Fuzzy Controller Design for Nonlinear Systems

In this article is studied problem of Fuzzy Controller Design For Nonlinear Systems With Case Study Of TORA System. Fuzzy control for nonlinear systems is proposed on the framework from model of Takagi-Sugeno fuzzy model and PDC(paralel distributed compensation) controller. A lyapanouv-based stabilizing fuzzy control design for nonlinear systems using Takagi-Sugeno fuzzy models is applied. The stability analysis and control design problems are reduced to linear of matrix inequality (LMI) problems. So that method of fuzzy controller design are solve a set of LMI. Approach of PDC, robust and optimal controller are applied to a nonlinear control benchmark problem with case study of TORA system. The designed fuzzy controllers are yield an asymtotic stable closed-loop system. The fuzzy controller Simulation results are given to ilustrate the utility of the present fuzzy control

Fuzzy H-infinity output feedback control of nonlinear systems under sampled measurements

This paper studies the problem of designing an H∞ fuzzy feedback control for a class of nonlinear systems described by a continuous-time fuzzy system model under sampled output measurements. The premise variables of the fuzzy system model are allowed to be unavailable. We develop a technique for designing an H∞ fuzzy feedback control that guarantees the L2 gain from an exogenous input to a controlled output is less than or equal to a prescribed value. A design algorithm for constructing the H∞ fuzzy feedback controller is given

Modeling, Analysis and Control of Fuzzy Systems

For the development of the field of fuzzy control systems, techniques for modeling fuzzy systems need to be developed, which makes analysis of the system and the design of control laws systematic. In this paper, a new model of fuzzy systems is proposed which is a variation of “Tagaki and Sugeno\u27s fuzzy model”. Analysis of this model in terms of stability, controllability, observability etc. Is much simpler. It also makes model-based control design easier, while retaining the derivations of connections of fuzzy blocks for piecewise continuous polynomial membership functions. Although the model is easier to analyze, it can represent highly nonlinear dynamics

Nonlinear Control and Estimation with General Performance Criteria

This dissertation is concerned with nonlinear systems control and estimation with general performance criteria. The purpose of this work is to propose general design methods to provide systematic and effective design frameworks for nonlinear system control and estimation problems. First, novel State Dependent Linear Matrix Inequality control approach is proposed, which is optimally robust for model uncertainties and resilient against control feedback gain perturbations in achieving general performance criteria to secure quadratic optimality with inherent asymptotic stability property together with quadratic dissipative type of disturbance reduction. By solving a state dependent linear matrix inequality at each time step, the sufficient condition for the control solution can be found which satisfies the general performance criteria. The results of this dissertation unify existing results on nonlinear quadratic regulator, Hinfinity and positive real control. Secondly, an H2-Hinfinity State Dependent Riccati Equation controller is proposed in this dissertation. By solving the generalized State Dependent Riccati Equation, the optimal control solution not only achieves the optimal quadratic regulation performance, but also has the capability of external disturbance reduction. Numerically efficient algorithms are developed to facilitate effective computation. Thirdly, a robust multi-criteria optimal fuzzy control of nonlinear systems is proposed. To improve the optimality and robustness, optimal fuzzy control is proposed for nonlinear systems with general performance criteria. The Takagi-Sugeno fuzzy model is used as an effective tool to control nonlinear systems through fuzzy rule models. General performance criteria have been used to design the controller and the relative weighting matrices of these criteria can be achieved by choosing different coefficient matrices. The optimal control can be achieved by solving the LMI at each time step. Lastly, since any type of controller and observer is subject to actuator failures and sensors failures respectively, novel robust and resilient controllers and estimators are also proposed for nonlinear stochastic systems to address these failure problems. The effectiveness of the proposed control and estimation techniques are demonstrated by simulations of nonlinear systems: the inverted pendulum on a cart and the Lorenz chaotic system, respectively

Output Feedback Control of Fuzzy Descriptor Systems with Interval Time-Varying Delay.

[[abstract]]This paper proposes output feedback control for fuzzy descriptor systems with interval time-varying delay. First, singular nonlinear dynamic systems with interval time-varying delay are taken into consideration. Then using a Takagi-Sugeno (T-S) fuzzy model, we design a fuzzy representation of the original nonlinear system. This fuzzy representation consists of local linear descriptor systems. To achieve the control objective, a fuzzy controller and observer is designed in a systematic manner. The stability analysis of the overall closed-loop fuzzy system leads to formulation of linear matrix inequalities. Using the observer and controller gains by solving LMIs, we carry out numerical simulations which verify theoretical statements.[[iscallforpapers]]

Optimal Control of Unknown Nonlinear System From Inputoutput Data

Optimal control designers usually require a plant model to design a controller. The problem is the controller\u27s performance heavily depends on the accuracy of the plant model. However, in many situations, it is very time-consuming to implement the system identification procedure and an accurate structure of a plant model is very difficult to obtain. On the other hand, neuro-fuzzy models with product inference engine, singleton fuzzifier, center average defuzzifier, and Gaussian membership functions can be easily trained by many well-established learning algorithms based on given input-output data pairs. Therefore, this kind of model is used in the current optimal controller design. Two approaches of designing optimal controllers of unknown nonlinear systems based on neuro-fuzzy models are presented in the thesis. The first approach first utilizes neuro-fuzzy models to approximate the unknown nonlinear systems, and then the feasible-direction algorithm is used to achieve the numerical solution of the Euler-Lagrange equations of the formulated optimal control problem. This algorithm uses the steepest descent to find the search direction and then apply a one-dimensional search routine to find the best step length. Finally several nonlinear optimal control problems are simulated and the results show that the performance of the proposed approach is quite similar to that of optimal control to the system represented by an explicit mathematical model. However, due to the limitation of the feasible-direction algorithm, this method cannot be applied to highly nonlinear and dimensional plants. Therefore, another approach that can overcome these drawbacks is proposed. This method utilizes Takagi-Sugeno (TS) fuzzy models to design the optimal controller. TS fuzzy models are first derived from the direct linearization of the neuro-fuzzy models, which is close to the local linearization of the nonlinear dynamic systems. The operating points are chosen so that the TS fuzzy model is a good approximation of the neuro-fuzzy model. Based on the TS fuzzy model, the optimal control is implemented for a nonlinear two-link flexible robot and a rigid asymmetric spacecraft, thus providing the possibility of implementing the well-established optimal control method on unknown nonlinear dynamic systems

An SOS-Based Control Lyapunov Function Design for Polynomial Fuzzy Control of Nonlinear Systems

This paper deals with a sum-of-squares (SOS)-based control Lyapunov function (CLF) design for polynomial fuzzy control of nonlinear systems. The design starts with exactly replacing (smooth) nonlinear systems dynamics with polynomial fuzzy models, which are known as universal approximators. Next, global stabilization conditions represented in terms of SOS are provided in the framework of the CLF design, i.e., a stabilizing controller with nonparallel distributed compensation form is explicitly designed by applying Sontag\u27s control law, once a CLF for a given nonlinear system is constructed. Furthermore, semiglobal stabilization conditions on operation domains are derived in the same fashion as in the global stabilization conditions. Both global and semiglobal stabilization problems are formulated as SOS optimization problems, which reduce to numerical feasibility problems. Five design examples are given to show the effectiveness of our proposed approach over the existing linear matrix inequality and SOS approaches

Neuro-Fuzzy-based Improved IMC for Speed Control of Nonlinear Heavy Duty Vehicles

A neuro-fuzzy based improved internal model control (I-IMC) is proposed for speed control of uncertain nonlinear heavy duty vehicle (HDV) as the standard IMC (S-IMC) can’t tackle the nonlinear systems effectively and degrades the performance of HDV system. Adaptive neuro-fuzzy inference system and artificial neural network with adaptive control are used for the design of I-IMC. The proposed control techniques are developed to achieve the better speed tracking performance and robustness of HDV system under the influence of road grade disturbance

Optimal Control of Fuzzy Systems with Application to Rigid Body Attitude Control

In this chapter, the author presents a theoretical result on the optimal control of nonlinear dynamic systems. In this theoretical result, the author presents the optimal control problem for nonlinear dynamic systems and shows that this problem can be solved by utilizing the dynamic programming approach and the inverse optimal approach. The author employs the dynamic programming approach to derive the Hamilton-Jacobi-Bellman (H-J-B) equation associated with the optimal control problem for nonlinear dynamic systems. Then, the author presents an analytic way to solve the H-J-B equation with the help of the inverse optimal approach. Based on the theoretical result presented in this chapter, the author establishes an optimal control design for TS-type fuzzy systems that guarantees the global asymptotic stability of an equilibrium point and the optimality with respect to a cost function and provides good convergence rates of state trajectories to an equilibrium point. The author considers the three-axis attitude stabilization problem of a rigid body to illustrate the optimal control design method for TS-type fuzzy systems. The author designs the optimal three-axis attitude stabilizing control law for a rigid body based on this optimal control design method and analyzes its control performance by numerical simulations