–32]. In contrast, we use an AFSMC with η-reachability condition ((A.7), Appendix A), in combination with an adaptive nonlinear compensator [25,26] to reduce the chattering.
In this paper, we present a novel decentralized robust methodology for control of quiet upright posture during arm-free paraplegic standing using functional electrical stimulation (FES). Each muscle–joint complex is considered as a subsystem and individual controllers are designed for each one. Each controller operates solely on its associated subsystem, with no exchange of information between them, and the interaction between the subsystems are taken as external disturbances. In order to achieve robustness with respect to external disturbances, unmodeled dynamics, model uncertainty and time-varying properties of muscle–joint dynamics, a robust control framework is proposed. The method is based on the synergistic combination of an adaptive nonlinear compensator with sliding mode control (SMC). Fuzzy logic system is used to represent unknown system dynamics for implementing SMC and an adaptive updating law is designed for online estimating the system parameters such that the global stability and asymptotic convergence to zero of tracking errors is guaranteed. The proposed controller requires no prior knowledge about the dynamics of system to be controlled and no offline learning phase. The results of experiments on three paraplegic subjects show that the proposed control strategy is able to maintain the vertical standing posture using only FES control of ankle dorsiflexion and plantarflexion without using upper limbs for support and to compensate the effect of external disturbances and muscle fatigue.
Second-order sliding mode control with experimental application
2010, ISA Transactions
In this article, a second-order sliding mode control (2-SMC) is proposed for second-order uncertain plants using equivalent control approach to improve the performance of control systems. A Proportional + Integral + Derivative (PID) sliding surface is used for the sliding mode. The sliding mode control law is derived using direct Lyapunov stability approach and asymptotic stability is proved theoretically. The performance of the closed-loop system is analysed through an experimental application to an electromechanical plant to show the feasibility and effectiveness of the proposed second-order sliding mode control and factors involved in the design. The second-order plant parameters are experimentally determined using input–output measured data. The results of the experimental application are presented to make a quantitative comparison with the traditional (first-order) sliding mode control (SMC) and PID control. It is demonstrated that the proposed 2-SMC system improves the performance of the closed-loop system with better tracking specifications in the case of external disturbances, better behavior of the output and faster convergence of the sliding surface while maintaining the stability.
An adaptive fuzzy sliding mode controller for remotely operated underwater vehicles
2010, Robotics and Autonomous Systems
Citation Excerpt :
Yoo and Ham [23] used fuzzy inference systems to approximate the unknown system dynamics within the sliding mode controller. Some improvements to this methodology are suggested in [24–28] and an application to an underwater vehicle is presented in [5]. A drawback of this approach is the adoption of the state variables in the premise of the fuzzy rules.
Sliding mode control is a very attractive control scheme because of its robustness against both structured and unstructured uncertainties as well as external disturbances. In this way, it has been widely employed for the dynamic positioning of remotely operated underwater vehicles. Nevertheless, in such situations the discontinuities in the control law must be smoothed out to avoid the undesirable chattering effects. The adoption of properly designed boundary layers has proven effective in completely eliminating chattering, however, leading to an inferior tracking performance. This work describes the development of a dynamic positioning system for remotely operated underwater vehicles. The adopted approach is primarily based on the sliding mode control strategy and enhanced by an adaptive fuzzy algorithm for uncertainty/disturbance compensation. Using the Lyapunov stability theory and Barbalat’s lemma, the boundedness and convergence properties of the closed-loop signals are analytically proven. The performance of the proposed control scheme is also evaluated by means of numerical simulations.

View all citing articles on Scopus

View full text

Adaptive fuzzy sliding mode control with GA-based reaching laws

Abstract

Dynamic structure neural networks for stable adaptive control of nonlinear systems

IEEE Trans. Neural Networks

Variable structure control of nonlinear systems: a new approach

IEEE Trans. Ind. Electron.

Genetic Algorithms & Engineering Design

Genetic Algorithms in Search, Optimization and Machine Learning

Robust Adaptive Control

Nonlinear Control Systems