This paper addresses the issue of robust fuzzy sliding mode control for continuous-time nonlinear Takagi–Sugeno fuzzy systems with semi-Markovian switching. The focus is on designing a novel fuzzy integral sliding surface without assuming that the input matrices are the same with full column rank and then developing a fuzzy sliding-mode controller for stochastic stability purpose. Based on Lyapunov theory, a set of newly developed linear matrix inequality conditions are established for stochastic stability of the sliding-mode dynamics with generally uncertain transition rates, and then extended to where the input matrix is plant-rule-independent, as discussed in most existing literatures. Furthermore, finite-time reachability of the sliding surface is also guaranteed by the proposed fuzzy sliding-mode control laws. A practical example is provided to demonstrate the effectiveness of the established method numerically.

A Novel Robust Fuzzy Integral Sliding Mode Control for Nonlinear Semi-Markovian Jump T–S Fuzzy Systems

In this paper, the problem of steering control is investigated for vehicle path tracking in the presence of parametric uncertainties and nonlinearities In practice, the vehicle mass varies due to the number of passengers or amount of payload, while the vehicle velocity also changes during normal cruising, which significantly influences vehicle dynamics Moreover, the vehicle dynamics are strongly nonlinear caused by the tire/road forces under different road surface conditions With fuzzy modeling method, the original nonlinear path tracking system with parameter variations is first formulated as a T–S fuzzy model with additive norm-bounded uncertainties, and then an approach to the fuzzy observer-based output feedback steering control for vehicle dynamics is proposed under a fuzzy Lyapunov function framework By employing matrix inequality convexifying techniques, a sufficient condition is developed in the form of linear matrix inequalities such that the closed-loop path tracking error system is asymptotically stable with a guaranteed $\mathcal {H}_{\infty }$ level Finally, the effectiveness of the proposed fuzzy observer-based output feedback controller is demonstrated in Carsim/Matlab joint simulation environment, via which the advantage of a T–S fuzzy observer-based output controller over the closed-loop driver model embedded in Carsim is also shown with parametric uncertainties and nonlinearities

A Novel Fuzzy Observer-Based Steering Control Approach for Path Tracking in Autonomous Vehicles

This paper presents the tracking control for a robotic manipulator type delta employing fractional order PID controllers with computed torque control strategy. It is contrasted with an integer order PID controller with computed torque control strategy. The mechanical structure, kinematics and dynamic models of the delta robot are descripted. A SOLIDWORKS/MSC-ADAMS/MATLAB cosimulation model of the delta robot is built and employed for the stages of identification, design, and validation of control strategies. Identification of the dynamic model of the robot is performed using the least squares algorithm. A linearized model of the robotic system is obtained employing the computed torque control strategy resulting in a decoupled double integrating system. From the linearized model of the delta robot, fractional order PID and integer order PID controllers are designed, analyzing the dynamical behavior for many evaluation trajectories. Controllers robustness is evaluated against external disturbances employing performance indexes for the joint and spatial error, applied torque in the joints and trajectory tracking. Results show that fractional order PID with the computed torque control strategy has a robust performance and active disturbance rejection when it is applied to parallel robotic manipulators on tracking tasks.

Fractional order PID for tracking control of a parallel robotic manipulator type delta.

This article proposes two novel modified techniques, namely Pythagorean fuzzy hybrid Order of Preference by Similarity to an Ideal Solution (PFH-TOPSIS) method and Pythagorean fuzzy hybrid ELimination and Choice Translating REality I (PFH-ELECTRE I) method, in order to measure risk rankings in failure modes and effects analysis (FMEA). These methods are designed to overcome the flaws and shortcomings of traditional crisp risk priority numbers and fuzzy FMEA techniques in risk rankings. The proposed methods consider subjective as well as objective weight values of all factors in risk rankings of identified failures. The FMEA experts team are allowed to submit their information by linguistic terms using Pythagorean fuzzy numbers. Both techniques use a Pythagorean fuzzy weighted averaging operator to aggregate their independent evaluations into group assessments. Subsequent steps are different. The PFH-TOPSIS approach computes the distances of failure modes from the Pythagorean fuzzy positive ideal solution and Pythagorean fuzzy negative ideal solution. To evaluate failure modes, the PFH-ELECTRE I approach produces Pythagorean fuzzy concordance and Pythagorean fuzzy discordance matrices. We illustrate the structure of both techniques with the help of flowcharts. The effectiveness of the methods that we develop is described by a numerical example, namely a case study of 1.8-in. color super-twisted nematic (CSTN). To validate their effectiveness and accuracy, we provide a comprehensive comparative analysis with existing techniques of risk evaluation, including intuitionistic fuzzy hybrid TOPSIS, intuitionistic fuzzy TOPSIS, IWF-TOPSIS, and fuzzy TOPSIS methods.

Risk evaluation in failure modes and effects analysis: hybrid TOPSIS and ELECTRE I solutions with Pythagorean fuzzy information

Trajectory tracking control of Skid-Steered Mobile Robot based on adaptive Second Order Sliding Mode Control

In this work, we study the structure regulator for the perturbations attenuation which is based on the infinite structure regulator. The structure regulator is able to attenuate the perturbations if the transfer function of the departures and perturbations has a numerical value almost equal to zero, and it does not require the perturbations to attenuate them. We apply the structure regulator and the infinite structure regulator to a quadrotor which maintains the horizontal position with respect to the earth for the step and sine perturbations.

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Structure Regulator for the Perturbations Attenuation in a Quadrotor

The steepest descent method is frequently used for neural network tuning. Mini-batches are commonly used to get better tuning of the steepest descent in the neural network. Nevertheless, steepest descent with mini-batches could be delayed in reaching a minimum. The Hessian could be quicker than the steepest descent in reaching a minimum, and it is easier to achieve this goal by using the Hessian with mini-batches. In this article, the Hessian is combined with mini-batches for neural network tuning. The discussed algorithm is applied for electrical demand prediction.

Hessian with Mini-Batches for Electrical Demand Prediction

In this research, a sliding mode regulator with sine mapping is suggested for the stabilization of electricity generators being affected by magnet interaction nonlinearities and generator nonlinearities. To reach this goal, our suggested regulator has the following contributions: (a) it starts from the sliding mode regulator with the modifications that the saturation mapping is used to reach a smoother performance instead of the signum mapping, and the sine mapping is applied to reach an upper bound in the proportional gain error, (b) it is used to reach some chosen constant behaviors for the angle position, angle speed, and current in the electricity generators, and (c) its stabilization is ensured based on the Lyapunov approach. We show the simulation of the suggested regulator in two electricity generators.

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Stabilization of Two Electricity Generators

The perturbations are the disturbances of motion presented in the plant inputs which affect the motion of the output and states. In this paper, a sliding mode regulator is recommended for the perturbations attenuation in the plant output and states. The novelty of the advised regulator is that it does not employ an observer for the perturbations estimation; consequently, it is more compact. The asymptotic stability of the regulator is ensured via the Lyapunov approach. The mentioned regulator is employed in two tank plants prototypes.

Sliding Mode Regulator for the Perturbations Attenuation in Two Tank Plants

The observers are used to estimate some variables of one system, they improve the sensors because the sensors obtain the measures with noise, while the observers obtain the measures without noise. Furthermore, the observers are less expensive than the sensors. In this paper, two novel observers are compared for the estimation of states. Exponential stability of both observers is assured. The proposed methods are verified by two examples.

Cesar Felipe Juarez

Papers

Structure Regulator for the Perturbations Attenuation in a Quadrotor

Hessian with Mini-Batches for Electrical Demand Prediction

Stabilization of Two Electricity Generators

Sliding Mode Regulator for the Perturbations Attenuation in Two Tank Plants

Comparison Between Two Observers