Fuzzy control based on quadratic performance function-a linear matrix inequality approach

In this paper, we study the optimal control problem for Takagi–Sugeno (T-S) fuzzy systems with disturbances. Due to the presence of disturbances in the T-S fuzzy systems, a fuzzy optimal state feedback control approach is presented by employing a two-player zero-sum game. Since the analytical optimal control solutions and the worst-case disturbance policies of T-S fuzzy systems can be boiled down to solving the algebraic Riccati equations (AREs), which are difficult to be obtained directly, a model-free policy iteration (PI) learning algorithm is proposed to obtain their approximation solutions. It is proved that the developed fuzzy optimal state feedback controller can ensure the fuzzy systems to be asymptotically stable and satisfy the disturbance attenuation condition simultaneously. Also, the designed PI learning algorithm can converge to their optimal solutions. Finally, we apply the developed fuzzy optimal state feedback control method to the truck-trailer system and the simulation results demonstrated the effectiveness of the developed scheme.

In this paper, we present a global optimal and stable fuzzy controller design method for both continuous- and discrete-time fuzzy systems under both finite and infinite horizons. First, a sufficient condition is proposed which indicates that the global optimal effect can be achieved by the fuzzily combined local optimal controllers. Based on this sufficient condition, we derive a local concept approach to designing the optimal fuzzy controller by applying traditional linear optimal control theory. The stability of the entire closed-loop continuous fuzzy system can be ensured by the designed optimal fuzzy controller. The optimal feedback continuous fuzzy system can not only be guaranteed to be exponentially stable, but also be stabilized to any desired degree. Also, the total energy of system output is absolutely finite. Moreover, the resultant feedback continuous fuzzy system possesses an infinite gain margin; that is, its stability is guaranteed no matter how large the feedback gain becomes. Two examples are given to illustrate the proposed optimal fuzzy controller design approach and to demonstrate the proved stability properties.

This paper presents new stability conditions and LMI (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy control systems, nonlinear systems are represented by Takagi-Sugeno fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy controllers from the Takagi-Sugeno fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers. The stability analysis of the feedback system is reduced to a problem of finding a common Lyapunov function for a set of linear matrix inequalities. Convex optimization techniques involving LMIs are utilized to find a common Lyapunov function. A procedure to design the fuzzy controller is constructed using the parallel distributed compensation and the relaxed stability conditions. Some stability issues are remarked. A simple example demonstrates the effects of the derived stability conditions.

An optimal fuzzy controller design scheme is proposed to address the influence of time delay and disturbance on the control performance of nonlinear batch processes. First, a two-dimensional (2D) equivalent Takagi-Suguno (T-S) fuzzy error model is formulated. By introducing a quadratic performance index function and adopting 2D Lyapunov-Krasovskii theory, the existence condition of the optimal fuzzy control law is given. Furthermore, its solvable condition, which depends on time-delay bounds, is constructed in terms of linear matrix inequalities, and its gain is obtained by using an optimization algorithm. This design has the advantages of faster tracking and better tracking performance. Finally, two different algorithms (with and without optimization) are used to control the water level of a triple-capacity water tank. The results show that the presented strategy is more effective and feasible.

An output-feedback fuzzy approach to guaranteed cost control of vehicle lateral motion

In this paper, we consider robust stability and stabilization of uncertain Takagi-Sugeno fuzzy time-delay systems where uncertainties come into the state and input matrices. Some stability conditions and robust stability conditions for fuzzy time-delay systems have already been obtained in the literature. However, those conditions are rather conservative and do not guarantee the stability of a wide class of fuzzy systems. This is true in case of designing stabilizing controllers for fuzzy time-delay systems and it thus leads to a conservative fuzzy controller design as well. We first consider rather relaxed robust stability conditions of uncertain fuzzy systems. To this end, we introduce an auxiliary system to the original fuzzy time-delay system to obtain generalized delay-dependent stability conditions. Such an auxiliary system has some arbitrary matrices that generalize not only the system representation but also delay-dependent stability conditions. Conditions we obtain here are delay-dependent conditions that depend on the upper bound of time-delay, and are given in terms of linear matrix inequalities (LMIs). Then, we compare our delay-dependent stability conditions with other conditions in the literature, and show that our conditions guarantee the stability of a wider class of systems than others. Next, we consider the robust stabilization problem with memoryless and delayed state feedback controllers. Based on our generalized robust stability conditions, we obtain delay-dependent sufficient conditions for the closed-loop system to be robustly stable, and give a design method of robustly stabilizing controllers. Finally, we give three examples that illustrate our results.

In real life, almost all systems are nonlinear in nature. The electromagnetic levitation system (EMLS) is one such system that has a wide range of applications due to its frictionless, fast, and affordable technique. Optimal control and sliding mode control (SMC) techniques are often used controllers for EMLS. However, these techniques can achieve the required levitation but lag in having perfect set-point tracking and robustness against uncertainties. To get over these drawbacks, this article proposes the design of unconstrained mismatched uncertainties, constrained mismatched uncertainties, and integral sliding mode control with mismatched uncertainties for the current-controlled-type electromagnetic levitation system (CC-EMLS). The modeled equations of CC-EMLS are transfomed in terms of the mismatched uncertainties, and the required control action is obtained with and without constraints on the control input. The quadratic performance function is suggested for the unconstrained control scheme and is solved using the Hamilton–Jacobi–Bellman (HJB) equation. The non-quadratic cost function is designed for the constrained control method, and the HJB equation is utilized to obtain the solution. Both control schemes provide robustness to the system, but deviations in the set point are observed in tracking the position of the ball when the changes in the payload occur in the system. Therefore, integral sliding mode control with robust–optimal (IOSMC) gain is proposed for the CC-EMLS to overcome the steady-state error in the other two schemes. The stability is proven using the direct method of Lyapunov stability. The essential studies based on the simulation are carried out to showcase the performance of the proposed control schemes. The integral performance indicators are compared for all three proposed control schemes to highlight the efficacy, robustness, and efficiency of the designed controllers.

Fuzzy optimal tracking control for nonlinear underactuated unmanned surface vehicles

A novel design technique for high performance drives employing both H/spl infin/ optimal control and fuzzy control is proposed in this paper. The fuzzy control design is equipped with an adaptive learning algorithm to achieve H/spl infin/ tracking performance with external disturbances. It gives elevation to the selection of optimal performance weights without any trial and error attempt. The idea is to establish a link between H/spl infin/ optimal control design and fuzzy control design, so as to provide H/spl infin/ tracking design with more intelligence and achieve better performance with fuzzy control design. The effect of both fuzzy logic approximation error and external disturbance on the tracking error is attenuated to an assigned level. The control strategy does not require explicit knowledge of the motor/load dynamics, which is a useful feature when dealing with parameter and load uncertainties. The robustness of the proposed methodology is displayed for different types of trajectories. Experimental and simulation results suggest that the effect of both the fuzzy approximation error and external disturbance on the tracking error can be attenuated efficiently by the H/spl infin/ adaptive fuzzy control. Accordingly, the proposed design method is suitable for the robust tracking control of the uncertain nonlinear drive systems and is an attractive control design philosophy. Test results obtained indicate excellent tracking performance for both speed and position. Test results illustrate the validity of the proposed approach.

Two architectures for designing optimal fuzzy control systems are proposed. In both cases, the membership functions in the fuzzy rule bases are tuned by the genetic algorithms. The objective is to explore a fuzzy controller by minimizing a quadratic cost function. In the first architecture, the employed controller is a conventional fuzzy logic controller which uses the system states as input variables. Consequently, the reciprocal of the cost function to be minimized could be directly applied towards evaluating the fitness of the controller. In the second architecture, a fuzzy sliding mode controller is adopted. The combined information of the system states, i.e. the sliding function, form a single input variable. The problem of minimizing the cost function in this case could be transformed to that of deriving an optimal sliding surface. Then, a faster hitting time and a smaller distance away from the sliding surface a controller has, a higher fitness it gets. Simulations and comparisons are taken on both cases.

In this paper, we apply a new approach called optimal fuzzy control based on linear TS type fuzzy model, to deal with nonlinear magnetic bearing systems. The linear TS type fuzzy model is used to represent the nonlinear plant. To obtain the linear TS fuzzy model, we use linear self-constructing neural fuzzy inference network (linear SONFIN) to model the nonlinear system. Once the TS fuzzy model of the magnetic bearing system is obtained, the optimal fuzzy controller can be applied if the system is completely controllable and observable. Simulation results show that the proposed optimal fuzzy controller can operate in a widely range of shaft positions.

A magnetically levitated (MagLev) vehicle prototype has independent levitation (attraction) and propulsion dynamics. We focus on the levitation behavior to obtain precise gap control of a 1/4 vehicle. An electromagnetic levitation system is highly nonlinear and naturally unstable, and its equilibrium region is severely restricted. It is therefore a tough task to achieve high-performance vehicle-levitated control. In this paper, a MagLev system is modeled by two self-organizing neural-fuzzy techniques to achieve linear and affine Takagi-Sugeno (T-S) fuzzy systems. The corresponding linear-type optimal fuzzy controllers are then used to regulate both physical systems (voltage- and current-controlled systems). On the other hand, an affine-type fuzzy control design scheme is proposed for the affine-type systems. Control performance and robustness to an external disturbance are shown in simulation results. Affine T-S fuzzy representation provides one more adjustable parameter in the neural-fuzzy learning process. Therefore, an affine T-S-based controller possesses better performance for a current-controlled system since it is nonlinear not only to system states but also to system inputs. This phenomenon is shown in simulation results. Technical contributions include a nonlinear affine-type optimal fuzzy control design scheme, self-organizing neural-learning-based linear and affine T-S fuzzy modeling for both MagLev systems, and the achievement of an integrated neural-fuzzy technique to stabilize current- and voltage-controlled MagLev systems under minimal energy-consumption conditions.

In power system any unpredictable variations of consumption load will cause fluctuation in frequency and the transferred power between the lines. Load frequency control is one of the main problems in the power system which synchronizes with automatic generation control. Checking the different factors that cause unbalance in power system is necessary and one of the important factors of them is the load that randomly varies. In this paper, a three area power system in deregulated environments with participation of synchronized generation of wind with Doubly Fed Induction Generator (DFIG), hydro and thermal power plants are studied. The load in this power system is considered as a random variable which periodically and randomly has frequency of 0.25 around nominal amount. Fluctuations are caused due to considering load as a random variable and using wind-powered turbine with DFIG in power system. To improve the response of power system, the optimal fuzzy logic, PID controller and FACTS devices will be used. Imperialist Competitive Algorithm (ICA) has been used for optimizing the parameters of a fuzzy logic controller. PID Controller parameters have been optimized with three intelligent algorithms, ICA, Genetic Algorithm (GA) and Particle Swarm Optimization (PSO) Algorithm and the results will be compared with each other. With comparison the result it is observed that in the case of using optimal fuzzy logic controller (OFLC) we have the fastest response with the minimum over shoot and under shoot, also in this case the transferred power between the areas is settled in the lowest value. The results show a significant reduction in losses in transmission lines.

Based on the ant colony system (ACS) algorithm and fuzzy logic control, a new design method for optimal fuzzy PID controller was proposed. In this method, the ACS algorithm was used to optimize the input/output scaling factors of fuzzy PID controller to generate the optimal fuzzy control rules and optimal real-time control action on a given controlled object. The designed controller, called the Fuzzy-ACS PID controller, was used to control the CIP-I intelligent leg. The simulation experiments demonstrate that this controller has good control performance. Compared with other three optimal PID controllers designed respectively by using the differential evolution algorithm, the real-coded genetic algorithm, and the simulated annealing, it was verified that the Fuzzy-ACS PID controller has better control performance. Furthermore, the simulation results also verify that the proposed ACS algorithm has quick convergence speed, small solution variation, good dynamic convergence behavior, and high computation efficiency in searching for the optimal input/output scaling factors.

New relaxed stability and stabilization conditions for continuous-time T–S fuzzy models