Discrete-time Takagi-Sugeno Fuzzy Model Research Articles

A Fuzzy Design for a Sliding Mode Observer-Based Control Scheme of Takagi-Sugeno Markov Jump Systems under Imperfect Premise Matching with Bio-Economic and Industrial Applications

Fuzzy theory is widely studied and applied. This article introduces an adaptive control scheme for a class of non-linear systems with Markov jump switching. The introduced scheme supposes that the system is submitted to external disturbances under imperfect premise matching. By using discrete-time Takagi–Sugeno fuzzy models, a sliding mode observer-based control scheme is utilized to estimate unmeasured states of the system. We build two fuzzy switching manifolds for the disturbance and sliding mode observer systems. Then, a linear matrix inequality-based criterion is developed using slack matrices. This criterion proves that the sliding mode dynamics are robustly admissible under an H-infinity performance often used in control theory. Hence, new adaptive sliding mode controllers are synthesized for the disturbance and sliding mode observer systems. This allows the reachability of pre-designed sliding surfaces to be guaranteed. Finally, experimental numerical illustrations on a bio-economic system and a tunnel diode circuit are presented to show potential applications, as well as validating the effectiveness of the scheme proposed in the present investigation.

Observer-based sliding mode control for discrete-time nonlinear system with time-varying delay

This work deals with the design observer-based sliding mode control for discrete-time Takagi–Sugeno fuzzy models with time-varying delay and subject to measurement noises. The sliding surface is developed by introducing the state and input vectors to overcome the restrictive assumption in most existing sliding mode control schemes which forces the input matrices of all linear subsystems to be equal. Sufficient stability conditions of the error system and sliding mode dynamics with disturbance attenuation level are developed using the augmented Lyapunov–Krasovskii functional and free-weighting matrix. Finally, a simulation example is presented to demonstrate the efficiency of the proposed results.

Nonlinear dynamic investigation and anti-bifurcation control of a boiler-turbine unit via dual-mode fuzzy model predictive control strategy

The increase in renewable energy sources connected to the grid has increased flexibility requirements in the operation of thermal power plants. Because of severe nonlinearity and various disturbances, the dynamic behavior of the boiler-turbine unit will change significantly at different operating conditions. Further, modeling uncertainties cofound definitive knowledge about the changes, exacerbating efforts to control. In this paper, a general disturbed model of the boiler-turbine unit for control design is determined through the nonlinear dynamic analysis on the concepts of bifurcation and limit cycles behavior rather than given by an artificial chosen. Then, a dual-mode fuzzy predictive control strategy is proposed on discrete-time Takagi-Sugeno fuzzy model. Online optimal problem of the approach is solved to accomplish the fast-tracking task; to achieve the anti-bifurcation control objective, a novel minimal robust positively invariant set corresponding with a local controller is offline obtained in order to change the undesired nonlinear behavior into stable limit cycles. With the input-to-state stability theory, the proposed control strategy is theoretically proved and given in terms of linear matrix inequalities. Simulation carried out on the boiler-turbine unit demonstrates that the proposed dual-mode control strategy achieves the disturbance suppression ability and the improvement of the nonlinear dynamic behavior.

Regional input-to-state stabilization of fuzzy state-delayed discrete-time systems with saturating actuators

We address the regional input-to-state stabilization of discrete-time Takagi-Sugeno fuzzy models under delayed state, saturating actuators, and external energy bounded disturbances. We propose a convex method to design state feedback-based non-parallel distributed compensation, ensuring the fuzzy closed-loop system’s regional stability. Moreover, we introduce a geometrical estimate of the region of attraction in an augmented space, allowing a more extensive set of safe initial sequences. Furthermore, the minimization of the ℓ2-gain from the external disturbance to the controlled output ensures closed-loop performance. Also, we provide optimization procedures allowing the maximization of the estimate of the region of attraction or the disturbance energy tolerance. By employing numerical examples, we compare our approach with similar ones found in the literature, showing our proposal’s efficacy, and its outperform concerning the compared methods.

Discrete-time robust fuzzy control synthesis for discretized and perturbed ship fin stabilizing systems subject to variance and pole location constraints

A discrete-time robust fuzzy controller design problem for the discretized and perturbed nonlinear ship fin stabilizing systems is studied in this paper. The discrete-time Takagi–Sugeno fuzzy model is used to represent the nonlinear ship fin stabilizing systems. The control performance considered in this paper includes stability requirement, pole location constraint, individual state variance constraint, and minimum output variance. Applying the Lyapunov theory, a discrete-time robust fuzzy controller is designed based on parallel distributed compensation technology and the relevant conditions are deduced in the form of linear matrix inequalities. By solving these conditions, a discrete-time robust fuzzy controller can be obtained to satisfy the above performance constraints. At last, a simulation for controlling a discrete-time nonlinear ship fin stabilizing system is provided to show the feasibility and applicability of the proposed robust fuzzy control method.

Nonlinear Model Predictive Control of Reentry Vehicles Based on Takagi-Sugeno Fuzzy Models

In this paper, we apply a discrete-time Takagi-Sugeno Fuzzy Model (TSFM) based model predictive controller (MPC) to a Martian aerocapture vehicle following an arbitrary trajectory. We compare two baseline controllers: a continuous-time TSFM based parallel distributed controller (PDC) and a finite-horizon linear quadratic regulator (LQR). We evaluate the change in velocity (ΔV) required to bring the orbit of the controlled exit conditions to the orbit of the reference trajectory exit conditions over a range of initial condition errors and perturbations to atmospheric density. The LQR controller was least robust but performed best in a smaller range of perturbations. The PDC controller was most robust but performed the worst. The MPC based controllers demonstrate a balance of robustness and performance.

Efficient LMI Conditions for Enhanced Stabilization of Discrete-Time Takagi–Sugeno Models via Delayed Nonquadratic Lyapunov Functions

This paper is concerned with the reduction of conservatism on stabilization conditions of discrete-time Takagi–Sugeno fuzzy models via delayed nonquadratic Lyapunov functions. A fruitful approach recently appeared in the literature, which, despite its benefits, dramatically increases the number of linear matrix inequalities needed to synthesize a controller. The two sets of sufficient conditions hereby proposed tackle this numerical problem while reducing conservatism and increasing the stabilization domain of existing conditions in literature, as illustrated in several examples.

Fuzzy Guaranteed Cost $$H\infty$$ Control of Uncertain Nonlinear Fuzzy Vehicle Active Suspension with Random Actuator Delay

This paper focuses on the fuzzy guaranteed cost $$H\infty$$ control problem for uncertain nonlinear vehicle active suspension system with random actuator time delay. Its main contribution to the literature is that a fuzzy guaranteed cost $$H\infty$$ controller (FGCHC) is proposed to ensure the resulting closed-loop vehicle active suspension system to be asymptotically stable and guarantee the performance index to be less than a preset upper bound. More specifically, taking the varying masses and the uncertainties caused by random actuator delay into consideration, a discrete-time Takagi-Sugeno fuzzy model for vehicle active suspension is obtained based on an augmented vector, which is without explicit of random actuator delay. By employing the Lyapunov stability theory and the linear matrix inequality (LMI) approach, the existence condition and the design approach for proposed FGCHC are presented. Meanwhile, the computability for proposed FGCHC is guaranteed by solving a corresponding convex optimization problem. By analyzing performance requirements for vehicle active suspension under different simulation scenarios, simulation results demonstrate that the proposed FGCHC can offset the vibration and compensate the varying masses and uncertainties for vehicle active suspension effectively.

Filtering of T–S Fuzzy Systems With Nonuniform Sampling

The problem of asynchronous filtering of nonlinear systems is investigated in this paper. To facilitate analysis, a discrete-time Takagi-Sugeno fuzzy model with a fast and uniform period is introduced to approximate continuous nonlinear systems. A slow and nonuniform sampler between system and filter is proposed to overcome the contradictions between fast sampling period and limited bandwidth. The nonuniform sampling interval of sampler is subject to a Markov chain. To make full use of the partial information of sampling interval which is accessible to the filter, the asynchronous filter which is described by the hidden Markov model is introduced to reduce conservatism. By resorting to the augmentation approach and the Lyapunov functional method which depends on nonuniform sampling interval, some sufficient conditions for the existence of asynchronous filer are given to guarantee the stability and dissipativity of the augmented system. The gains of asynchronous filter are given via solving a set of linear matrix inequalities. Two examples are utilized to illustrate the validity of the developed filter design technique where the relationships between optimal dissipative performance indices and the mode synchronization rate are given.

Multi-constrained fuzzy intelligent control for uncertain discrete systems with complex noises: an application to ship steering systems

ABSTRACTIn this paper, a performance constrained fuzzy controller design is investigated for the nonlinear uncertain discrete-time ship steering system with complex noises. The performance constraints considered in this paper include individual state variance constraint and passivity constraint. The nonlinear discrete-time ship steering system considered in this paper is represented by a discrete-time Takagi–Sugeno fuzzy model with perturbations, additional noise and multiplicative noise. According to this complex nonlinear discrete-time stochastic system, a fuzzy controller design approach is investigated based on Lyapunov theory, passivity theory and covariance control theory. Some sufficient conditions are derived to satisfy stability constraint, individual state variance constraint and passivity constraint, simultaneously. These sufficient conditions are constructed as linear matrix inequality forms that can be solved by the convex optimal programming algorithm. Finally, some simulation results are provided to verify the validity and applicability of the proposed fuzzy control approach with multiple performance constraints.

Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.