Optimal fuzzy controller design: local concept approach

Bellman’s discrete dynamic programming is one of the most general approaches to solve optimal control problems. For discrete-time dynamical systems, it is, at least theoretically, capable to determine globally optimal control laws. In most practical cases, both state and control variables are subject to constraints. Due to the necessity for gridding of the range of both state and control variables in numerical implementations of dynamic programming, the computational effort grows exponentially with increasing system dimensions. This fact is well known as the curse of dimensionality. Furthermore, gridding of intervals representing uncertain system parameters is inevitable, if dynamic programming is used for the design of optimal controllers for systems with uncertainties. In this contribution, an interval arithmetic procedure for the design of optimal and robust controllers is presented. This procedure relies on the basic concepts of dynamic programming. Sophisticated techniques for the exclusion of non-optimal control strategies significantly reduce the computational burden. Since interval techniques can be applied to both continuous-time and discrete-time dynamical systems, the interval arithmetic optimization approach presented in this chapter is applicable to both cases. In addition, the inclusion of effects of uncertain parameters in the underlying optimality criteria is demonstrated. For that purpose, interval arithmetic routines for analysis and design of optimal and robust controllers have been developed. Details about computationally efficient implementations of interval arithmetic optimization procedures and numerical results for a mechanical positioning system with statedependent switchings between different dynamical models for viscous and Coulomb friction are summarized.

Summary form only given. This paper presents a computational approach for an offline measurement based design of an optimal damping controller using adaptive critics for a new type of FACTS device - the gate controlled series capacitor (GCSC). Remote measurements are provided to the controller to damp out system modes. The optimal controller is developed based on the heuristic dynamic programming (HDP) approach. Three multi-layer perceptron (MLP) neural networks are used in the design - the identifier/model network to identify the dynamics of the power system; the critic network to evaluate the performance of the damping controller; and the controller network to provide optimal damping. This measurement based technique provides an alternative to the classical linear model based optimal control design. The eigenvalue analysis of the closed loop system is performed with time domain responses using the Prony method. Analysis of the simulation results show potential of the HDP based optimal damping controller on a GCSC for enhancing the stability of the power system.

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, the model of three-axis dual rotor helicopter is built, through a new motor control algorithm of real-time grouping, the decoupling and independent control of pitch, yaw and roll channels is realized; then the “dead zone” is introduced to design the attitude controller on the basis of the optimal control law which minimize the weighted sum of response time and energy consumption, to achieve optimal control of the attitude of the helicopter; finally, the simulation model of the attitude control system is established in the MATLAB/Simulink environment. Simulation results show the feasibility of the optimal attitude controller design.

The function of the robot is being complex and various. The robot with various inputs generates various outputs. A proper controller is needed to control such a complex robot. We introduce a 2-layer fuzzy controller (2LFC). It can control robustly and has the small number of rules in many input variables. It can not only deal with various inputs but also generate various outputs. The main problem in the fuzzy system is how to design the fuzzy knowledge base. For this specific problem, we optimize the fuzzy controller using the schema co-evolutionary algorithm (SCEA) to find a global optimal solution. Through the design of the optimal fuzzy controller using the SCEA and the simulation of the mobile robot, we verify the efficacy of the 2-layer fuzzy controller and the schema co-evolutionary algorithm.

This paper presents a method for the design of optimal fuzzy controller of a DC motor using a fuzzy model based approach with emphasis on minimal knowledge on the controlled system. In the first part of the paper we describe the method of the black-box fuzzy model design based only on the system´s measured input/output data without the necessity of preliminary knowledge of its internal structure and parameters. This fuzzy model is in the second part used in the design of optimal fuzzy controller based on finding the sequence of input signal values that will transfer the controlled system into the desired state in accordance with the selected optimality criterion. The realized simulation and experimental measurements performed on HIL platform have confirmed the correctness and effectiveness of the proposed design method and also its applicability to others dynamic systems with as little previous knowledge as possible.

Presents an LMI approach to optimal fuzzy control based on a quadratic performance function. First, stability conditions are presented by relaxing the previous stability results. The relaxed stability conditions are represented in terms of LMIs. The optimal fuzzy controller design utilizing the relaxed stability conditions is proposed. The optimal fuzzy controller is designed by solving the minimization problem that minimizes the upper bound of a given quadratic performance function. Finally, a design example for the well-known nonlinear control benchmark problem, the TORA system, demonstrates the utility of the optimal fuzzy control based on a quadratic performance function.

ABSTRACTA systematical design method of optimal control for non-minimum phase integrating processes with time delay using disturbance observer-based (DOB) control scheme is presented. All stabilising controllers and the filter of DOBs for integrating plants are developed. Then the optimal set-point tracking controller and the optimal filter of DOB are systematically derived by minimising the H2 norm performance specifications. The proposed design method has three main advantages. First, the design procedure is systematical and simple. Specified weight functions are chosen for step inputs and inputs similar to steps. The designed set-point tracking controller and the filter of DOB are given in analytical forms. Second, the designed set-point tracking controller and the filter of the DOB are optimal. They are derived from minimising the performance indexes of set-point tracking and input load disturbance rejection (ILDR). Finally, the set-point tracking performance specification and ILDR specification can be quantitatively achieved by conveniently tuning the adjustable parameters. Numerical simulations are given to illustrate the effectiveness of the proposed method.

Design of an intelligent optimal neural network-based tracking controller for nonholonomic mobile robot systems

We present in this paper a novel method (called PID design through numerical optimization) for the design of adaptive fuzzy PID controllers to achieve optimal control performance. By applying the numerical optimization, the fuzzy PID design problem is transferred to a numerical optimization problem. First, a fuzzy parameter tuner is built to generate initial PID parameters, including positions and shapes of fuzzy membership functions and scaling factors. Then the gradient-based Sequential Quadratic programming (SQP) algorithm is employed to iteratively minimize the cost function by iterating the parameters. Unlike conventional PID design, this method is capable of reaching the desired control performance, such as minimum overshoot or long term stability. Another unique feature is that the optimized adaptive PID controller is applicable to a wide variety of time-varying and nonlinear systems. The proposed method is applied to the induction motor control problem and the experimental results are presented to demonstrate its effectiveness and performance.

Genetic synthesis of fuzzy logic controllers in turning

By combining optimal control theory and linear regulator theory with the Takagi-Sugeno fuzzy methodology, a global optimal and stable fuzzy controller is presented to achieve trajectory tracking for a specific underactuated robot: the pendubot. The stability of the entire close-loop system is ensured by the designed optimal fuzzy controller. The paper includes a description of the pendubot system and the real-time control results.

An improved data-driven predictive optimal control approach for designing hybrid electric vehicle energy management strategies

The issue of optimal controller design which is based on exact linearization of state feedback in the uncertain and chaotic systems with external disturbances is researched. First, based on the mature quadratic optimal control theory, the nonlinear chaotic system model with disturbance is converted to an equivalent linear system model without disturbance. Second, an optimal controller design method based on quadratic performance index is given which aims at pseudo-linear-system. The optimal control rate is shown after equation solution, and then the nonlinear chaotic system is changed into an equivalent linear system with Lie derivative transformation which makes the project simple and easily realized. With the simulation for parameter uncertainty in Liu chaotic systems, the result shows that the control quality has been greatly improved.

To present an application of optimal controller design to a block-ice production process using dynamic programming. First, we develop mathematical models for such a process by employing system identification techniques. In particular, we build two parametric models, namely, linear model and neural network model. Linear models are built with Auto-Regressive model with exogenous inputs (linear ARX model). Feedforward neural networks (NNARX model) are constructed using the information provided by the linear ARX models. In addition, the Optimal Brain Surgeon (OBS) method is employed to prune the neural network models. Comparing the experimental results obtained from these models, it indicates that linear ARX models yield reasonably good performance in terms of the model fit. Then, using the obtained models, we investigate the energy consumption and operation cost of an ice factory when using time of use (TOU) tariff and time of day (TOD) tariff. Specifically, we develop an optimal control design for block-ice production process. The optimal strategy aims to minimize the electricity cost over a finite-time horizon and is subjected to constraints involving the control input of compressors, the brine temperature, and the number of block-ices ready for sales. Moreover, various factors in the design criteria have been analyzed with respect to the energy consumption and the operation cost. We compare the performance of the optimal controllers and the conventional control strategy. The simulation reveals that the proposed optimal control design has better performance than that of the conventional control. Furthermore, the optimal control using TOU tariff can reduce the operation cost when comparing to the one using TOD tariff.