Adaptive robot under fuzzy control

This paper deals with the problem of ranking n fuzzy subsets of the unit interval. A number of methods suggested in the literature is reviewed and tested on a group of selected examples, where the fuzzy sets can be nonnormal and/or nonconvex.The ranking is obtained from: (i) the index of strict preference defined by Watson, (ii) three indexes proposed by Yager, (iii) the algorithm used by Chang, (iv) three versions of the a-preference index suggested by Adamo, (v) the index defined by Baas and Kwakernaak, (vi) three modified versions used by Baldwin and Guild, (vii) the method proposed by Kerre, (viii) three forms of the index suggested by Jain, (ix) the four grades of dominance studied by Dubois and Prade.In simple cases the results are good for all the methods, with some exceptions. In questionable cases, where the decision must be probably modelled in accordance with the context in which it is imbedded, the best indexes seem to be the dominances suggested by Dubois and Prade. These indexes do not force any particular choice, but clearly describe the situation, hence allowing the decision-maker himself to make his ‘best’ choice.     

High-order sliding modes in control systems

The article considers the properties of a new type of solutions that arise in discontinuous dynamic systems. A specific feature of these solutions is the tangency of the phase velocity vectors to the manifold of the right-hand side discontinuities, instead of the transversal intersection of the manifold typically observed for ordinary sliding modes. The solutions identified in this case are high-order sliding modes, and the order of the mode is determined by the smoothness of tangency of the sliding manifold. Second-order sliding modes are considered in detail. Examples of systems with such modes are given; application of the theory to stabilization of uncertain dynamic systems is described. It is shown that the sensitivity of high-order sliding modes to small variations in the right-hand side of the discontinuous system is an order of magnitude higher than for ordinary sliding modes.Translated from Nelineinye Dinamicheskie Sistemy: Kachestvennyi Analiz i Upravlenie Sbornik Trudov, No. 2, pp. 39–70, 1993.     

Approximation theorem for a nonlinear control system with sliding modes

We consider the question of validity of the extension of a nonlinear control system by introducing the so-called sliding modes (i.e., by convexifying the set of admissible velocities) in the presence of constraints imposed on the endpoints of trajectories. We prove that a trajectory of the extended system can be approximated by trajectories of the original system if the equality constraints of the extended system are nondegenerate in the first order. The proof is based on a nonlocal estimate for the distance to the zero set of the nonlinear operator corresponding to the extended system, and involves a specific iteration process of corrections. Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2007, Vol. 256, pp. 102–114.     

Robust fuzzy control of a class of fuzzy bilinear systems with time-delay

This paper presents robust fuzzy controllers for a class of T–S fuzzy bilinear systems (FBSs) with time-delay. First, we adopt the parallel distributed compensation (PDC) method to design a fuzzy controller to stabilize the T–S FBS with time-delay. The stability conditions of the overall fuzzy control system are formulated by linear matrix inequalities (LMIs). Secondly, we propound some LMI conditions to set up the robust controller to stabilize the uncertain T–S FBS with time-delay. Finally, the validity and applicability of the proposed schemes are demonstrated by simulations.     

Mathematical modeling and fuzzy control of a flexible-link robot arm

In this paper, the Timoshenko theory is applied to investigate a new mathematical model for the “shoulder-elbow-like” single flexible-link robot arm with dampings. Detailed analysis and derivation are given to support the mathematical modeling of this particular flexible mechanism. A new design of a fuzzy-logic-based (PI + D)² control scheme is developed for both vibration suppression and set-point tracking. Computer simulation results for the modeling are performed to observe the significant vibration modes, and simulation results for the control scheme demonstrate that the controllers perform very well for the tracking based on this flexible-link model. A newly developed method for stability analysis using the “two-straight-lines” criterion is also presented.     

Adaptive fuzzy sliding mode control scheme for uncertain systems

Most physical systems inherently contain nonlinearities which are commonly unknown to the system designer. Therefore, in modeling and analysis of such dynamic systems, one needs to handle unknown nonlinearities and/or uncertain parameters. This paper proposes a new adaptive tracking fuzzy sliding mode controller for a class of nonlinear systems in the presence of uncertainties and external disturbances. The main contribution of the proposed method is that the structure of the controlled system is partially unknown and does not require the bounds of uncertainty and disturbance of the system to be known; meanwhile, the chattering phenomenon that frequently appears in the conventional variable structure systems is also eliminated without deteriorating the system robustness. The performance of the proposed approach is evaluated for two well-known benchmark problems. The simulation results illustrate the effectiveness of our proposed controller.     

Unknown nonlinear chaotic gyros synchronization using adaptive fuzzy sliding mode control with unknown dead-zone input

In this paper, the problem of synchronizing two chaotic gyros in the presence of uncertainties, external disturbances and dead-zone nonlinearity in the control input is studied while the structure of the gyros, parameters of the dead-zone and the bounds of uncertainties and external disturbances are unknown. The dead-zone nonlinearity in the control input might cause the perturbed chaotic system to show unpredictable behavior. This is due to the high sensitivity of these systems to small changes in their parameters. Thereby, the effect of these issues should not be ignored in the control design for these systems. In order to eliminate the effects from the dead-zone nonlinearity, in this paper, a robust adaptive fuzzy sliding mode control scheme is proposed to overcome the synchronization problem for a class of unknown nonlinear chaotic gyros. The main contribution of our paper in comparison with other works that attempt to solve the problem of dead-zone in the synchronization of chaotic gyros is that we assume that the structure of the system, uncertainties, external disturbances, and dead-zone are fully unknown. Simulation results are provided to illustrate the effectiveness of the proposed method.     

Adaptive fuzzy sliding mode control of the cart-pole underactuated system

In this work, an intelligent control scheme is proposed for the stabilization of the cart-pole underactuated system. The adopted approach is primarily based on a smooth sliding mode controller, but an adaptive fuzzy inference system is embedded within the boundary layer in order to improve the control performance. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Robust intelligent sliding model control using recurrent cerebellar model articulation controller for uncertain nonlinear chaotic systems

In this paper, a robust intelligent sliding model control (RISMC) scheme using an adaptive recurrent cerebellar model articulation controller (RCMAC) is developed for a class of uncertain nonlinear chaotic systems. This RISMC system offers a design approach to drive the state trajectory to track a desired trajectory, and it is comprised of an adaptive RCMAC and a robust controller. The adaptive RCMAC is used to mimic an ideal sliding mode control (SMC) due to unknown system dynamics, and a robust controller is designed to recover the residual approximation error for guaranteeing the stable characteristic. Moreover, the Taylor linearization technique is employed to derive the linearized model of the RCMAC. The all adaptation laws of the RISMC system are derived based on the Lyapunov stability analysis and projection algorithm, so that the stability of the system can be guaranteed. Finally, the proposed RISMC system is applied to control a Van der Pol oscillator, a Genesio chaotic system and a Chua’s chaotic circuit. The effectiveness of the proposed control scheme is verified by some simulation results with unknown system dynamics and existence of external disturbance. In addition, the advantages of the proposed RISMC are indicated in comparison with a SMC system.     

Enhanced adaptive fuzzy sliding mode control for uncertain nonlinear systems

In this article, a novel Adaptive Fuzzy Sliding Mode Control (AFSMC) methodology is proposed based on the integration of Sliding Mode Control (SMC) and Adaptive Fuzzy Control (AFC). Making use of the SMC design framework, we propose two fuzzy systems to be used as reaching and equivalent parts of the SMC. In this way, we make use of the fuzzy logic to handle uncertainty/disturbance in the design of the equivalent part and provide a chattering free control for the design of the reaching part. To construct the equivalent control law, an adaptive fuzzy inference engine is used to approximate the unknown parts of the system. To get rid of the chattering, a fuzzy logic model is assigned for reaching control law, which acting like the saturation function technique. The main advantage of our proposed methodology is that the structure of the system is unknown and no knowledge of the bounds of parameters, uncertainties and external disturbance are required in advance. Using Lyapunov stability theory and Barbalat’s lemma, the closed-loop system is proved to be stable and convergence properties of the system is assured. Simulation examples are presented to verify the effectiveness of the method. Results are compared with some other methods proposed in the past research.     

Robust stabilization of internally delayed uncertain systems via sliding mode control

Summary The problem of robust stabilization of internally delayed uncertain systems via sliding mode controllers (SMC's) is studied in this paper. The robustness property and assymptotic stability of the system are discussed. Some sufficient conditions for the design of SMC and the switching hyperplane are given. Further generalization results, which lead to a simple design and implementation, are made for the system being described in companion form. A method is suggested for the elimination of limit cycles in systems being regulated by a relay SMC while allowing the generation of sliding motion and thus ensuring the closed-loop asymptotic stability.     

Robust output feedback sliding mode control for uncertain discrete time systems

This paper proposes a robust output feedback controller for a class of uncertain discrete-time, multi-input multi-output, linear, systems. This method, which is based on the combination of discrete-time sliding mode control (DTSMC) and Kalman estimator, ensures the stability, robustness and an output tracking against the modeling uncertainties at large sampling periods. For this purpose, an appropriate structure is considered for sliding surface and the Lyapunov theory for the mismatched uncertain system is then used to design its parameter. This problem leads to solve a set of linear matrix inequalities. A new method is then proposed to reach the quasi-sliding mode and stay thereafter. Simulation studies show the effectiveness of the proposed method in the presence of parameter uncertainties and external disturbances at large sampling periods.     

Disturbance-observer-based fuzzy terminal sliding mode control for MIMO uncertain nonlinear systems

This study is concerned with the design of a disturbance-observer-based fuzzy terminal sliding mode controller (FTSMC) for multi-input multi-output (MIMO) uncertain nonlinear systems by considering unknown non-symmetric input saturation and control singularity. The disturbance observer is proposed for the unmeasured external disturbance and guarantees the convergence of the disturbance estimation error to zero in a finite time. The terminal sliding mode controller (TSMC) is designed for MIMO uncertain nonlinear systems by utilizing the output of the proposed disturbance observer. This control scheme combines the disturbance-observer-based TSMC with a fuzzy logic system in the presence of unknown non-symmetric input saturation and control singularity in order to reduce chattering phenomena. Finite time asymptotic stability, convergence of the disturbance observer, and convergence of the closed-loop system are proved via Lyapunov stability theorem. In addition, a five-rotor unmanned aerial vehicle (UAV) is employed in the numerical simulations to demonstrate the effectiveness and performance of the proposed control scheme. Disturbance observer estimates the payload and flight endurance of the five-rotor UAV. Genetic algorithm (GA) optimization is used to specify the parameters of the disturbance-observer-based TSMC (GATSMC) to decrease chattering. Finally, the superior performance of FTSMC is investigated over TSMC and GATSMC.     

Robust ISS-satisficing variable universe indirect fuzzy control for chaotic systems

In the conventional robust input to state stable (ISS)-satisficing control system, all parameters of the system must be known beforehand, so the application area is limited. In this paper, an attempt is made to create a bridge between two important design techniques, i.e., the robust ISS-satisficing control strategy and the fuzzy control strategy, and the new control method we first proposed has both the inverse optimality of robust ISS-satisficing control and the robust and predictive performance of fuzzy control. By control Lyapunov method, the overall closed-loop system is shown to be stable. In this work, we combine these two control methods, make them learn from the other’s strong points, offset its weakness. The simulation results are given to confirm the control algorithm is feasible and performances well.     

Robust controlling hyperchaos of the Rössler system subject to input nonlinearities by using sliding mode control

A sliding mode control is designed to stabilize the well-known hyperchaos of Rössler system to equilibrium points subject to sector nonlinear input. The proposed control law is robust against both the input nonlinearity and external disturbance. The error bound can be arbitrarily set by assigning the corresponding dynamics to the sliding surfaces when the desired state is not an equilibrium point. Simulation results show that the system state can be regulated to an equilibrium point in the state space. It is also seen that the system still possesses advantage of fast response and good transient performance even though the control input is nonlinear.     

Adaptive fuzzy sliding mode control for synchronization of uncertain fractional order chaotic systems

This paper deals with chaos synchronization between two different uncertain fractional order chaotic systems based on adaptive fuzzy sliding mode control (AFSMC). With the definition of fractional derivatives and integrals, a fuzzy Lyapunov synthesis approach is proposed to tune free parameters of the adaptive fuzzy controller on line by output feedback control law and adaptive law. Moreover, chattering phenomena in the control efforts can be reduced. The sliding mode design procedure not only guarantees the stability and robustness of the proposed AFSMC, but also the external disturbance on the synchronization error can be attenuated. The simulation example is included to confirm validity and synchronization performance of the advocated design methodology.     

Nonlinear and chaos control of a micro-electro-mechanical system by using second-order fast terminal sliding mode control

In this paper, a novel second-order fast terminal sliding mode control (SFTSMC) scheme is proposed to suppress the chaotic motion of a micro-mechanical resonator with system uncertainty and external disturbance. To obtain a better disturbance rejection property, a fuzzy logic system is introduced to estimate the upper boundary of the sum of system uncertainty and external disturbance. Moreover, we employ the finite-time technique to obtain the properties of fast response and high precision. Finally, numerical simulations demonstrate the effectiveness of the proposed control scheme.     

Adaptive fuzzy output feedback control for a single-link flexible robot manipulator driven DC motor via backstepping

In this paper, an adaptive fuzzy output feedback approach is proposed for a single-link robotic manipulator coupled to a brushed direct current (DC) motor with a nonrigid joint. The controller is designed to compensate for the nonlinear dynamics associated with the mechanical subsystem and the electrical subsystems while only requiring the measurements of link position. Using fuzzy logic systems to approximate the unknown nonlinearities, an adaptive fuzzy filter observer is designed to estimate the immeasurable states. By combining the adaptive backstepping and dynamic surface control (DSC) techniques, an adaptive fuzzy output feedback control approach is developed. Stability proof of the overall closed-loop system is given via the Lyapunov direct method. Three key advantages of our scheme are as follows: (i) the proposed adaptive fuzzy control approach does not require that all the states of the system be measured directly, (ii) the proposed control approach can solve the control problem of robotic manipulators with unknown nonlinear uncertainties, and (iii) the problem of “explosion of complexity” existing in the conventional backstepping control methods is avoided. The detailed simulation results are provided to demonstrate the effectiveness of the proposed controller.     

Robust synchronization of drive–response chaotic systems via adaptive sliding mode control

A robust adaptive sliding control scheme is developed in this study to achieve synchronization for two identical chaotic systems in the presence of uncertain system parameters, external disturbances and nonlinear control inputs. An adaptation algorithm is given based on the Lyapunov stability theory. Using this adaptation technique to estimate the upper-bounds of parameter variation and external disturbance uncertainties, an adaptive sliding mode controller is then constructed without requiring the bounds of parameter and disturbance uncertainties to be known in advance. It is proven that the proposed adaptive sliding mode controller can maintain the existence of sliding mode in finite time in uncertain chaotic systems. Finally, numerical simulations are presented to show the effectiveness of the proposed control scheme.