In this paper, we study asymptotic stability of the Takagi-Sugeno-Kang (TSK) fuzzy PI control system using the circle criterion theorem. We first divide a TSK fuzzy PI controller into a memoryless nonlinear part and a linear dynamic unit, and merge the linear dynamic unit with a linear plant to be controlled and form a new augmented plant. The system is then reconstructed as a new interconnected form of the augmented linear plant and the memoryless nonlinear part. We then derive transfer function matrix of the augmented linear plant and sector condition of the memoryless nonlinear part. Based on the derived transfer function matrix and the sector condition, we determine sufficient conditions that guarantee asymptotic stability of the TSK fuzzy PI control system by using the circle criterion. Two examples are presented to demonstrate the feasibility of the proposed method.

In this paper, we present the design and stability analysis of Takagi-Sugeno-Kang (TSK)-type full-scale fuzzy proportional-integral-derivative (PID) controller. We reveal the analytical structure of a TSK-type full-scale fuzzy PID controller relative to the conventional PID controller. This controller consists of two input fuzzy sets for each of the three input variables, singleton fuzzifier, center average defuzzifier and the MIN operator for the AND operation. We prove that this type of fuzzy controller is actually a nonlinear PID controller with the variable gains. Then, we present BIBO stability analysis of TSK-type full-scale fuzzy PID controller using Small-Gain Theorem.

Monotonic input-output relationship is common in many physical systems. When modeling a physical system whose input-output relationship is monotonic, it is desired for a model to have the monotonicity. In this paper, we construct a model with single input rule modules (SIRMs) connected fuzzy system to solve “the curse of dimensionality”, and propose sufficient conditions for the constructed fuzzy system to have monotonic input-output relationship. The conditions are obtained by restricting the first derivative of the fuzzy system to be nonnegative. The derived conditions can be classified into two parts: the condition on the consequent part parameters of fuzzy rules and the condition on the input membership functions. The simulation results show the validity of the derived conditions.

The use of conventional kinematic equations for Mecanum wheel based omni-directional mobile robot suffers from position errors mainly because of slips on the wheels. To overcome the problem, we first identify the sources that originate position errors and then introduce the wheel parameter adjustment to reduce the position errors of the robot system. The experimental results show that the presented wheel parameter adjustment indeed reduces position errors and provides a good calibration mechanism.

This paper derives sufficient conditions for a single-input single-output fuzzy system whose output is convex with respect to its input. They are composed of two parts: the constraint on input membership functions and the constraint on the THEN parts of fuzzy rule base. And we prove in a constructive manner that any continuously differentiable single-input single-output convex function can be approximated with any degree of accuracy by a single-input single-output fuzzy system with the above conditions.

This paper ments a multiobjective genetic algorithm (MOGA) to find the optimal guideway networks (GNs) of personal rapid transit (PRT). The objective of the GN design problem (GNDP) is to find the GNs that minimize the construction cost and peak-hour traffic while satisfying the connectivity constraint. To solve the GNDP, we develop an MOGA by modifying an impmved nondominated sorting genetic algorithm (NSGA-11). The developed MOGA inherits the advantages of NSGA-I1 and adopts a GNDP-specific mutation operator, which provides better solution quality. To verify the effectiveness and efficiency of the developed MOGA, we conducted numerical experiments on the GNDPs with up to 15 stations and 210 links.

This paper presents a class of hierarchical fuzzy systems where previous layer outputs are used not in IF-parts, but only in THEN-parts of the fuzzy rules of the current layer. The proposed scheme is shown to be a universal approximator to any real continuous function on a compact set if complete fuzzy sets are used in the IF-parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier. From the example of ball-and-beam control system simulation, it is demonstrated that the proposed scheme approximates with high accuracy a model nonlinear controller with fewer fuzzy rules than a centralized fuzzy system, and its control performance is comparable to that of a nonlinear controller.

This article presents a new way of generating a generalized state equation that is useful for analyzing the token flow of the Petri Net (PN) with priority. The transition values in the firing vector as used in the conventional state equation are replaced with transition variables, which are generated by multiplying a series of firing condition functions taking the weighted inhibitor arc into account. The actual value of a transition variable is determined by taking priority and the present marking into account. The proposed state equation generalizes the conventional one by using the transition variable form and by containing the formulation of priority. Given the initial marking, the subsequent marking evolution can be determined successively from the generalized state equation as the simultaneous firings occur. A PN with deadlock is analyzed as an example to establish the validity of the generalized state equation. © 2003 Wiley Periodicals, Inc.

An appropriate mutation operator of the evolutionary algorithm (EA) maintains a balance between exploration and exploitation. This balance is usually satisfied by using the combined mutation operators (CMOs) of the Gaussian and Cauchy random variables. This paper studies the convergence property of the CMO. As a good model of the CMO, it proposes to use the decision factor /spl alpha/, the probability of choosing the Gaussian random variable between the Gaussian and Cauchy random variables for a mutation operator. This paper shows that the optimal convergence rate and the associated optimal mutation step size are monotonically decreasing with respect to /spl alpha/.

This paper presents a special hierarchical fuzzy system where the outputs of the previous layer are not used in the IF-parts, but used only in the THEN-parts of the fuzzy rules of the current layer. The proposed scheme can be shown to be a universal approximator to any continuous function on a compact set if complete fuzzy sets are used in the IF-parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier.

Introduces an evolutionary computation (EC)-based identification method of a Takagi-Sugeno-Kang (TSK) fuzzy system constrained by a monotonic input-output relationship. The differentiation of a TSK fuzzy system output with respect to its input yields a sufficient condition of the fuzzy system parameters that makes the fuzzy system monotonic. By using the derived condition, we suggest a new EC-based fuzzy system identification method whose fuzzy model preserves monotonicity at every identification stage by means of modified representation and mutation paradigms. Simulation results show that the proposed identification technique is better than conventional methods in its convergence rate, generalization characteristic, and robustness.

This paper presents the process for converting A and B contacts in the ladder diagram (LD) into a Petri net (PN). In order to represent the A and B contacts in the LD program with the PN graph, the concept of preservation arc is introduced. The resulting PN is then compared with the conventional PN using a timing chart. The state equation for the A and B contacts is constructed in a transition vector. Using the equation, each state equation for the LD program is created, such as the A contact function and the B contact function. The state equations are validated using examples.

This paper presents an adaptive iterative learning control scheme that is applicable to a class of nonlinear systems. The control scheme guarantees system stability and boundedness by using the feedback controller coupled with the fuzzy compensator and achieves precise tracking by using the iterative learning rules. In the feedback plus fuzzy compensator unit, the feedback control part stabilizes the overall closed-loop system and keeps its error bounded, and the fuzzy compensator estimates and compensates for the nonlinear part of the system, thereby keeping the feedback gains reasonably low in the feedback controller. The fuzzy compensator is designed by applying the fuzzy approximation technique to the uncertain nonlinear term to be compensated. In the iterative learning controller, a simple learning control rule is used to achieve precise tracking of the reference signal and a parameter learning algorithm is used to update the parameters in the fuzzy compensator so as to identify the uncertain nonlinearity as much as possible. © 2000 John Wiley & Sons, Inc.

This paper presents a fast and effective visual tracking and location prediction algorithm for cooperative multiple soccer robots playing a soccer game. The picture image is captured by the system and the motion parameters of each object are then computed from the captured image. Then, an image is selected as a template and 2D color image pattern is extracted from the incoming image and a sequence of images are generated by using a simple linear predictor that speeds up the processing time. Based on the computed tracking parameters, a heuristic path is generated. By using a vision-based command to line-of-sight (CLOS) guidance method that predicts and generates next robot motions. Monitoring the selected object using visual images, the vision system tracks the object and adjusts the velocities and directions of the robots to cope with sudden changes of direction such as bounded ball from an obstacle or expected position errors of the selected object. The simulation results as well as experimental results show that the presented algorithm works well for the soccer game.

A method of environment modelling is presented which is based on the stochastic approximation technique. The environment is represented in this paper as stochastic obstacle regions equipped with their own stochastic variables such as mean, variance and eigenvalues. The stochastic variables in each obstacle region are updated by using the distance information of the obstacles, which is acquired from the laser scanner sampling time. The representation of the environment with the stochastic variables enables us to save CPU time and memory consumption in building the map. This technique can also detect if the obstacles are removed and is applicable to the quasi-static environment. If the eigenvalues of the covariance matrix in a certain region are known, then the feature of that region can be extracted as a line or as an ellipse. Thus, the algorithm presented can be used for the navigation and the localization of the mobile robot. The algorithm presented is successfully tested on our mobile robot ARES-II system equipped with the LADAR 2D-laser scanner.

The control of flexible joint robot manipulators by backstepping design approach is presented. In contrast with the other controllers for flexible joint robot manipulators, the proposed controller neither assumes weak joint flexibility nor requires joint acceleration measurements. With the proposed controller, the link position and velocity errors converge to zero exponentially fast. The simulation results prove that the proposed controller performs superior to the other controllers as the flexibility increases in the joints.

The authors propose a learning controller with parameter adaptation for constrained motion of robot manipulators. The additional computed torque error term is used in this controller to reduce the load from feedback and keeps its gain reasonably low. Position and force trackings are achieved by applying the position learning control algorithms to position controlled axes and the force learning control algorithms to force control axes. Joint acceleration terms are never used in the controller and the PE condition is not required for force tracking. The uniform convergence of position, velocity, acceleration and force trajectories is obtained under simple conditions.

An iterative learning scheme comprising a unique feedforward learning controller and a linear feedback controller is presented. In the feedback loop, the fixed-gain PD controller provides a stable open neighborhood along a desired trajectory. In the feedforward path, on the other hand, a learning control strategy is exploited to predict the desired actuator torques. It is shown that the predicted actuator torque converges to the desired one as the iteration number increases. The convergence is established based on the Lyapunov stability theory. The proposed learning scheme is structurally simple and computationally efficient. Moreover, it possesses two major advantages: the ability to reject unknown deterministic disturbances and the ability to adapt itself to the unknown system parameters.>