Approximation Capability Of Fuzzy Systems Research Articles

Chattering suppression and hydrodynamic disturbance estimation of underwater manipulators using adaptive fuzzy sliding mode control

Robotic manipulators are nowadays widely used in various underwater scenarios, but their motion control remains a challenging task due to hydrodynamic effects. This article proposes a novel adaptive fuzzy sliding mode control (AFSMC) strategy for precise and robust control of underwater manipulators. To simulate the movement of the robotic manipulators in the underwater environment, the Unified Robot Description Format (URDF) file of a custom-designed electric underwater manipulator is imported into the Simscape Multibody and the hydrodynamic disturbance is modeled according to Morison’s equation. Furthermore, the proposed control strategy takes advantage of the universal approximation capability of fuzzy systems to avoid chattering and observe disturbances by adjusting the control gains of classical sliding mode control (CSMC). And adaptive laws are designed to update the parameters of the fuzzy systems. The strong friction caused by the seal is also compensated by actual test data. In the simulation experiments, a special environment of water flow and variable loads is considered. The results demonstrate that the AFSMC strategy can achieve high precision and strong robustness against disturbances for trajectory tracking. More importantly, the chattering caused by CSMC can be eliminated and the hydrodynamic disturbance can be estimated with high precision through the proposed control strategy.

Adaptive Interval Type-2 Fuzzy Tracking Control of PV Grid-Connected Inverters

Fuzzy logic systems with approximation capabilities provide effective control for nonlinear and uncertain systems. Due to the characteristics of photovoltaic (PV) and the PWM method, a grid-connected PV system is a considerably nonlinear system with unpredictable parameters. In this study, a new adaptive interval type-2 fuzzy approximation-based controller (AIT2FAC) was developed to control a three-phase grid-connected PV system. The proposed controller can be implemented without any prior knowledge of the system mathematical model. In the presence of both parametric and modeling uncertainty, the developed controller can achieve the control objectives. The proposed controller utilizes the principle of input-output feedback linearization and the approximation capability of fuzzy systems to the control inverter current components to track prescribed reference values. The proposed AIT2FAC controller is capable of handling system uncertainties due to the interval type-2 fuzzy logic system capability to cope with a high level of uncertainty. Lyapunov analysis is used to determine the closed-loop system stability and the updating laws of the proposed controller parameters. The effectiveness of the designed controller to achieve the required tracking is validated for different operating cases, including system disturbances, modelling, and parameter uncertainties. For evaluation, the proposed type-2 fuzzy controller is compared to a type-1 fuzzy controller in terms of some performance measures. The comparison results demonstrate that the proposed type-2 fuzzy controller has better tracking performance than the type-1 fuzzy controller in terms of the settling time, the maximum overshoot, the integral absolute error (IAE) and the integral time of absolute error (ITAE).

Automatic fuzzy rules production based on clustering and implication selection

This paper deals with improving the approximation capability of fuzzy systems. Fuzzy negations produced via conical sections are a promising methodology towards better fuzzy implications in fuzzy rules. The linguistic variables and the fuzzy rules are induced automatically following a fuzzy equivalence relation. The uncertainty of linear or nonlinear systems is thus dealt with. In this study, the clustering is optimized without human intervention, but also the best inference mechanism for a particular dataset is prescribed. It has been found that clustering based on fuzzy equivalence relation and fuzzy inference via conical sections leads to remarkably accurate approximations. A fuzzy rule based system with fewer control parameters is proposed. An application on telecom data shows the use of the methodology, its applicability to a real problem and its performance compared to other alternatives in terms of quality.

Hybrid force/position control of robotic arms manipulating in uncertain environments based on adaptive fuzzy sliding mode control

In this study, the hybrid force/position control of robotic manipulators operating in uncertain environments is addressed by integrating the fuzzy logic with conventional sliding mode control (SMC). After decomposition of the manipulator dynamics into position, force, and redundant joint subspaces, the universal approximation capability of fuzzy systems is employed to approximate the equivalent part of the control input constructed based on SMC concept. The robust part of the controller is estimated by an adaptive PI controller to compensate for deviations due to the presence of model uncertainties and perturbations. Furthermore, some adaptation laws are derived for updating the parameters online when some changes in the system dynamics are made. The proposed adaptive fuzzy sliding mode control (AFSMC) requires the minimum information about the manipulator dynamic structure and environment physical properties among the other hybrid force/position control methods presented so far. Indeed, it needs neither estimation of the dynamic model nor bounds of uncertainties in advance. The asymptotic stability of the proposed controller is also proved in the sense of Lyapunov theorem. The simulation results show the good performance of the proposed controller in coping with uncertainties. The proposed scheme is also compared with standard SMC methodology, and its superior robustness is shown in comparison with those methods which require an estimation of the plant mathematical model.

Adaptive fuzzy controller for a class of nonlinear systems with unknown backlash-like hysteresis

ABSTRACTThis paper proposes an adaptive fuzzy logic control scheme for a class of strict-feedback nonlinear systems with unknown backlash-like hysteresis. The proposed controller exploits the properties of the newly developed adaptive control in conjunction with the approximation capability of fuzzy systems. The developed controller is fast, the adaptation can be as fast as the CPU permits, and robust by virtue of the adaptive control structure and the direct estimation of the system nonlinear functions via fuzzy logic systems. As a result, the proposed adaptive fuzzy controller has a simpler form and requires fewer adaptation parameters. The inverted pendulum and Duffing forced oscillation systems are used in simulation studies to verify the effectiveness of the proposed adaptive fuzzy control scheme.

A fuzzy adaptive control approach for nonlinear systems with unknown control gain sign

In this paper, a new direct adaptive controller for nonlinear SISO systems with unknown control gain sign is investigated. The controller design is based on the approximation capability of fuzzy systems. A Nussbaum function is incorporated in the adaptation laws to deal with the unknown control direction (i.e. with the unknown control gain sign). The stability of the closed-loop system is proven using a Lyapunov approach. Finally, simulation results are given to verify the feasibility and effectiveness of the proposed controller.

Adaptive fuzzy logic load frequency control of multi-area power system

Abstract Based on indirect adaptive fuzzy control technique, a new load frequency control (LFC) scheme for multi-area power system is proposed. The power systems under study have the characterization of unknown parameters. Local load frequency controller is designed using the frequency and tie-line power deviations of each area. In the controller design, the approximation capabilities of fuzzy systems are employed to identify the unknown functions, formulate suitable adaptive control law and updating algorithms for the controller parameters. It is proved that the proposed controller ensures the boundedness of all variables of the closed-loop system and the tracking error. Moreover, in the proposed controller an auxiliary control signal is introduced to attenuate the effect of fuzzy approximation error and to mitigate the effect of external disturbance on the tracking performance. Simulation results of a three-area power system are presented to validate the effectiveness of the proposed LFC and show its superiority over a classical PID controller.

Bayesian-Game-Based Fuzzy Reinforcement Learning Control for Decentralized POMDPs

This paper proposes a Bayesian-game-based fuzzy reinforcement learning (RL) controller for decentralized partially observable Markov decision processes (Dec-POMDPs). Dec-POMDPs have recently emerged as a powerful platform for optimizing multiagent sequential decision making in partially observable stochastic environments. However, finding exact optimal solutions to a Dec-POMDP is provably intractable (NEXP-complete), necessitating the use of approximate/suboptimal solution approaches. This approach proposes an approximate solution by employing fuzzy inference systems (FISs) in a game-based RL setting. It uses the powerful universal approximation capability of fuzzy systems to compactly represent a Dec-POMDP as a fuzzy Dec-POMDP, allowing the controller to progressively learn and update an approximate solution to the underlying Dec-POMDP. The proposed controller envisages an FIS-based RL controller for Dec-POMDPs modeled as a sequence of Bayesian games (BGs). We implement the proposed controller for two scenarios: 1) Dec-POMDPs with free communication between agents; and 2) Dec-POMDPs without communication. We empirically evaluate the proposed approach on three standard benchmark problems: 1) multiagent tiger; 2) multiaccess broadcast channel; and 3) recycling robot. Simulation results and comparative evaluation against other Dec-POMDP solution approaches elucidate the effectiveness and feasibility of employing FIS-based game-theoretic RL for designing Dec-POMDP controllers.

Indirect adaptive fuzzy and impulsive control of nonlinear systems

The problem of indirect adaptive fuzzy and impulsive control for a class of nonlinear systems is investigated. Based on the approximation capability of fuzzy systems, a novel adaptive fuzzy and impulsive control strategy with supervisory controller is developed. With the help of a supervisory controller, global stability of the resulting closed-loop system is established in the sense that all signals involved are uniformly bounded. Furthermore, the adaptive compensation term of the upper bound function of the sum of residual and approximation error is adopted to reduce the effects of modeling error. By the generalized Barbalat's lemma, the tracking error between the output of the system and the reference signal is proved to be convergent to zero asymptotically. Simulation results illustrate the effectiveness of the proposed approach.

Neuro fuzzy modeling of axial field machines behavior

PurposeThis paper aims to study modeling of the nonlinear behavior of the Torus machine back EMF using an adaptive networks fuzzy inference system (ANFIS). The model can be used to study the steady‐state as well as the dynamic performances of the machine operating as a motor or as a generator.Design/methodology/approachUsing the universal approximation capability of fuzzy systems the authors designed an ANFIS network to model the nonlinear behavior of the back EMF of the Torus motor. The ANFIS is trained using an actual set machine measurements data to generate the motor back EMF for different operating conditions.FindingsSimulation results of the ANFIS model of the Torus motor at different loads proved the ability of the algorithm to effectively model the complex electromagnetic behavior of the machine. Such efficient modeling can directly help in improving and optimizing the Torus motor drive system design.Originality/valueIt demonstrates that ANFIS can model the nonlinear behavior of the back EMF of the Torus motor with excellent accuracy.

A note on smooth approximation capabilities of fuzzy systems

Modeling and prediction in some systems requires the simultaneous approximation of mappings and their derivatives to a certain finite order. In this paper, universal approximation capabilities of fuzzy systems are extended to this situation, by showing the denseness of some general classes of fuzzy models in appropriate function spaces where distance between functions is defined in terms of their derivatives. Requirements are generally very mild, and are often limited to imposing sufficient differentiability conditions on the classes of fuzzy systems to be used. The cases covered by this paper include additive fuzzy systems with Gaussian membership functions and general additive fuzzy models with realistic membership functions. Some potential application fields are considered, including examples from economics and time series prediction.

The minimum worst case error of fuzzy approximators

The approximation capability of fuzzy systems is an important topic of research when the systems are regarded as input-output maps. By using the notion of information-based complexity (IBC), we derive the minimum worst case error of a fuzzy approximator, which is independent of the detailed construction of the fuzzy rule bases.

A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators

Universal approximation is the basis of theoretical research and practical applications of fuzzy systems. Studies on the universal approximation capability of fuzzy systems have achieved great progress in recent years. In this paper, linear Takagi-Sugeno (TS) fuzzy systems that use linear functions of input variables as rule consequent and their special case, named simplified fuzzy systems that use fuzzy singletons as rule consequent, are investigated. On condition that overlapped fuzzy sets are employed, new sufficient conditions for simplified fuzzy systems and linear TS fuzzy systems as universal approximators are given, respectively. Then, a comparative study on existing sufficient conditions is carried out with numeric examples.

On universal approximation capability of fuzzy systems

The universal approximation capability of fuzzy systems using translations and dilations of one fixed function (called basis function) as their membership functions is discussed. Such types of fuzzy systems are proved to be universal approximators under conditions that the basis function is integrable, with nonvanishing integral, and a. e. continuous. This result enlarges the family of fuzzy systems which can be universal approximators. Two simulation experiments are designed to verify the conclusion.

Decentralized adaptive fuzzy control for large-scale nonlinear systems

A decentralized adaptive fuzzy control scheme for a class of large-scale nonlinear systems is proposed in this paper. The design is based on the principle of sliding mode control and the approximation capability of fuzzy systems. The control architecture employs decentralized fuzzy systems to adaptively compensate for plant uncertainties. By using the Lyapunov function method, the control algorithm is proved to be globally stable, with tracking errors converging to a neighborhood of zero.

Approximation capability of fuzzy systems using translations and dilations of one fixed function as membership functions

This paper reports on a related study on approximation theory of fuzzy systems. First, some basic principles are presented to construct membership functions. Then, an approach is proposed to form membership functions by using translations and dilations of one fixed function (called a basis function) which is very similar to that in wavelets analysis. The properties of this type of membership function reflect the advantages of the given approach. Finally, it is proved that fuzzy systems based on such membership functions are universal approximators under certain mild conditions on the basis function. This conclusion expands the family of fuzzy systems which can be universal approximators.