Tiechao Wang

Stability analysis of SIRMs based type-2 fuzzy logic control systems

This paper tries to provide a stability analysis approach for the single input rule modules (SIRMs) based type-2 fuzzy logic control systems. First, in the neighbor of the equilibrium point, the closed-form input-output mappings of type-2 SIRMs (T2SIRMs) are explored, and the derivatives of T2SIRMs at the equilibrium point are computed. Then, how to compute the Jacobian matrix of the SIRMs based type-2 fuzzy logic control systems, which is a fundamental step for local stability analysis, is presented. At last, two examples on stabilization control of the TORA system and the inverted pendulum system are given. The results in both examples demonstrate that the stability analysis results agree completely with the control results.

Adaptive Inverse Control of Cable-Driven Parallel System Based on Type-2 Fuzzy Logic Systems

This paper is concerned with the problem of type-2 fuzzy adaptive inverse control for a cable-driven parallel system. Based on the heuristics and prior knowledge of the system, the system is divided into six subsystems. The proposed control scheme for each subsystem contains a forward model and a fuzzy adaptive inverse controller (FAIC), which are expressed by an interval type-2 fuzzy nonlinear autoregressive exogenous (NARX) model, respectively. To construct the antecedents of the interval type-2 fuzzy NARX forward models and FAICs, the monotonic property of the fuzzy NARX model is first proved, and then, their antecedent parameters can be determined by this property. Furthermore, the consequent parameters of the forward models are computed offline via a constrained least squares algorithm, and the consequent parameters of the FAIC are adjusted online via a recursive least squares algorithm. Experiment results are provided to show that the proposed type-2 fuzzy control scheme can realize the control objectives and achieve a good control performance.

On the properties of SIRMs connected type-1 and type-2 fuzzy inference systems

This paper tries to show some important properties of the single input rule modules (SIRMs) connected fuzzy inference systems (FIS), including both type-1 (T1) and interval type-2 (IT2) FISs. Three kinds of properties — continuity, monotonicity and robustness — are explored. First, conditions on the parameters are derived to ensure that the SIRMs connected FISs are continuous and monotonic. Then, a methodology for the robustness analysis of the SIRMs connected FISs are presented. At last, an example is given to show the correctness of the theorems on the continuity and monotonicity and to demonstrate the effectiveness of the proposed methodology for robustness analysis. These results can not only deepen our understanding of the SIRMs connected FISs, but also provide us guidelines for the design of the SIRMs connected FISs.

The monotonicity and convexity of unnormalized interval type-2 TSK Fuzzy Logic Systems

This paper applies prior knowledge — monotonicity and convexity — to a Single-Input-Single-Output (SISO) un-normalized interval type-2 Takagi-Sugeno-Kang (TSK) Fuzzy Logic System (FLS). Sufficient conditions are provided to guarantee its monotonicity and convexity with respect to its input, respectively. The derived monotonic conditions focus on a zeroth-order TSK fuzzy model. Also, the corresponding proofs for the convex conditions of both the zeroth-order and first-order TSK fuzzy models are given, respectively. For the zeroth-order fuzzy systems, simulation examples demonstrate the validity of the theorems.

Multi-source knowledge based Unnormalized Interval Type-2 Fuzzy Logic Systems design

In this paper we propose an effective method to design a Single-Input Single-Output (SISO) Unnormalized Interval Type-2 Takagi-Sugeno-Kang (TSK) Fuzzy Logic System (UIT2FLS) for noisy regression problems based on multi-source knowledge which includes here the information from sample data and the prior knowledge of bounded range, symmetry and monotonicity. The sufficient conditions are given which ensure that the prior knowledge can be embedded into the UIT2FLS, and then the UIT2FLS is designed so that the target function can be approached as accurately as possible via constrained least squares algorithm. The performance of the UIT2FLS is verified through comparisons with unnormalized type-1 Fuzzy Logic Systems (FLSs) and normalized interval type-2 FLSs under three different noisy circumstances. Simulation results verify the correctness of the sufficient conditions, and demonstrate that the UIT2FLS has the best overall performance.

Design of interval type-2 fuzzy logic systems using prior knowledge via optimization algorithms

The paper presents the methods of integrating prior knowledge with a first-order Single-Input Single-Output (SISO) Interval Type-2 Takagi-Sugeno-Kang (TSK) Fuzzy Logic System (IT2FLS) for function approximation under noisy circumstances. Firstly, sufficient conditions on the antecedent and the consequent parameters of the IT2FLS are given to ensure that three kinds of prior knowledge — monotonicity, symmetry and special points, can be embedded into the IT2FLS. And then, we use three optimization algorithms — constrained least squares algorithm, active-set algorithm and hybrid learning algorithm to design the IT2FLS, respectively. The effectiveness of the three algorithms and the comparisons of their performance are demonstrated by simulation examples.