Fuzzy static output feedback H infinity control for nonlinear systems with time-varying delay: An LMI approach

This paper is concerned with a new control method for path tracking of autonomous ground vehicles. We exploit the fuzzy model-based control framework to deal with the time-varying feature of the vehicle speed and the highly uncertain behaviors of the tire-road forces involved in the nonlinear vehicle dynamics. To avoid using costly vehicle sensors for feedback control while favoring the simplest control structure for real-time implementation, a new fuzzy static output feedback (SOF) scheme is proposed. In particular, though the robust set-invariance property and Lyapunov-based arguments, the physical constraints on the steering input saturation and the vehicle state can be taken into account in the control design to improve the driving safety and comfort. The theoretical development relies on the use of fuzzy Lyapunov functions and the non-parallel distributed compensation control concept to reduce the design conservatism. Exploiting some specific convexification techniques, the control design is reformulated as an optimization problem under linear matrix inequalities with a single line search, which are efficiently solved via semidefinite programming techniques. The proposed fuzzy path tracking controller is evaluated through various dynamic driving tests conducted with high-fidelity CarSim/Matlab co-simulations. Moreover, to emphasize the advantages of the new fuzzy SOF controller, a performance comparison with the CarSim driver model is also performed.

This paper is concerned with the problem of delay-derivative-dependent stability analysis for Markovian jumping neutral-type interval time-varying delay systems with mixed delays. The first, based on the Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality approach, a delay-range-dependent condition for neutral-type Markovian jumping systems (NMJSs) with time-varying delays is obtained, which can guarantee global asymptotical stability of these NMJSs. Unlike the previous methods, the upper bound of the discrete delay and neutral delay derivative is taken into consideration even if this upper bound is larger than or equal to $$1(\dot{h}(t)<1,\dot{\tau}(t)<1)$$ . It is proved that the obtained results are less conservative than the existing ones. In our result, the time-varying delays are only assumed to be bounded. This has undoubtedly extended its application range. To better handle the problem on stability for neutral control systems, in which time-varying delay was involved, a stability criterion with less conservatism was put forward. Moreover, because our results in this paper are all based on the linear matrix inequality (LMI) approach, we can utilize Matlab’s LMI Control Toolbox to verify the global stability of correlation systems conveniently. As far as we are aware, this paper seems to be the first to discuss stability problems for neutral-type Markovian jumping systems with delay-derivative-dependence and delay-range-dependence.

This paper studies the fuzzy H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> filter design problem for signal estimation of nonlinear discrete-time systems with multiple time delays and unknown bounded disturbances. First, the Takagi-Sugeno (T-S) fuzzy model is used to represent the state-space model of nonlinear discrete-time systems with time delays. Next, we design a stable fuzzy H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> filter based on the T-S fuzzy model, which guarantees asymptotic stability and a prescribed H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> index for the filtering error system, irrespective of the time delays and uncertain disturbances. A sufficient condition for the existence of such a filter is established by using the linear matrix inequality (LMI) approach. The proposed LMI problem can be efficiently solved with global convergence guarantee using convex optimization techniques such as the interior point algorithm. Simulation examples are provided to illustrate the design procedure of the present method.

This paper presents a Takagi-Sugeno (TS) fuzzy state-feedback controller based on a linear matrix inequality (LMI) approach for the permanent magnet synchronous generator of wind energy conversion system (PMSG-WECS). A dc/dc converter is considered to regulate the maximum power output of the system. To show its effectiveness, the dynamic model is replaced by the TS fuzzy model, which the proposed controller can be applied to the PMSG-WECS, while the controller gains can be obtained by solving set of a LMI approach. The proposed controller guarantees the stability of the system. Therefore, the performance of the proposed TS fuzzy state-feedback controller is assessed through the computer simulation.

This paper focuses on the problem of robust guaranteed cost control for a class of nonlinear systems described by the Takagi-Sugeno (T-S ) fuzzy descriptor model with time-varying delay and parameter uncertainties. The less conservative sufficient conditions for the existence of robust guaranteed cost controller via state feedback are given in terms of linear matrix inequalities (LMIs). And the design of optimal guaranteed cost controller can be reduced to a convex optimization problem. The designed controller not only guarantees the robust quadratic stability of the closed-loop system, but also provides a minimized upper bound of the guaranteed cost. At last, a numerical example is given to illustrate the effectiveness of the proposed method and the perfect performance of the optimal guaranteed cost controller.

This paper designs a preview repetitive control (PRC) policy for a class of Takagi–Sugeno (T–S) fuzzy systems with time-varying delay and external disturbances. First, the T–S fuzzy model is employed to represent a nonlinear plant, once the nonlinear plant is represented by a T–S fuzzy model, a fuzzy improved-equivalent-input-disturbance (IEID)-based PRC law can be designed to achieve better tracking performance and disturbance rejection. Next, based on a new equality constraint, we derive a continuous-discrete two-dimensional (2D) system that paves the way to solve the design problem of the IEID-based PRC law using linear matrix inequality (LMI) approach. Then, by solving LMIs, the gains of the controller and state observer can be obtained. Finally, a numerical example is included to show the effectiveness of the proposed method.

Complex nonlinear systems can be represented to a set of linear sub-models by using fuzzy sets and fuzzy reasoning via ordinary Takagi-Sugeno (TS) fuzzy models. In this paper, the exponential stability of TS fuzzy bidirectional associative memory (BAM) neural networks with impulsive effect and time-varying delays is investigated. The model of fuzzy impulsive BAM neural networks with time-varying delays established as a modified TS fuzzy model is new in which the consequent parts are composed of a set of impulsive BAM neural networks with time-varying delays. Further the exponential stability for fuzzy impulsive BAM neural networks is presented by utilizing the Lyapunov-Krasovskii functional and the linear matrix inequality (LMI) technique without tuning any parameters. In addition, an example is provided to illustrate the applicability of the result using LMI control toolbox in MATLAB.

An improved model-free adaptive control for nonlinear systems: An LMI approach

In this parer, a sliding mode control algorithm based on Takagi-Sugeno (T-S) fuzzy model for a class of nonlinear systems is proposed. The nonlinear system is approximately represent by a T-S fuzzy model with mismatched parameter uncertainties and time-varying delay. An asymptotically stable sliding surface is designed by means of linear matrix inequality (LMI). The sliding surface can compensate for the effect of mismatched parameter uncertainties in system state. A robust sliding mode controller is designed to ensure the existence of a sliding mode and to overcome the effect of the time-varying delay and the uncertainties of the system. In addition, a novel reaching condition that can obviously reduce chattering around the sliding surface is also proposed. Matlab simulation results are offered to verify the effectiveness of the proposed algorithm.

This paper addresses the issue of tracking the output of an activated sludge process using fuzzy integral control. First, the dynamics of the nonlinear process are modeled with a dynamic state space fuzzy model integrating the effect of external disturbances, and then an additional integral state of the output tracking error is introduced to obtain an augmented Takagi-Sugeno (TS) fuzzy model. The TS fuzzy model is able to describe the dynamics of complex nonlinear systems with an excellent degree of accuracy. It is formulated by fuzzy if-then rules which can give local linear representation of the overall nonlinear system. Second, the design of the fuzzy integral control is performed, in which the state feedback gains are obtained by solving linear matrix inequalities (LMI). The objective is to ensure trajectory tracking of an activated sludge process (ASP) by controlling two key variables: the substrate concentration and the level of dissolved oxygen. To assess the performance of the proposed control strategy, a comparative analysis is carried out with a gain scheduling PI (GS-PI) controller. Simulation results are provided to illustrate the effectiveness of the proposed approach. Where, the fuzzy integral control reduces the high energy consumption in water treatment plants.

For nonlinear space-varying parabolic partial differential equation systems (PPDESs) with random time-varying delay, this article introduces a dynamic fuzzy boundary output feedback (DFBOF) control under noncollocated boundary measurement (NCBM). Initially, the nonlinear delayed PPDESs are represented by Takagi–Sugeno (T–S) fuzzy models and random time-varying delay is considered by taking the influence of uncertain factors, which belongs to two intervals in a probabilistic way. Since the system state is not fully available and NCBM makes the boundary control design very difficult, a fuzzy observer under NCBM is presented to surmount the design difficulty. Subsequently, an observer-based fuzzy boundary controller is proposed and spatial linear matrix inequality (SLMI)-based sufficient conditions to ensure mean-square exponential stability are obtained for closed-loop delayed PPDESs by utilizing the Lyapunov direct method and Wirtinger inequality. Then, to solve the SLMIs, the feasibility conditions of DFBOF controller design for nonlinear delayed PPDES are expressed in LMIs. Finally, two examples are offered to demonstrate the validity of the presented dynamic fuzzy boundary control approach.

This paper determines the designing of a non-fragile H∞ output feedback controller for a class of nonlinear uncertain dynamical systems with multiple timescales described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a non-fragile H∞ output feedback controller which guarantees the L2-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value for this class of uncertain fuzzy dynamical systems with multiple time-scales. A numerical example is provided to illustrate the design developed in this paper.

This paper studies the robust static output feedback (SOF) problem considering pole placement constraints for linear systems with polytopic uncertainty as well as linear parameter varying (LPV) systems. New linear matrix inequality (LMI) approaches are proposed for the SOF controller design while the pole placement, H2, and H∞ constraints are guaranteed. In addition, the gain-scheduled SOF controller will be designed for LPV systems if system parameters are measured. The proposed methods can be applied to general linear systems without imposing any constraints on system matrices. The performance and effectiveness of the proposed methods are shown using two examples.

This paper proposed a method of improved genetic algorithm (IGA)-based secure communications in multiple time delay chaotic (MTDC) systems with optimal H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> performance and advanced encryption standard (AES). First, we apply an initial round key via AES encryption function to acquire the encrypted message. The encrypted message is used to carry out double encryption by chaotic synchronization. A robust fuzzy control design is then presented to address the effects of modeling errors between the MTDC systems and Takagi-Sugeno (T-S) fuzzy models. Next, in terms of Lyapunov's direct method, a delay dependent exponential stability criterion is derived to guarantee that the trajectories of the slave system can approach those of the master system. Subsequently, the stability conditions of this criterion are transformed into linear matrix inequalities (LMIs). In addition, the genetic algorithm (GA) has drawn great attention from researchers due to the capability of GA in random search for achieving near-optimal solutions. The lower and upper bounds of the search space based on the LMI approach can be set so that the GA will seek better feedback gains of fuzzy controllers in order to speed up the synchronization. However, the GA has the shortcomings of premature convergence and local search. Therefore, an improved genetic algorithm (IGA) is proposed in this study to effectively overcome the weakness of the traditional GA. On the basis of the IGA, a fuzzy controller is synthesized to not only realize the exponential synchronization, but also achieve optimal H <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sup> performance by minimizing the disturbance attenuation level. Finally, a numerical example with simulations is given to demonstrate the effectiveness of our approach.

In this paper, a stable fuzzy controller in the form of linear matrix inequalities (LMIs) is designed for an electric vehicle (EV). The proposed controller evaluates the stabilization of the EV speed with robust disturbance rejection approach throughout both transient and steady states and in the presence of external disturbances and parametric uncertainties. In order to achieve an efficient control, EV's battery voltage, as control input, and EV speed, as system output, are constrained. The proposed control strategy is based on Takagi-Sugeno (T-S) fuzzy model and the parallel distributed compensation (PDC) fuzzy controller. Proposed controller can be practically implemented due to low computational load of control input that is owing to the offline process of obtaining the feedback gains, very small amplitude of control input and low power consumption. To evaluate the performance of the designed controller, simulations in five steps are conducted on an EV equipped with a brushed direct current (BDC) motor as a case study in MATLAB simulation environment. Ultimately, the real-time digital simulation results using real-time digital power system simulator (RTDS) confirm the efficiency of the proposed input-output constrained robust disturbance rejection stable fuzzy controller (IOCRDRSFC) in stabilizing the EV speed. The simulation results obtained from MATLAB and the RTDS confirm the energy-efficient and robust performance of the proposed controller in quick stabilization of the EV speed in the presence of all structured and unstructured uncertainties.