Optimal Robust Control Design for Constrained Uncertain Systems: A Fuzzy-Set Theoretic Approach

Yang

Mathematical Problems in Engineering

et al. 2020

In this paper, a new approach to the decentralized control design for vehicle platooning for uncertain automated highway systems is proposed. The uncertainty in the system, which is nonlinear and (possibly) fast time-varying, is bounded. The bound is assumed to be within a prescribed fuzzy set. A creative transformation is made to the system, which converts a local problem to a global problem. Based on the fuzzy description of the uncertainty bound and the transformation, a class of decentralized control is proposed in which each vehicle only needs the knowledge of its preceding vehicle in the platoon. No acceleration feedback or the information of the leading vehicle is required. Both the vehicle platooning system and the control are deterministic, hence not if-then fuzzy rule-based. The performance of the resulting controlled system is twofold. First, the collision avoidance performance is guaranteed under any safe initial conditions regardless of the value of the uncertainty. Second, the minimization of a fuzzy-based performance index is guaranteed based on an optimal choice of a control design parameter. Numerical simulations are conducted to validate the efficiency of the proposed algorithm.

Section: Robust Control Designmentioning

confidence: 99%

A New Approach to the Robust Control Design of Fuzzy Automated Highway Systems

Yang

Mathematical Problems in Engineering

et al. 2020

“…For the systems described in (14), the output PDF describing the plume temperature can be approximated by the following B-spline, ϕ k (y) (k=1, 2, 3): The nonlinearity of the system is caused mainly by output weight ω 1 in V (t), where ω 1 has two related fuzzy sets {ω 1 = 0.05π} and {ω 1 = 0.25π }. Then, i = 1, 2, and the corresponding membership functions are given by…”

Section: Simulationmentioning

confidence: 99%

“…In [13], authors studied the leader following consensus problem of multiple Euler-Lagra-nge systems subject to an uncertain leader system. In [14], by fuzzy description of the uncertainty bound, the optimal design of the control gain was proposed, which minim-ized a fuzzy performance index associated with both the fuzzy system performance and the control effort. The singular systems represent a class of systems that contain both fast and slow-response control loops, therefore solving singularity problems require more complicated methods.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Adaptive Hybrid Compensation for Actuator-Sensor Compound Faults of Non-Gaussian Uncertain Systems

Yusup

Cheng

et al. 2020

IEEE Access

This paper presents a hybrid fault-tolerant control (FTC) method to handle actuator-sensor compound faults in non-Gaussian uncertain stochastic systems with approximation errors. Considering that multi-source nonlinearities of a class of stochastic systems cannot be approximated by a unified method, fuzzy logic is used to linearize nonlinear parameters, and the Lipschitz condition helps to proof the stability of FTC systems with nonlinear sensing functions. Moreover, to handle compound faults, an adaptive hybrid fault compensation scheme is devised. When only a sensor fault occurs, the feedback contains the fault information, and a feedback error composite function in the controller direct compensates the fault passively. When multiple actuator faults and a sensor fault occur, an adaptive fusion observer simultaneously implements sensor fault masking and actuator fault estimation, and then an active-passive hybrid FTC algorithm uses a compensation function and fault estimation to perform both passive compensation of the sensor fault and active FTC of actuator faults. Furthermore, an adaptive algorithm that resembles the animal predation behavior makes the controller more sensitive to incipient fault deviations. Lyapunov functions prove the robust stability of the proposed fault tolerant systems with approximation errors, and simulation experiment verifies the performance compared to a state-of-the-art method.

Asian Journal of Control

“…Remark Compared with [22], the contributions are twofold. First, the control design in this paper can be applied for both the matched uncertain constrained system and the mismatched uncertain constrained system, while the control in [22] can only be applied for the matched uncertain constrained system. The proposed control in this paper has a wider application range.…”

Section: Performance Analysis Of the Proposed Controlmentioning

confidence: 99%

Guaranteeing performance for uncertain nonlinear systems with bounded state constraint and mismatching condition

Fang

Chen

et al. 2019

Self Cite

The control design problem for the uncertain nonlinear system with bounded state constraint and mismatching condition is considered in this paper. The uncertainty in the system, which may be due to unknown system parameters and external disturbance, is nonlinear and time‐varying. The state of the system is constrained to be bounded. The system does not satisfy the (global) matching condition. A creative one‐to‐one state transformation is proposed by converting the bounded states into the unbounded ones. A step‐by‐step state transformation is proposed to convert the mismatched system into a matched system. The robust control is then proposed based on the transformed system. The control is demonstrated to be able to guarantee the uniform boundedness and uniform ultimate boundedness of the system in the presence of uncertainty, while the state constraint can be always guaranteed.