Fuzzy interval optimal control problem

Fuzzy approximation-based optimal consensus control for nonlinear multiagent systems via adaptive dynamic programming

In this article, an observer-based fuzzy adaptive inverse optimal output feedback control problem is studied for a class of nonlinear systems in strict-feedback form. The considered nonlinear systems contain unknown nonlinear dynamics and their states are not measured directly. Fuzzy logic systems are applied to identify the unknown nonlinear dynamics and an auxiliary nonlinear system is constructed. Based on this auxiliary system, a fuzzy state observer is first designed to estimate the immeasurable states. By using the inverse optimal principle and adaptive backstepping design theory, an observer-based fuzzy adaptive inverse optimal output feedback control scheme is then developed. The proposed inverse optimal control scheme need not assume that the states are measurable. It also guarantees that the closed-loop system is semiglobally uniformly ultimately bounded, and achieves the optimal control objective as well. Finally, two simulation examples are provided to check the validity of the presented control method.

This paper investigates adaptive fuzzy output feedback fault-tolerant optimal control problem for a class of single-input and single-output nonlinear systems in strict feedback form. The considered nonlinear systems contain unknown nonaffine nonlinear faults and unmeasured states. Fuzzy logic systems are used to approximate cost function and unknown nonlinear functions, respectively. It is assumed that the states of the systems to be controlled are unmeasurable, thus an adaptive state observer is developed. To solve the nonaffine nonlinear fault control design problem, filtered signals are introduced into the adaptive backstepping control design procedures, and in the framework of adaptive critic technique and fault-tolerant control technique, a novel adaptive fuzzy fault-tolerant optimal control scheme is developed. The stability of the closed-loop system is proved by using Lyapunov stability theory. The simulation results verify the effectiveness of the proposed control strategy.

This paper investigates fuzzy adaptive output feedback optimal control problem for a class of strict-feedback nonlinear systems. With the help of fuzzy logic systems approximating the unknown nonlinear functions and cost function, the unmeasured states are estimated by designing fuzzy adaptive state observer. Combining state observer with backstepping design technique, a feedforward controller is designed. Based on the designed feedforward control strategy, the controlled nonlinear system can be converted to an equivalence nonlinear system in affine-form. Finally, a fuzzy adaptive optimal controller with parameters adaptive laws is developed. The whole control scheme consists of a feedforward controller and a feedback optimal controller. It is shown that the proposed output feedback optimal control approach can guarantee that all signals in the closed-loop system are bounded, and the system output can track the reference signal. In addition, the proposed control approach can guarantee cost function is the smallest. Simulation results are given to demonstrate the effectiveness of the proposed control approach.

Sub-optimal control of fuzzy linear dynamical systems under granular differentiability concept

This paper proposes a fuzzy interval optimization approach to solve the Environmental/Economic Dispatch (EED) problem with uncertain parameters in the constraints and the objective functions. The objective functions considered are fuel cost and the gaseous emissions of the generating units. Two different types of fuel cost functions are considered in this study, namely, the conventional quadratic function and the augmented quadratic function to introduce more accurate modeling that incorporates the valve loading effects. The latter model presents non-differentiable and nonconvex regions that challenge most gradient-based optimization algorithms. In the proposed approach, objective functions are fuzzified and integrated to represent the fuzzy decision value. On the other hand, load uncertainties are modeled using fuzzy intervals. This fuzzy EED problem formulation provides a modeling flexibility, relaxation in constraints and allows the method to seek a practical solution. The obtained fuzzy multi-objective optimization problem is solved using non-dominated sorting genetic algorithm-II, known for its global searching capabilities, to get the best compromise among all the objectives. The performance of this solution is examined and applied to the standard IEEE 30-bus six-generator test system and the Indian power network of 82-bus by comparing its results with that of the existing methods. Different cases with different complexities have been considered in the study reported in this paper.

Optimal control for multistage uncertain random dynamic systems with multiple time delays

A new optimum interval type-2 fuzzy fractional-order controller for a class of nonlinear systems with incipient actuator and system component faults is introduced in this study. The faults of the actuator and system component (leak) are taken into account using an additive model. The Interval Type-2 Fuzzy Sets (IT2FS) is used to design an optimal fuzzy fractional order controller, and two different nature inspired metaheuristic algorithms, Follower Pollination Algorithm (FPA) and Genetic Algorithm (GA), are used to optimize the parameters of the fuzzy PID controller and Interval Type-2 Fuzzy Tilt-Integral-Derivative Controller (IT2FTID) for nonlinear system. The suggested control approach consists of two parts: an Interval Type-2 Fuzzy Logic Controller (IT2FLC) controller and a fractional order TID controller. Additionally, the two inputs of the IT2FLC are also calibrated using two fine tuning parameters and , respectively. The stability of the proposed controller is presented with some conditions. In addition to unknown dynamics, some unknown process disturbances, such as rapid changes in the control variable, are taken into account to check the efficacy of the proposed control scheme. Two nonlinear conical two-tank level systems are used in the simulation as a case study. The performance of the suggested approach is also compared to that of a widely recognized Interval Type-2 Fuzzy Proportional-Integral-Derivative (IT2FPID) Controller. Finally, the proposed control scheme's fault-tolerant behaviour is demonstrated using fault-recovery time results and statistical Z-tests for both controllers, and the proposed IT2FTID controller's effectiveness is demonstrated when compared to IT2FPID and existing passive fault tolerant controllers in recent literature.

International audience

This paper considers the modelling and designing of a production-flow scheduler based on fuzzy interval system. Particularly, the supervisory control is built according to the satisfaction degree of conflicting objectives which are quantified by fuzzy intervals. The control system aims at adjusting the machine's production rates in such a way that satisfies the demand while maintaining the overall performances within acceptable limits. At the shop-floor level, the actual dispatching times are determined from the continuous production rates through a sampling procedure. A decision for the actual part to be processed is taken using some criterions which represent a measure of the job's priority. A case study demonstrates the efficiency of the proposed control approach.

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. Recently, Hong [Fuzzy Sets and Systems 158(2007) 739-746] defined a broader class of bell-shaped fuzzy intervals. Then he study t-norms which are consistent with these particular types of fuzzy intervals as applications of a result proved by Mesiar on a strict f-norm based shape preserving additions of LR-fuzzy intervals with unbounded support. In this note, we give a direct proof of the main results of Hong.

Discrete-time hybrid control in Borel spaces: Average cost optimality criterion

In this paper, the optimal low thrust planar orbit transfer problem is solved utilizing a fuzzy optimal control algorithm. Firstly, dynamic equations are presented in a discretized form, then all the design variables and constraints are transformed to fuzzy space, while minimizing the performance index and also satisfying transversallity conditions. Applying the concept of membership functions based on expert experience, the designed cost function associated with operational constraints are transformed to fuzzy relations through specific membership functions. Applying Bellman-Zadeh approach, the optimal control problem can be converted to a parameter optimization. Combining the performance index and problem's constraints in a scalar function, necessary optimality conditions are achieved in a form of nonlinear algebraic equations. Finally, to solve this set of equations, the gradient-based method is used. In comparison with the exact form of the problem, the efficiency of the proposed algorithm is highlighted in terms of time and accuracy. In the fuzzy optimal control, a control designer could take advantage of determining the allowed limit for cost function. This algorithm could be successfully extended to fixed state or fixed control problems which is time-consuming in scope of the classical optimal control.

A fuzzy type-2 fault detection methodology to minimize false alarm rate in induction motor monitoring applications

Fuzzy Dynamic Equations, Dynamic Inclusions, and Optimal Control Problems on Time Scales