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In recent years, since the unique advantages in automotive structures, the vehicle active suspension systems have received widespread attentions. A good active suspension system can reduce the vibration and improve the overall performance of the vehicle. Therefore, the design of the controller for the active suspension system to perform autonomous adjustment plays a vital role in vehicle comfort and safety. For the active suspension of the seven-DOF sport utility vehicle (SUV) model, this paper takes the vehicle body acceleration, tire dynamic load and suspension dynamic travel as the indicators to evaluate the performance, and the proportional-integral-derivative (PID) controller is designed to improve the performance of the vehicle active suspension system. Based on the software of MATLAB/Simulink and Carsim, a closed-loop co-simulation model diagram is established, which includes a PID controller module. Meanwhile, the random road input model and the whole vehicle model are constructed in Carsim. Finally, at the speeds of 70, 90, and 120 km/h, the active suspension system under the designed PID controller is simulated and compared with the passive suspension system. The simulation results show that the active suspension system based on PID controller can effectively improve the overall performance of the vehicle, and then the comfort and safety of the vehicle can be further enhanced.

This paper studies the issue of adaptive fuzzy output-feedback event-triggered control (ETC) for a fractional-order nonlinear system (FONS). The considered fractional-order system is subject to unmeasurable states. Fuzzy-logic systems (FLSs) are used to approximate unknown nonlinear functions, and a fuzzy state observer is founded to estimate the unmeasurable states. By constructing appropriate Lyapunov functions and utilizing the backstepping dynamic surface control (DSC) design technique, an adaptive fuzzy output-feedback ETC scheme is developed to reduce the usage of communication resources. It is proved that the controlled fractional-order system is stable, the tracking and observer errors are able to converge to a neighborhood of zero, and the Zeno phenomenon is excluded. A simulation example is given to verify the availability of the proposed ETC algorithm.

Abstract In this work the fuzzy adaptive control issue is investigated for multiple‐input multiple‐output (MIMO) uncertain nonlinear systems in strict‐feedback form. The controlled systems under consideration of this work contain the immeasurable states, unknown control gain functions and input time delays. The immeasurable states are estimated by constructing a fuzzy state observer, and the uncertain nonlinear functions are approximated by utilizing the fuzzy logic systems (FLSs). In addition, the Pade approximation method is employed to handle the input time delays problem. An observer‐based fuzzy adaptive centralized control algorithm is presented by employing the adaptive backstepping control design technique and constructing the Logarithm Lyapunov functions. The designed fuzzy adaptive robust control algorithm can make sure that all signals in the closed‐loop system are semi‐globally uniformly ultimately boundedness (SGUUB). Finally, a numerical simulation example and a practical system example are considered to testify the availability of the designed centralized controllers.

This paper addresses the decentralized control issue for the fractional-order (FO) nonlinear large-scale strict-feedback systems with unmodeled dynamics. The unknown nonlinear functions are identified by fuzzy logic systems (FLSs) and the FO dynamic signals are introduced to dominate the unmodeled dynamics. Additionally, the fractional-order dynamic surface control (FODSC) design technique is introduced into the adaptive backstepping control algorithm to avoid the issue of “explosion of complexity”. Then, an adaptive fuzzy decentralized control scheme is developed via the FO Lyapunov stability criterion. It is proved that the controlled FO systems are stable and the tracking errors can converge to a small neighborhood of zero. The simulation example is provided to confirm the validity of the put forward control scheme.

In this study, an adaptive fuzzy inverse optimal control problem is investigated for a class of vehicle active suspension systems. Since active suspension systems have dynamic characteristics of complexities and spring non‐linearities, the fuzzy logic systems are utilised to learn the unknown non‐linear dynamics. In addition, there exist the constraints of the displacements of the sprung and unsprung masses, vertical vibration speeds, and current intensity in the considered suspension system, therefore, the Barrier Lyapunov functions are introduced into the control design to ensure that the full‐state constraints are not overstepped. The inverse optimal control method is adopted by constructing an auxiliary system, which circumvents the assignment of solving a Hamilton–Jacobi–Bellman equation and brings about an inverse optimal controller associated with a meaningful objective functional. Based on Lyapunov stability theory and backstepping recursive design algorithm, a fuzzy adaptive optimal control scheme is developed. It is proved that the proposed control scheme not only guarantees that the vertical vibration of the vehicle is stabilised by the electromagnetic actuator but also achieves the goal of inverse optimality with regard to the cost functional. Finally, the simulation studies check the validity of the presented control strategy.

This paper investigates the adaptive fuzzy output feedback prescribed performance control (PPC) problem for multiple-input and multiple-output (MIMO) stochastic nonlinear systems in the nonstrict-feedback form. The study of MIMO nonlinear stochastic systems is assumed to have non-structural uncertainty, unknown control directions, and unknown dead zones. The fuzzy logic systems are adopted to approximate the unknown nonlinear functions, and a state observer is designed to estimate the unmeasured states. By combining backstepping recursive design principle with PPC theory, an observer-based adaptive fuzzy prescribed performance tracking control method is presented. In order to overcome the problem of unknown control directions in nonlinear stochastic systems, the Nussbaum gain function is introduced into adaptive fuzzy control design algorithm. The stability is proven based on the Lyapunov stability theory, which demonstrated that all the signals of the closed-loop systems are semi-globally uniformly ultimately bounded (SGUUB) in probability and the tracking errors remain a small neighborhood of the origin within the prescribed performance boundeds. Finally, two simulation examples are provided to illustrate the effectiveness of the proposed approach.

The problem of tracking error constrained adaptive fuzzy output feedback control is investigated for a class of single-input and single-output (SISO) stochastic nonlinear systems with actuator faults, unknown time-delay, and unmeasured states. The considered faults are modeled as both loss of effectiveness and lock-in-place. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy adaptive observer is designed for estimating the unmeasured states. By transforming the tracking errors into new virtual error variables and based on backstepping recursive design technique, a new fuzzy adaptive output feedback control method is developed. It is shown that all the signals of the resulting closed-loop system are bounded in probability and the tracking error remains an adjustable neighborhood of the origin within the prescribed bounds. The simulation results are provided to show the effectiveness of the proposed approach.

A prescribed performance fuzzy adaptive output-feedback control approach is proposed for a class of single-input and single-output nonlinear stochastic systems with unmeasured states. Fuzzy logic systems are used to identify the unknown nonlinear system, and a fuzzy state observer is designed for estimating the unmeasured states. Based on the backstepping recursive design technique and the predefined performance technique, a new fuzzy adaptive output-feedback control method is developed. It is shown that all the signals of the resulting closed-loop system are bounded in probability and the tracking error remains an adjustable neighborhood of the origin with the prescribed performance bounds. A simulation example is provided to show the effectiveness of the proposed approach.