Probabilistic fuzzy logic controller for uncertain nonlinear systems

There are a lot of approaches in logistics demand forecasting field and perform different characters. The probabilistic fuzzy set (PFS) and probabilistic fuzzy logic system is designed for handling the uncertainties in both stochastic and nonstochastic nature. In this paper, an asymmetric probabilistic fuzzy set is proposed by randomly varying the width of asymmetric Gaussian membership function. And the related PFLS is constructed to be applied to a logistics demand forecasting. The performance discloses that the asymmetry-width probabilistic fuzzy set performs better than precious symmetric one. It is because the asymmetric probabilistic fuzzy sets variability and malleability is higher than this of the symmetric probabilistic fuzzy set.

In this study, a new adaptive fuzzy terminal sliding mode (AFTSM) control is presented for control of uncertain nonlinear systems with disturbances. The proposed controller incorporates terminal-based gradient descent (GD) algorithm and fuzzy logic system into a continuous nonsingular terminal sliding mode. The nonlinear dynamics of the system to be controlled are approximated with the fuzzy logic system and an adaptive law based on the terminal-based GD is proposed for online updating the parameters. The most advantage of the proposed terminal-based GD is the finite-time convergence compared to the conventional GD learning algorithm. It is proved that under the proposed terminal sliding mode and updating law, the tracking and approximation errors converge to the neighbourhood of zero in a very short time. Simulation results are given to illustrate the performance of the proposed AFTSM control through the control of a second-order system and a two-link rigid robotic manipulator. The simulation results show that faster and high-precision tracking performance is obtained compared with the conventional continuous terminal sliding mode control methods. Moreover, the proposed terminal sliding mode is applied to control of joint movement generated by functional electrical stimulation. The experiment results verify that accurate control of movement is obtained using the proposed control scheme.

The asynchronous machine has qualities that make it a preferred candidate for variable speed drives, but this simplicity is accompanied by great physical complexity due to the electromagnetic interactions between the stator and the rotor. This paper presented a comparison between fuzzy PI logic and PI traditional controllers based for the speed control of the asynchronous machine (ASM); the analysis was achieved in MATLAB/SIMULINK environment. At first, it described the ASM indirect vector control, which consists in eliminating the coupling between the armature and the inductor to reduce its operation comparable to that of a DC machine. In addition, it described the PI controller; the fuzzy logic controller that does not deal with a well-defined mathematical relationship, but uses inferences with multiple rules control, then, compared their performance. The results of all the controllers have been compared. The machine started at t = 0.1 s from zero speed to t = 0.4 s at no load, and at t = 5 s, a load torque of T = 10 N m was applied to observe the controllers’ performance. As for the comparison of the controllers’ speed response, it can be observed that the PI controller has the highest and that the fuzzy PI has the lowest overshoot of (rad/s). Besides, the settling time for the fuzzy PI is lower than that of PI. The results showed the effectiveness and robustness of the fuzzy control system compared to PI controller for indirect vector control of asynchronous machine.KeywordsAsynchronous machine (ASM)Indirect field-oriented control (IFOC)PI controllerFuzzy logic controllerVector control

In this paper, we present a new scheme to design adaptive fuzzy output-feedback controller for uncertain nonlinear systems in the presence of input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is synthesized. Unlike some existing control schemes for systems with input saturation, the developed controller dose not require assumptions on the states available and nonlinear systems satisfying the matching condition. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach.

This paper presents a composite fuzzy learning finite-time prescribed performance control (PPC) approach for uncertain nonlinear systems with dead-zone inputs. First, a finite-time performance function is constructed by a quartic polynomial. Subsequently, with the help of an error transformation function, the restriction problem of the tracking error performance is transformed into a stability problem of an equivalent transformation system. In order to ensure that all signals of the closed-loop system are bounded, a finite-time PPC method combined with fuzzy logic systems (FLSs) is proposed. Although the tracking error can be guaranteed to be limited within a predefined range, the proposed finite-time PPC method only uses instantaneous data, which cannot guarantee the accurate estimation of unknown functions under the influence of dead-zone inputs. Therefore, based on the persistent excitation (PE) condition, a predictive error is defined by using online recorded data and instantaneous data, and a corresponding composite learning finite-time PPC method with parameter updating the law, which can not only achieve the control aim of the former method but also improve the control effect, is designed. The simulation results verified that the composite learning finite-time PPC method is more effective than the finite-time PPC method without learning.

A concept of probabilistic fuzzy logic is introduced as a way of representing and/or modeling existing randomness in many real world systems and natural language propositions. The approach is based on combining both the concepts of probability of truth and degree of truth in a unique framework. This combination is carried out in both fuzzy sets and fuzzy rules resulting in the concepts of probabilistic fuzzy sets and probabilistic fuzzy rules, respectively. Having one of these probabilistic elements, a probabilistic fuzzy system is then introduced as a fuzzy-probabilistic model of a complex nondeterministic system. In a simple example, human skepticism about the optimal fuzzy rule base is modeled through substituting a probabilistic fuzzy rule base for a conventional one. The closed loop response of the resulting controller for tank level control is shown through simulation and is compared with a conventional fuzzy controller.

Decentralized neural identification and control for uncertain nonlinear systems: Application to planar robot

Synthesis of smoother robust control for nonlinear uncertain dynamical systems is considered. The existing saturation-type robust controller guarantees asymptotic stability or stability of uniform ultimate boundedness. It is shown that, mainly due to the part of uncertainties that is bounded by a constant, the controller may potentially have a very large rate of change in order to achieve a small ultimate bound for the state. This study, on its gain or the property of its partial derivative, reveals the need for designing smoother nonlinear robust controller along two directions. First, in a recursive design of robust control, fictitious robust control must be designed to be as smooth as possible so that the actual robust control will not have too large of a magnitude for implementation purposes. Second, if the uncertainties are known to have bounded rate of change, it is both practically and theoretically important to design a robust controller which rate of change is limited by that of the uncertainties. The objective of this paper is to design smoother robust controls by providing results on those two topics. >

In this paper, an adaptive fuzzy output feedback control approach is presented for a class of single-input single-output uncertain nonlinear systems with unknown backlash-like hysteresis and unmeasured states. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a state filter observer is designed to estimate unmeasured states. Combining the backstepping recursive design with modular design techniques, a new adaptive fuzzy output control scheme is developed. It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semiglobally uniformly ultimately bounded, and the tracking error converges to a small neighborhood of the origin. A simulation is included to illustrate the effectiveness of the proposed approach. The important feature of the proposed control approach is that it can solve the states immeasurable problem of nonlinear systems with unknown backlash-like hysteresis and the problem of unknown virtual control coefficients.

In this paper, a robust adaptive fuzzy control for a class of nonlinear uncertain systems preceded by an unknown dead-zone and with unknown upper bound of uncertainties is developed. The dead-zones are quite commonly encountered in many systems (e.g., DC servosystem, robot, and machine tools), are usually poorly known, and may severely limit the performance of control. In addition, the system uncertainties (e.g., parameter variations, or external load, unmodeled dynamics) often exist. Therefore, the controllers are required to deal with the robust stability and performance of the systems with unknown dead-zone and in the presence of uncertainties, whose upper bound is generally unknown. In the beginning, an adaptive dead-zone compensation is employed to improve system performance. Then the unknown system functions and the unknown upper bound of system uncertainties are respectively approximated by fuzzy logic systems with unknown weights. The unknown bounds caused by the learning error of the slope of dead-zone and the system functions are also tackled by an extra learning law. The above weights are all on-line learned to provide for the controller design. Moreover, the projection terms in these learning laws are designed such that the boundedness of the learning weight can be assured.

Event-triggered low-computation adaptive output-feedback fuzzy tracking control of uncertain nonlinear systems

Typical Takagi–Sugeno PI and PD fuzzy controllers: analytical structures and stability analysis

This paper introduces a novel adaptive inverse multilayer T-S fuzzy controller (AIMFC) optimally identified with an optimization soft computing algorithm available for a class of robust control applied in uncertain nonlinear SISO systems. The parameters of multilayer T-S fuzzy model are optimally identified by the differential evolution (DE) algorithm to create offline the inverse nonlinear plant with uncertain coefficients. Then, the adaptive fuzzy-based sliding mode surface is applied to ensure that the closed-loop system is asymptotically stable in which the stability is satisfied using Lyapunov stability concept. The control quality of the proposed AIMFC algorithm is compared with the three recent advanced control algorithms applied in the Spring-Mass-Damper (SMD) benchmark system. Simulation and experiment results with different control parameters show that the proposed algorithm is better than the inverse fuzzy controller and the conventional adaptive fuzzy controller comparatively applied in both SMD system and the coupled-liquid tank system with the performance index using the least mean squares (LMS) error, which is investigated to demonstrate the efficiency and the robustness of the proposed AIMFC control approach.

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

DVRs commonly use PI controllers. In spite of the fact that the required Proportional Integral controller does not alone provide the output, by using gains which are fixed when there is a variations in the operating conditions or system parameters. This problem is solved by an adaptive Proportional integral with fuzzy logic. The fuzzy controller will adjust the error and rate of error of the Proportional Integral controller according to respective readings and fuzzy control rules, in order to get adjusted to any operating conditions variations. The corresponding results of simulation proved that the method of adaptive Proportional Integral with fuzzy logic control considerably improves the DVR performance as compared to the normal Proportional Integral controller.