There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

비만아 부모의 돌봄 경험: q 방법론

Fuzzy logic control was originally introduced and developed as a model free control design approach. However, it unfortunately suffers from criticism of lacking of systematic stability analysis and controller design though it has a great success in industry applications. In the past ten years or so, prevailing research efforts on fuzzy logic control have been devoted to model-based fuzzy control systems that guarantee not only stability but also performance of closed-loop fuzzy control systems. This paper presents a survey on recent developments (or state of the art) of analysis and design of model based fuzzy control systems. Attention will be focused on stability analysis and controller design based on the so-called Takagi-Sugeno fuzzy models or fuzzy dynamic models. Perspectives of model based fuzzy control in future are also discussed

/pdf/a-survey-on-analysis-and-design-of-model-based-fuzzy-control-3hrjlrel0k.pdf

A Survey on Analysis and Design of Model-Based Fuzzy Control Systems

This paper studies the problem of fuzzy adaptive event-triggered control for a class of pure-feedback nonlinear systems, which contain unknown smooth functions and unmeasured states. Fuzzy logic systems are adopted to approximate unknown smooth functions and a fuzzy state observer is designed to estimate unmeasured states. Via the event-triggered control technique, the control signal of the fixed threshold strategy is obtained. By converting the tracking error into a new virtual error variable, an observer-based fuzzy adaptive event-triggered prescribed performance control strategy is designed. The key advantage is that the proposed method does not require a $priori$ knowledge of partial derivatives of system functions, i.e., it relaxes the restrictive condition that the partial derivatives of system functions need to be known for pure-feedback nonlinear systems. Simulation results confirm the efficiency of the proposed method.

Observer-Based Fuzzy Adaptive Event-Triggered Control for Pure-Feedback Nonlinear Systems With Prescribed Performance

The problem of adaptive fuzzy control is investigated for a class of nontriangular structural stochastic switched nonlinear systems with full state constraints in this paper. A remarkable feature of the nontriangular structural nonlinear system is the so-called algebraic loop problem in the existing backstepping-based analysis and design. Properties of fuzzy basis functions are utilized to circumvent this algebraic loop problem. Based on the Barrier Lyapunov function, an adaptive fuzzy stochastic switched control scheme is designed. It is proven that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded with full state constraints. The effectiveness of the proposed control scheme is verified via simulation studies.

Adaptive Fuzzy Control for Nontriangular Structural Stochastic Switched Nonlinear Systems With Full State Constraints

In real-time problems, the possibilities of having a precise mathematical model describing the dynamics of the nonlinear system are scarce. Besides, the measurements invariably are tainted with noise which makes the problem of estimating the actual states of the system more difficult. The most common way of solving this issue involves the application of the Kalman Filter (KF) or the Extended Kalman Filter (EKF), for linear and nonlinear systems, respectively; although in both cases, the estimation heavily relies on linear techniques. In a different way, the James-Stein Filter provides a robust approach to estimate linear and nonlinear systems under parametric uncertainties of the mathematical model. In this brief note, a slightly different James-Stein State Estimator (JSSE), named Modified James-Stein State Estimator (JSSE-M), is presented as an alternative to filtering the states of nonlinear systems within a control scheme. The main contribution of this paper is the comparison of performance between KF, EKF, JSSE, and JSSE-M when they are used on a relatively complex nonlinear system which is extremely dependent on its parameters, namely the quadrotor. In this sense, some interesting comparisons focused on both, the effectiveness and processing time are provided.

On the Estimation and Control of Nonlinear Systems With Parametric Uncertainties and Noisy Outputs

Neural network updating via argument Kalman filter for modeling of Takagi-Sugeno fuzzy models

In this paper, it is theoretically demonstrated that a quadrotor can track trajectories using a low-cost global positioning system with signal losses in unpredictable instants. The lack of a continuous altitude output and the signal loss are solved with certain limitations using two-hybrid linear observers. This type of observer is originally employed to compensate for data loss in computer networks. This was possible due to the sufficient conditions for uniform global asymptotic stability theorems of hybrid systems with persistent jumping. This concept is based on a dynamic hybrid system that guarantees a jumping condition with a Lyapunov function constant when the system flows and decreases during jumps. The quadrotor was modeled like a linear time-invariant system. The results are presented using simulations.

Theoretical Application of a Hybrid Observer on Altitude Tracking of Quadrotor Losing GPS Signal

The exact output regulation for Takagi-Sugeno (T-S) fuzzy models depends on two conditions: 1) The local steady-state zero-error manifolds have to be the same for every local subsystem, and 2) the local input matrices have to be the same for every local subsystem included in the T-S fuzzy model. These conditions are difficult to satisfy in general. In this paper, those conditions are relaxed by solving the fuzzy regulation problem directly on the overall T-S fuzzy model, instead of constructing the fuzzy regulator on the basis of linear local controllers. By considering the fuzzy model as a special class of linear time-varying systems, existence conditions are rigorously derived. These new conditions, which can be solved by means of any mathematical software, depend on the solution of a set of symbolic simultaneous linear equations depending on the membership values of the plant and/or the exosystem. Two examples are given to illustrate the construction of the proposed regulator and to validate the improvement that is achieved with the proposed approach.

Exact Output Regulation for Nonlinear Systems Described by Takagi–Sugeno Fuzzy Models

In this paper, the controllability property for a class of Takagi–Sugeno (T–S) fuzzy models is analyzed, while a fully nonlinear stabilizer is designed in a practical way. It is shown that global fuzzy stabilizers can be constructed in a nonconservative way by means of a relatively simple approach. The existence of such controllers depends on the fuzzy controllability conditions, which are derived in a straightforward way. The main advantage of the proposed approach is that the convergence of the closed-loop system can be imposed arbitrarily. Some examples are given in order to illustrate the validity of the method. Finally, the proposed controller is applied on an underactuated system known as “pendubot” and the results are compared with an stabilizer designed on the basis of LMIs.

Jesus Alberto Meda-Campana

Papers

On the Estimation and Control of Nonlinear Systems With Parametric Uncertainties and Noisy Outputs

Neural network updating via argument Kalman filter for modeling of Takagi-Sugeno fuzzy models

Theoretical Application of a Hybrid Observer on Altitude Tracking of Quadrotor Losing GPS Signal

Exact Output Regulation for Nonlinear Systems Described by Takagi–Sugeno Fuzzy Models

Analysis of the Fuzzy Controllability Property and Stabilization for a Class of T–S Fuzzy Models