This article presents a novel path-following-method-based polynomial fuzzy control design. By examining the stabilization problem, the nonconvex stabilization criterion represented in terms of bilinear sum-of-squares (SOS) constraints is proposed to complement the existing convex stabilization criteria. Based on the polynomial Lyapunov function and considering the operation domain, the stabilization control is designed with a systematic region of attraction (ROA) analysis method. Since the proposed stabilization criterion remains in nonconvex form, the conservativeness caused by the transformation from nonconvex (bilinear SOS) constraints into convex (SOS) constraints can be avoided. Moreover, the restriction on the Lyapunov function candidates for the convex transformation in the literature does not exist in the proposed nonconvex stabilization criterion. The stabilization analysis for polynomial fuzzy control systems is concerned with the double fuzzy summation problem that can be treated as the copositivity problem. Therefore, the SOS-based copositive relaxation technique is applied for the proposed stabilization criterion. Since the proposed nonconvex stabilization criterion is represented in terms of bilinear SOS constraints, the path-following method is employed for solving the bilinear SOS problem. Finally, design examples are provided to demonstrate that the proposed nonconvex stabilization criterion complements the existing convex stabilization criteria.

This correspondence paper presents a framework for practical model construction and stable altitude control of an unmanned aerial vehicle with a parafoil-type wing (UAV-PW). To design a stable controller, we first construct a dynamical longitudinal model of the UAV-PW. Since there exist no aerodynamics data of the parafoil shape in our UAV-PW, aerodynamics coefficients balanced at the trimmed equilibrium are employed. The model accuracy is investigated by comparing the model outputs with the real test flight experimental data. Next, stable controller design conditions for the UAV-PW model with uncertainties are derived in terms of linear matrix inequalities (LMIs). By solving the LMI conditions, we design a stable controller that asymptotically stabilizes the UAV-PW model with the uncertainties on a considered operation domain. The experimental results demonstrate the viability of the model construction and the stable altitude control.

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's 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.

This paper presents a new sum-of-squares (SOS, for brevity) design framework for robust control of polynomial fuzzy systems with uncertainties. Two kinds of robust stabilization conditions are derived in terms of SOS. One is global SOS robust stabilization conditions that guarantee the global and asymptotical stability of polynomial fuzzy control systems. The other is semiglobal SOS robust stabilization conditions. The latter is available for very complicated systems that are difficult to guarantee the global and asymptotical stability of polynomial fuzzy control systems. The main feature of all the SOS robust stabilization conditions derived in this paper are to be expressed as nonconvex formulations with respect to polynomial Lyapunov function parameters and polynomial feedback gains. Since a typical transformation from nonconvex SOS design conditions to convex SOS design conditions often results in some conservative issues, the new design framework presented in this paper gives key ideas to avoid the conservative issues. The first key idea is that we directly solve nonconvex SOS design conditions without applying the typical transformation. The second key idea is that we bring a so-called copositivity concept. These ideas provide some advantages in addition to relaxations. To solve our SOS robust stabilization conditions efficiently, we introduce a gradient algorithm formulated as a minimizing optimization problem of the upper bound of the time derivative of an SOS polynomial that can be regarded as a candidate of polynomial Lyapunov functions. Three design examples are provided to illustrate the validity and applicability of the proposed design framework. The examples demonstrate advantages of our new SOS design framework for the existing linear matrix inequality approaches and the existing convex SOS approach.

This paper proposes sum-of-squares (SOS) methodologies for stability analysis and region-of-attraction (ROA) estimation for nonlinear systems represented by polynomial fuzzy models via piecewise polynomial Lyapunov functions (PPLFs). At first, two SOS-based global stability criteria are proposed by applying maximum-type and minimum-type PPLFs, respectively. It is known that less-conservative results can be obtained by reducing global stability to local stability, since it is usually the case for nonlinear systems that the stability cannot be reached globally. Therefore, based on the two types of PPLFs, two local stability criteria are further proposed with the algorithms that enlarge the estimated ROA as much as possible. The constraints for checking (global and local) stability and enlarging the estimated ROA are represented in terms of bilinear SOS problems. Hence, the path-following method is applied to solve the bilinear SOS problems in the proposed methodologies. Finally, some examples are provided to illustrate the utility of the proposed methodologies.

This paper presents a sum-of-squares (SOS) based methodology to obtain inner bounds on the region-of-attraction (ROA) for nonlinear systems represented by polynomial fuzzy systems. The methodology searches a polynomial Lyapunov function to guarantee the local stability and the invariant subset of the ROA is presented as the level set of the polynomial Lyapunov function. At first the methodology checks whether the considered system can be guaranteed to be locally asymptotically stable. After confirming that the system is guaranteed to be locally asymptotically stable, the methodology enlarges the invariant subset of the ROA as much as possible. The constraints for both of checking stability and enlarging contractively invariant set are represented in terms of bilinear SOS optimization problems. The path-following method is applied to solve the bilinear SOS optimization problems in the methodology.

This paper presents a novel method for stabilization analysis of the single-input polynomial fuzzy systems using a sum of squares (SOS) approach to construct control Lyapunov functions (CLFs) for the systems. First, we represent a nonlinear system as a polynomial fuzzy system. Then, sufficient conditions in SOS terms for a positive definite function to become a CLF is presented. We solve the sufficient conditions using SOS optimization technique to construct the CLF. Finally, after a CLF is constructed, the controller for the system is designed using Sontag's formula. To illustrate the validity of the proposed approach, a design example is provided.

This paper presents development of an autonomous flying robot (unmanned aerial vehicle) and its verification via flight control experiment. The autonomous flying robot has a global positioning system (GPS) sensor to control its altitude and also a wireless camera to gather visual information from the air. First, we construct a longitudinal model of the autonomous flying robot to design a stable controller using a common Lyapunov approach. The longitudinal model has three degree of freedom, i.e., the altitude, the horizontal position and the pitch angle. A stable controller is designed so as to guarantee the stability of the trajectory tracking control system for the three-degree-of-freedom model. The experimental result demonstrates the viability of the stable trajectory tracking control.

This paper presents fuzzy model-based servo control for a class of nonlinear descriptor systems. In our previous paper, servo control based on error dynamics using error vector and input difference was proposed. In this paper, we extend the servo control technique to nonlinear descriptor systems. The descriptor system can represent larger class of nonlinear systems than the typical state-space models. We show the construction method of fuzzy descriptor system for servo control and derive servo controller design conditions for fuzzy descriptor systems in the form of LMI. Moreover, the servo control which is applicable to switching of target point is also discussed. Design examples illustrate the utility of this approach.

This paper proposes the minimum-type piecewise-Lyapunov-function-based switching fuzzy controller that switches accompanying the piecewise Lyapunov function. By applying this switching fuzzy controller with the minimum-type piecewise Lyapunov function, the relaxed stabilization criterion is obtained for continuous Takagi-Sugeno (T-S) fuzzy systems. Some conditions of the relaxed stabilization criterion are represented by bilinear matrix inequalities (BMIs), which contain some bilinear terms as the product of a full matrix and a scalar. According to the literature, the path-following method is very effective for this kind of BMI problem; hence, it is utilized to obtain solutions of the criterion. Xie et al. in 1997 chose two types (i.e., minimum type and maximum type) of piecewise Lyapunov functions as the Lyapunov function candidates. The reasons for why this study only chooses the minimum-type piecewise Lyapunov function as the Lyapunov function candidate are illustrated. Moreover, the numerical example shows the relaxation of the proposed criterion.

This paper presents a sum-of-squares (SOS) approach to polynomial fuzzy observer designs for three classes of polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results with respect to a polynomial fuzzy system that is a more general representation of the well-known T-S fuzzy system. Next, we propose polynomial fuzzy observers to estimate states in three classes of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions for the first two classes (Classes I and II) is that they realize the so-called separation principle, i.e., the polynomial fuzzy controller and observer for each class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. Although, for the last class (Class III), the separation principle does not hold, we propose an algorithm to design polynomial fuzzy controller and observer satisfying the stability of the overall control system in addition to converging state-estimation error (via the observer) to zero. All the design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recently developed SOSTOOLS and a semidefinite-program solver, respectively. To illustrate the validity and applicability of the proposed approach, three design examples are provided. The examples demonstrate the advantages of the SOS-based approaches for the existing LMI approaches to T-S fuzzy observer designs.

This paper presents a polynomial fuzzy observer design for a wider class of polynomial fuzzy systems via a sum of squares (SOS, for brevity) approach. The proposed SOS-based framework provides a number of innovations and improvements over the existing LMI-based approaches to Takagi-Sugeno (T-S) fuzzy controller and observer designs. First, we briefly summarize previous results for a class of polynomial fuzzy systems that is more general representation of the well-known T-S fuzzy system. Next, we propose a polynomial fuzzy observer to estimate states in a wider class of polynomial fuzzy systems and derive SOS conditions to design polynomial fuzzy controllers and observers. A remarkable feature of the SOS design conditions is that they realize the so-called separation principle, that is, that a polynomial fuzzy controller and observer for this class can be separately designed without lack of guaranteeing the stability of the overall control system in addition to converging state estimation error (via the observer) to zero. The design conditions in the proposed approach can be represented in terms of SOS and are symbolically and numerically solved via the recent developed SOSTOOLS and a semidefinite program (SDP) solver, respectively. To illustrate the validity and applicability of the proposed approach, a design example is provided. The example demonstrates advantages of the SOS-based approach for the existing LMI approaches to T-S fuzzy observer designs.

This paper presents stability analysis of nonlinear systems using a new type of Lyapunov functions. We define so-called multiple mixed max-min based Lyapunov functions that contain existing piecewise Lyapunov functions as a special case. The extension is realized by multiple mixed connection of max and min operations for plural local quadratic functions. Hence, stability analysis discussed in this paper is more relaxed than those based on existing piecewise Lyapunov functions in addition to quadratic Lyapunov functions. Relaxed stability conditions based on multiple mixed max-min based Lyapunov functions are derived by considering switching conditions among the plural local quadratic functions. The derived stability conditions are represented in terms of bilinear matrix inequalities (BMIs). Unfortunately, BMIs cannot be generally solved via LMI solvers. Therefore, to simply solve BMIs, we propose a practical way that combines an LMI solver and particle swarm optimization. In this paper, two analytical examples are provided. The examples illustrate that our approach provides more relaxed stability results than existing piecewise Lyapunov functions approaches.

Based on the piecewise Lyapunov function, this study proposes a switching fuzzy controller, which switches depending on the Lyapunov function, to get relaxed stabilization conditions for the continuous T-S fuzzy system. The relaxed conditions are bilinear with the s-procedure parameters, therefore the particle swarm optimization (PSO) algorithm is utilized with the LMI tool to solve the relaxed conditions. Two simulation examples are given to show the relaxation and effectiveness of the proposed method.

This paper presents switching fuzzy model construction based on optimal dividing planes. In our previous papers, we proposed the switching fuzzy model with arbitrary dividing planes. However, dividing planes have been selected by controller designers before constructing the switching fuzzy model. Unfortunately, it is difficult to find suitable dividing planes for complicated nonlinear systems. Moreover, the switching fuzzy models constructed from different dividing planes are different. Therefore, the model construction affects the stability analysis results. In this paper, we propose switching fuzzy model construction method using multi-dimensional sector nonlinearity concept based on optimal dividing planes. The linear consequent parts of the switching fuzzy model based on optimal dividing planes are constructed from sectors which have minimum distance between a nonlinear system and sectors, and have richer information of the nonlinear system than the consequent parts of the ordinary Takagi-Sugeno fuzzy model. Two examples are provided to illustrate the validity of this approach.

This paper discusses the improvement of the simulation model and the development of the new mechanism for flight control of a flying robot with the cyclogyro wing. In past study, we focused high maneuverability of the flying robots with the cyclogyro wing, whose rotor had rotation along horizontal axis, and developed some prototypes. The simulation model was also constructed based on the pressure of air. However the Reynolds number was not considered in the constructed simulation model. As a results, the model's accuracy was not enough. On the other hand, the control mechanism for the flight of cyclogyro wing is not yet developed. In this paper, the simulation model is improved by considering the cyclogyro's Reynolds number. The utility of the improved simulation model is verified by comparing simulation results with experimental results. Moreover the new mechanism is suggested for the flight control by controlling the generated force direction. The prototype of the new mechanism is developed and validated by the experiment.

This paper presents a sum of squares (SOS) approach for modeling and control of nonlinear dynamical systems using polynomial fuzzy systems. The proposed SOS-based framework provides a number of innovations and improvements over the existing linear matrix inequality (LMI)-based approaches to Takagi-Sugeno (T-S) fuzzy modeling and control. First, we propose a polynomial fuzzy modeling and control framework that is more general and effective than the well-known T--S fuzzy modeling and control. Secondly, we obtain stability and stabilizability conditions of the polynomial fuzzy systems based on polynomial Lyapunov functions that contain quadratic Lyapunov functions as a special case. Hence, the stability and stabilizability conditions presented in this paper are more general and relaxed than those of the existing LMI-based approaches to T-S fuzzy modeling and control. Moreover, the derived stability and stabilizability conditions are represented in terms of SOS and can be numerically (partially symbolically) solved via the recently developed SOSTOOLS. To illustrate the validity and applicability of the proposed approach, a number of analysis and design examples are provided. The first example shows that the SOS approach renders more relaxed stability results than those of both the LMI-based approaches and a polynomial system approach. The second example presents an extensive application of the SOS approach in comparison with a piecewise Lyapunov function approach. The last example is a design exercise that demonstrates the viability of the SOS-based approach to synthesizing a stabilizing controller.

We develop a flying robot with a new pantograph-based variable wing mechanism for horizontal-axis rotorcrafts (cyclogyro rotorcrafts). A key feature of the new mechanism is to have a unique trajectory of variable wings that not only change angles of attack but also expand and contract according to wing positions. As a first step, this paper focuses on demonstrating the possibility of the flying robot with this mechanism. After addressing the pantograph-based variable wing mechanism and its features, a simulation model of this mechanism is constructed. Next, we present some comparison results (between the simulation model and experimental data) for a prototype body with the proposed pantograph-based variable wing mechanism. Both simulation and experimental results show that the flying robot with this new mechanism can generate enough lift forces to keep itself in the air. Furthermore, we construct a more precise simulation model by considering rotational motion of each wing. As a result of optimizing design parameters using the precise simulation model, flight performance experimental results demonstrate that the robot with the optimal design parameters can generate not only enough lift forces but a 155 gf payload as well.

This correspondence presents servo and nonlinear model following controls for a class of nonlinear systems using the Takagi-Sugeno fuzzy model-based control approach. First, the construction method of the augmented fuzzy system for continuous-time nonlinear systems is proposed by differentiating the original nonlinear system. Second, the dynamic fuzzy servo controller and the dynamic fuzzy model following controller, which can make outputs of the nonlinear system converge to target points and to outputs of the reference system, respectively, are introduced. Finally, the servo and model following controller design conditions are given in terms of linear matrix inequalities. Design examples illustrate the utility of this approach.

This paper presents the guaranteed cost control of polynomial fuzzy systems via a sum of squares (SOS) approach. First, we present a polynomial fuzzy model and controller that are more general representations of the well-known Takagi-Sugeno (T-S) fuzzy model and controller, respectively. Second, we derive a guaranteed cost control design condition based on polynomial Lyapunov functions. Hence, the design approach discussed in this paper is more general than the existing LMI approaches (to T-S fuzzy control system designs) based on quadratic Lyapunov functions. The design condition realizes a guaranteed cost control by minimizing the upper bound of a given performance function. In addition, the design condition in the proposed approach can be represented in terms of SOS and is numerically (partially symbolically) solved via the recent developed SOSTOOLS. To illustrate the validity of the design approach, two design examples are provided. The first example deals with a complicated nonlinear system. The second example presents micro helicopter control. Both the examples show that our approach provides more extensive design results for the existing LMI approach.

This paper presents nonlinear model following control for discrete-time nonlinear systems using the switching fuzzy model-based control approach. We propose the construction method of augmented switching fuzzy model following control system for discrete-time nonlinear systems. Then we introduce the switching fuzzy controller which can make outputs of the nonlinear system converge to outputs of the reference nonlinear system, and derive the controller design conditions in terms of LMIs.

This paper presents a comparison result of micro helicopter control via a typical linear matrix inequality (LMI) approach and a sum of squares (SOS) approach. First we construct a dynamical model of a micro helicopter and convert it to a Takagi-Sugeno fuzzy model. Next, this paper summarizes a recent developed SOS design approach for polynomial fuzzy control systems based on polynomial Lyapunov functions. We emphasize that the SOS design approach to polynomial fuzzy control systems is more general than that based on the existing LMI design approaches to T-S fuzzy control systems. The control results of a micro helicopter show that the SOS design approach provides better control results than the LMI design approach.

We develop a flying robot with a new pantograph-based variable wing mechanism for horizontal-axis rotorcrafts (cyclogyro rotorcrafts). A key feature of the new mechanism is a unique trajectory of variable wings that not only change angles of attack but also expand and contract according to wing positions. Experimental results show that the developed flying robot can generate 144% lift force for its own weight (equivalently 100 gf payload). Furthermore, as a result of optimizing design parameters of the robot through computer simulation, we arrive at the optimal design parameters with 200 gf payload. Both simulation and experimental results show the utility of the developed flying robot with the new mechanism.

This paper discusses a simulation model of flying robots (developed in our previous paper) with a variable attack angle mechanism. The simulation model constructed in this paper are divided into three parts. The first part is a so- called attack angle model to compute the change of angle of attack. The second part is a so-called lift force model to compute lift force based on the computational result from the first part. In the second part, we compensate lift and drag coefficients with aero dynamical (experimental) data in previous studies on pitching (motion) wing since the variable attack angle mechanism realizes a pitching motion. The third part is a so- called power model to compute the electrical power of motors. The utility of the simulation model is verified by comparing simulation results with experimental results.

There has been a flurry of research activities in the analysis and design of fuzzy control systems based on linear matrix inequalities (LMIs). This paper presents a descriptor system approach to fuzzy control system design using fuzzy Lyapunov functions. The design conditions are still cast in terms of LMIs but the proposed approach takes advantage of the redundancy of descriptor systems to reduce the number of LMI conditions which leads to less computational requirement. To obtain relaxed LMI conditions, new types of fuzzy controller and fuzzy Lyapunov function are proposed. A salient feature of the LMI conditions derived in this paper is to relate the feasibility of the LMIs to the switching speed of each linear subsystem (to be exact, to the lower bounds of time derivatives of membership functions). To illustrate the validity and applicability of the proposed approach, two design examples are provided. The first example shows that the LMI conditions based on the fuzzy Lyapunov function are less conservative than those based on a common (standard) Lyapunov function. The second example illustrates the utility of the fuzzy Lyapunov function approach in comparison with a piecewise Lyapunov function approach.

Fuzzy model-based control mainly deals with dynamical systems which affinely depend on control inputs. In this paper, we propose the switching fuzzy model construction and controller design for dynamical systems which is permitted to have nonlinearity not only in the states, but also in the inputs. By utilizing the dynamic state feedback control approach, we show that we can deal with membership functions which depend on control inputs and that the number of the fuzzy model rules which fire simultaneously can be decreased in comparison with the ordinary switching fuzzy model. We design the switching fuzzy dynamic state feedback controller and derive the controller design conditions based on the switching Lyapunov function in terms of LMIs. A design example illustrates the utility of this approach.

This paper presents dynamic output feedback control designs for discrete Takagi-Sugeno fuzzy systems. A dynamic output feedback controller is constructed based on the concept of dynamic parallel distributed compensation (DPDC). Design conditions for optimal dynamic feedback control are obtained in terms of linear matrix inequalities (LMIs). In application to a vehicle with triple trailers setup, we utilize the optimal design conditions to avoid the jack-knife phenomenon. Our results demonstrate that the optimal dynamic output feedback design effectively achieves the backing up control of the vehicle with triple trailers while avoiding the jackknife phenomenon. More importantly, we demonstrate that the designed optimal control can achieve the backing up control without two potentiometers that were employed to measure the relative angles (of a vehicle with triple trailers) in our previous experiments.

This paper presents a study on the development and control of a micro biped walking robot using shape memory alloys (SMAs). We propose a flexible flat plate (FFP) consisting of a polyethylene plate and SMAs. Based on a detailed investigation of the properties of the SMA-based FFP structure, we develop a lightweight micro walking robot incorporating multiple SMA-based FFPs. The walking robot has four degrees of freedom and is controlled by switching the ON-OFF current signals to the SMA-based FFPs. The switching timing, central to the control strategy to achieve walking behavior, is determined through experiments. The micro robot realizes biped walking by transferring the elastic potential energy (generated by deflections of the SMA-based FFPs) to kinematic energy. The resulting micro biped walking robot weighs a mere 2.8 g (with a height of 70 mm). Our experimental results demonstrate the viability and utility of the micro walking robot with the proposed SMA-based FFPs and the control strategy to achieve walking behavior

We develop a cyclogyro-based flying robot with a new variable attack angle mechanism. Cyclogyro is a flying machine which is supported in the air by power-driven rotors, which rotate about a horizontal axis, like the paddle-wheels of a steamboat. Machines of this type have been designed by some companies, but there is no record of any successful flights. The new variable attack angle mechanism proposed in this paper has an eccentric (rotational) point in addition to a rotational point connecting to a motor. The variable attack angle mechanism is a kind of double crank mechanism consisting of the two different rotational points and wings. The main feature of the mechanism with the eccentric point is to be able to change attack of angles according to the wing positions (according to the rotational angles of the cyclogyro) without actuators. The mechanism generates enough lift force to fly. We determine design parameters (wing span, the number of wings and eccentric distance) of the flying robot through experiments. Experimental results show that the developed cyclogyro-based flying robot with the new variable attack angle mechanism can hover along a vertical guide

This paper presents a recursive pointwise design (RPD) method for a class of nonlinear systems represented by x(t)=f(x(t))+g(x(t))u(t). A main feature of the RPD method is to recursively design a stable controller by using pointwise information of a system. The design philosophy is that f(x(t)) and g(x(t)) can be approximated as constant vectors in very small local state spaces. Based on the design philosophy, we numerically determine constant control inputs in very small local state spaces by solving linear matrix inequalities (LMIs) derived in this paper. The designed controller switches to another constant control input when the states move to another local state space. Although the design philosophy is simple and natural, the controller does not always guarantee the stability of the original nonlinear system x(t)=f(x(t))+g(x(t))u(t). Therefore, this paper gives ideas of compensating the approximation caused by the design philosophy. After addressing outline of the pointwise design, we provide design conditions that exactly guarantee the stability of the original system. The controller design conditions require to give the maximum and minimum values of elements in the functions f(x(t)) and g(x(t)) in each local state - space. Therefore, we also present design conditions for unknown cases of the maximum and minimum values. Furthermore, we construct an effective design procedure using the pointwise design. A feature of the design procedure is to subdivide only infeasible regions and to solve LMIs again only for the subdivided infeasible regions. The recursive procedure saves effort to design a controller. A design example demonstrates the utility of the RPD method

This paper presents a switching fuzzy controller design for a class of nonlinear systems. A switching fuzzy model is employed to represent the dynamics of a nonlinear system. In our previous papers, we proposed the switching fuzzy model and a switching Lyapunov function and derived stability conditions for open-loop systems. In this paper, we design a switching fuzzy controller. We firstly show that switching fuzzy controller design conditions based on the switching Lyapunov function are given in terms of bilinear matrix inequalities, which is difficult to design the controller numerically. Then, we propose a new controller design approach utilizing an augmented system. By introducing the augmented system which consists of the switching fuzzy model and a stable linear system, the controller design conditions based on the switching Lyapunov function are given in terms of linear matrix inequalities (LMIs). Therefore, we can effectively design the switching fuzzy controller via LMI-based approach. A design example illustrates the utility of this approach. Moreover, we show that the approach proposed in this paper is available in the research area of piecewise linear control.

A Takagi-Sugeno (T-S) model is employed to represent a networked control system (NCS) with different network-induced delays. Comparing with existing NCS modeling methods, this approach does not require the knowledge of exact values of network-induced delays. Instead, it addresses situations involving all possible network-induced delays. Moreover, this approach also handles data-packet loss. As an application of the T-S-based modeling method, a parity-equation approach and a fuzzy-observer-based approach for fault detection of an NCS were developed. An example of a two-link inverted pendulum is used to illustrate the utility and viability of the proposed approaches.

This paper presents new controller design conditions based on a parameter-dependent Lyapunov function for the polar coordinate fuzzy systems which were proposed in our previous papers. In the previous papers, we considered stability conditions and controller design conditions based on the so-called common quadratic Lyapunov function for the systems. In this paper, we utilize the descriptor system representation for the polar coordinate fuzzy system and the corresponding controller, and we derive the stabilizability conditions based on the parameter-dependent Lyapunov function to determine the feedback gains in the controller. The conditions are given in terms of LMIs

This paper proposes shared control in Internet-based remote stabilization for nonlinear systems. This paper consists of two parts. The first part addresses the basis of Internet-based remote stabilization for a single nonlinear system with time-varying delay. We derive a delay dependent sufficient condition for ensuring the stability of Takagi-Sugeno (T-S) fuzzy models with time-varying delays that are globally (or semi-globally at least) equivalent to nonlinear systems with network time-delays. A feature of the derived condition is to be able to obtain the maximum time-delay for ensuring the stability of Internet-based remote control system for given feedback gains. The second part presents shared control of plural nonlinear systems via a single controller. To design a (common) shared controller to stabilize plural nonlinear systems simultaneously, we derive also a shared control version of the stability condition for T-S fuzzy models with time-varying delays. Design examples demonstrate the utility of this proposed design approach

This paper presents a study on electroencephalogram (EEG)-based control of an electric wheelchair. The objective is to control the direction of an electric wheelchair using only EEG signals. In other words, this is an attempt to use brain signals to control mechanical devices such as wheelchairs. To achieve this goal, we have developed a recursive training algorithm to generate recognition patterns from EEG signals. Our experimental results demonstrate the utility of the proposed recursive training algorithm and the viability of accomplishing direction control of an electric wheelchair by only EEG signals.

This work presents Internet-based remote stabilization for nonlinear systems. In Internet-based remote control, we need to deal with time varying delays. If the system is nonlinear, the system is reduces to a time varying delay nonlinear control problem, which is the one of the most challenging control problems. We derive a design condition to stabilize the Internet-based remote control system. First, a class of nonlinear time varying delay systems is represented as the Takagi-Sugeno (T-S) fuzzy model. A model-based fuzzy stabilization design utilizing the concept of parallel-distributed compensation (PDC) is employed. A design condition is derived by considering time delay dependent sufficient conditions for ensuring the stability of closed-loop systems. In addition, the maximum time-delay for ensuring the stability of Internet-based remote control system can be obtained from the derived design condition. Simulation results show the utility of this proposed design approach.

In this paper, we discussed the problem of dynamic output variable structure control in a singular distributed parameter system based on output information. We give the dynamic output variable structure control method. Applying the Fourier method and based on separating principle, we prove that system can be observed and controlled. Through structuring special switching manifold, we established the law of variable structure control, realized real sliding mode movement of the mould and made the system is asymptotic stability. To make this clearer, an illustrative example is given for demonstration.

In this paper, the problem of bifurcation of the triharmonic equation is discussed by the best embedding constant and Nhari-type variation method. The harmonic equation has at least two solutions and its solution has bifurcation. The biharmonic equation has at least a radial positive solution, but bifurcation of the solution can't be discovered. In triharmonic equation, the best embedding constant and Palais-Smale condition are given by the defined function, the triharmonic equation has at least a radial positive solution and a nonradial positive solution, bifurcation phenomenon can be discovered in the solution. We also supply method for discussing existence of solution of polyharmonic equation.

This paper presents acrobatic control of an underactuated two-link robot called the pendubot. To achieve acrobatic control for the pendubot, we design a fuzzy controller for keeping first link swinging periodically while the second link maintains standing vertically. To facilitate the controller design, we represent the pendubot dynamics with a Takagi-Sugeno fuzzy model. We derive a linear matrix inequality (LMI) design condition to realize the acrobatic behavior. To accomplish the numerical feasibility design, we need to select carefully reference fuzzy model dynamics by taking into account some constraints. After selecting reference fuzzy model dynamics, an acrobatic controller is designed by solving the LMI condition. Simulation results show the utility of the proposed acrobatic control.

This paper describes stable control for the polar coordinate fuzzy systems that were proposed in our previous paper. The previous paper considered stability conditions for the open-loop systems. This paper mainly discusses stabilization for the systems. First, we address polar coordinate fuzzy model construction for a class of nonlinear systems with control input. Next, we propose a polar coordinate fuzzy controller to stabilize the systems. An interesting feature of the controller is to have the properties of both fuzzy controller and linear parameter varying controller. Furthermore, we derive LMI conditions to determine feedback gains of the controller. A design example shows that this approach provides more relaxed stabilization results than Takagi-Sugeno fuzzy model approach.

This paper addresses stability analysis and stabilization for Takagi-Sugeno fuzzy systems via a so-called fuzzy Lyapunov function which is a multiple Lyapunov function. The fuzzy Lyapunov function is defined by fuzzily blending quadratic Lyapunov functions. Based on the fuzzy Lyapunov function approach, we give stability conditions for open-loop fuzzy systems and stabilization conditions for closed-loop fuzzy systems. To take full advantage of a fuzzy Lyapunov function, we propose a new parallel distributed compensation (PDC) scheme that feedbacks the time derivatives of premise membership functions. The new PDC contains the ordinary PDC as a special case. A design example illustrates the utility of the fuzzy Lyapunov function approach and the new PDC stabilization method.

Presents two cases of multi-objective structure designs for mechanical systems described by Takagi-Sugeno fuzzy models. One is a state feedback case. The other is a dynamic output feedback case. The design purpose is to determine not only feedback gains of a fuzzy controller but also structure parameters of a controlled object. In each case, structure-oriented design conditions are derived from decay rate and optimal control performance points of view. In the dynamic output feedback case, we derive LMI conditions by introducing a new type of fuzzy controller. The multi-objective structure designs are applied to a parallel-type double inverted pendulum system. Simulation results show the effectiveness of the multi-objective structure designs.

This paper presents a new stability condition based on a switching Lyapunov function for a class of nonlinear systems. In our previous paper (2001), we propose a switching fuzzy model based on the sector nonlinearity concept. The switching fuzzy model can exactly represent a class of nonlinear systems globally or semi-globally. This paper describes a construction method of a switching Lyapunov function for the switching fuzzy model. The switching Lyapunov function is constructed by mirroring structure of the switching fuzzy model. An example illustrates the utility of this approach.

Presents a dual design problem via multiple Lyapunov functions. Based on a multiple Lyapunov approach, we introduce two important concepts. One is a dual design concept that minimizes/maximizes upper bounds of the time derivative of premise membership functions in a Takagi-Sugeno fuzzy system. The other is a stability margin concept for switching speed among if-then rules. It is related to avoiding conservatism of stability analysis and guaranteeing system response performance. A design example illustrates the utility of the dual design via the multiple Lyapunov function approach.

Presents a structure-oriented design for Takagi-Sugeno fuzzy control systems. Structure-oriented design conditions that simultaneously determine the feedback gains and the structure of a given control system are derived from a performance index optimization point of view. Furthermore, we discuss an LMI constraint on the time derivative of states from a practical actuator performance point of view. Simulation results show the effectiveness of the optimal feedback design and the structure-oriented design.

This paper presents a systematic procedure of fuzzy control system design that consists of fuzzy model construction, rule reduction, and robust compensation for nonlinear systems. The model construction part replaces the nonlinear dynamics of a system with a generalized form of Takagi-Sugeno fuzzy systems, which is newly developed by us. The generalized form has a decomposed structure for each element of A/sub i/ and B/sub i/ matrices in consequent parts. The key feature of this structure is that it is suitable for constructing IF-THEN rules and reducing the number of IF-THEN rules. The rule reduction part provides a successive procedure to reduce the number of IF-THEN rules. Furthermore, we convert the reduction error between reduced fuzzy models and a system to model uncertainties of reduced fuzzy models. The robust compensation part achieves the decay rate controller design guaranteeing robust stability for the model uncertainties. Finally, two examples demonstrate the utility of the systematic procedure developed.

This paper presents stable switching control of an radio-controlled (R/C) hovercraft that is a nonholonomic (nonlinear) system. To exactly represent its nonlinear dynamics, more importantly, to maintain controllability of the system, we newly propose a switching fuzzy model that has locally Takagi-Sugeno (T-S) fuzzy models and switches them according to states, external variables, and/or time. A switching fuzzy controller is constructed by mirroring the rule structure of the switching fuzzy model of an R/C hovercraft. We derive linear matrix inequality (LMI) conditions for ensuring the stability of the closed-loop system consisting of a switching fuzzy model and controller. Furthermore, to guarantee smooth switching of control input at switching boundaries, we also derive a smooth switching condition represented in terms of LMIs. A stable switching fuzzy controller satisfying the smooth switching condition is designed by simultaneously solving both of the LMIs. The simulation and experimental results for the trajectory control of an R/C hovercraft show the validity of the switching fuzzy model and controller design, particularly, the smooth switching condition.

This paper describes stable switching fuzzy control and its application to a hovercraft type vehicle (HTV). A switching fuzzy system is employed to represent the nonlinear dynamics of the HTV that is a typical nonholonomic system. A switching fuzzy controller is constructed by mirroring the structure of the switching fuzzy system. LMI stability conditions to design the switching fuzzy controller are presented. The design technique is applied to trajectory control of the HTV. The simulation results for the trajectory control show the validity of the switching fuzzy model and controller design.

Presents model reduction and robust control using a generalized form of Takagi-Sugeno fuzzy systems. We first define a generalized form of Takagi-Sugeno fuzzy systems. The generalized form has a decomposed structure for each element of A/sub i/ and B/sub i/ matrices in consequent parts. The key feature of this structure is that it is suitable for reducing the number of rules. Conditions to reduce the number of rules are represented in terms of LMIs. The main idea is to find a structure of if-then rules of the reduced model that agrees well with dynamics of the original model. Furthermore, we estimate the lower bound of the norm of model uncertainty of the Takagi-Sugeno fuzzy system that can cover the reduction error. Finally, an example of model reduction and robust control for a nonlinear system is illustrated. In this example, we achieve a robust controller design so as to compensate the uncertainly of the Takagi Sugeno fuzzy system.

We present two results concerning the fuzzy modeling and control of nonlinear systems. The first result is on the approximation of smooth nonlinear dynamical systems using linear Takagi-Sugeno (T-S) fuzzy models. The second result is on the approximation of smooth nonlinear state-feedback controllers using the so-called parallel distributed compensation (PDC) controller. Both results are based on the effectiveness of using linear Takagi-Sugeno systems to approximate nonlinear function, which is also proved in this paper.

This paper defines a fuzzy descriptor system by extending the ordinary Takagi-Sugeno (T-S) fuzzy model. Several kinds of stability conditions for the fuzzy descriptor system are derived and represented in terms of linear matrix inequalities (LMIs). We illustrate an example of defining the fuzzy descriptor system instead of the ordinary T-S fuzzy model. An LMI design approach is employed to find stable feedback gains and a common Lyapunov function. In addition, this paper presents a nonlinear model following control for the fuzzy descriptor system. A new parallel distributed compensation, the so-called "twin parallel distributed compensations" (TPDC) to realize the nonlinear model following control, is proposed. We present a design technique based on the TPDC. The proposed method is a unified approach to nonlinear model following control. It contains the regulation and servo control problems as special cases.

This paper presents new relaxed stability conditions and LMI- (linear matrix inequality) based designs for both continuous and discrete fuzzy control systems. They are applied to design problems of fuzzy regulators and fuzzy observers. First, Takagi and Sugeno's fuzzy models and some stability results are recalled. To design fuzzy regulators and fuzzy observers, nonlinear systems are represented by Takagi-Sugeno's (TS) fuzzy models. The concept of parallel distributed compensation is employed to design fuzzy regulators and fuzzy observers from the TS fuzzy models. New stability conditions are obtained by relaxing the stability conditions derived in previous papers, LMI-based design procedures for fuzzy regulators and fuzzy observers are constructed using the parallel distributed compensation and the relaxed stability conditions. Other LMI's with respect to decay rate and constraints on control input and output are also derived and utilized in the design procedures. Design examples for nonlinear systems demonstrate the utility of the relaxed stability conditions and the LMI-based design procedures.

The paper presents backing control of computer simulated mobile robots with multiple trailers by fuzzy modeling and control. We deal with two kinds of mobile robots: a mobile robot with five trailers and a mobile robot with ten trailers. To design fuzzy controllers, nonlinear models of the mobile robots with multiple trailers are represented by Takagi-Sugeno fuzzy models (TS fuzzy model). Before making TS fuzzy models, we simplify the nonlinear dynamics of the mobile robots. Under an assumption, TS fuzzy models are made from the simplified nonlinear models. The so-called parallel distributed compensation (PDC) is employed to design fuzzy controllers from the TS fuzzy models. Next, we derive a stability condition based on the Lyapunov approach. The stability condition of the designed fuzzy control system is cast in terms of linear matrix inequalities (LMI's) since it is reduced to a problem of finding a common Lyapunov function for a set of Lyapunov inequalities. Convex optimization techniques based on LMI's are utilized to solve the problem of finding stable feedback gains and a common Lyapunov function for the designed fuzzy control system. The simulation results show the effects of the fuzzy modeling, the controller design via the PDC, and the stability analysis based on LMIs.

This paper presents stability analysis for a class of uncertain nonlinear systems and a method for designing robust fuzzy controllers to stabilize the uncertain nonlinear systems, First, a stability condition for Takagi and Sugeno's fuzzy model is given in terms of Lyapunov stability theory. Next, new stability conditions for a generalized class of uncertain systems are derived from robust control techniques such as quadratic stabilization, H/sup /spl infin// control theory, and linear matrix inequalities. The derived stability conditions are used to analyze the stability of Takagi and Sugeno's fuzzy control systems with uncertainty which can be regarded as a generalized class of uncertain nonlinear systems, The design method employs the so-called parallel distributed compensation, important issues for the stability analysis and design are remarked. Finally, three design examples of fuzzy controllers for stabilizing nonlinear systems and uncertain nonlinear systems are presented.

Presents a design methodology for stabilization of a class of nonlinear systems. First, the authors represent a nonlinear plant with a Takagi-Sugeno fuzzy model. Then a model-based fuzzy controller design utilizing the concept of the so-called "parallel distributed compensation" is employed. The main idea of the controller design is to derive each control rule so as to compensate each rule of a fuzzy system. The design procedure is conceptually simple and natural. Moreover, the stability analysis and control design problems can be reduced to linear matrix inequality (LMI) problems. Therefore, they can be solved efficiently in practice by convex programming techniques for LMIs. The design methodology is illustrated by application to the problem of balancing and swing-up of an inverted pendulum on a cart.