• Smart Structures and Systems
• /
• v.30 no.1
• /
• pp.1-15
• /
• 2022

This article focuses on stability analysis and fuzzy controller synthesis for large neural network (NN) systems consisting of several interconnected subsystems represented by the NN model. Advanced and fuzzy NN differential inclusion (NNDI) for stability based on the developed algorithm with H infinity can be designed based on the evolved biological design. This representation is constructed using sector linearity for NN models. Sector linearity transforms a non-linear model into a linear model based on proposed operations. New sufficient conditions are realized in the form of LMI (linear matrix inequalities) to ensure the asymptotic stability of the trans-Lyapunov function. This transforms the nonlinear model into a linear model based on multiple rules. At last, a numerical case study with simulations is derived as illustration to prove its feasibility in real nonlinear structures.

• Journal of the Korean Society for Precision Engineering
• /
• v.34 no.2
• /
• pp.125-131
• /
• 2017

2-Axis Pan and Tilt Motion Platform, a complex multivariate non-linear system, may incur any disturbance, thus requiring system controller with robustness against various disturbances. In this study, we designed an adaptive backstepping compensated controller by estimating the disturbance and error using the Radial Basis Function Neural Network (RBF NN). In this process, Uniformly Ultimately Bounded (UUB) was demonstrated via Lyapunov and stability was confirmed. By generating progressive disturbance to the irregular frequency and amplitude changes, it was verified for various environmental disturbances. In addition, by setting the RBF NN input vector to the minimum, the estimated disturbance compensation process was analyzed. Only two input vectors facilitated compensatory function of RBF NN via estimating the modeling and control error values as well as irregular disturbance; the application of the process resulted in improved backstepping controller performance that was confirmed through simulation.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.22 no.1
• /
• pp.28-35
• /
• 2012

This paper presents the method for $H_{\infty}$ fuzzy controller design of discrete-time fuzzy Markovian jump systems with state and input time delays. The Takagi and Sugeno fuzzy model is employed to represent a delayed nonlinear system that possesses Markovian jump parameters. A stochastic mode dependent Lyapunov function is employed to analyze the stability and $H_{\infty}$ disturbance attenuation performance of the fuzzy Markovian jump systems with state and input time delays. A sufficient condition for the existence of fuzzy $H_{\infty}$ controller is given in terms of matrix inequalities. Also numerical example is presented to illustrate the efficiency of the proposed design method.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.12 no.3
• /
• pp.239-245
• /
• 2002

In this Paper, we present a method for designing fuzzy $H_2/H_{\infty}$ controllers of delayed nonlinear systems with saturating input. Takagi-Sugeno fuzzy model is employed to represent delayed nonlinear systems with saturating input. The fuzzy control systems utilize the concept of the so-called parallel distributed compensation(PDC). Using a single quadratic Lyapunov function, the globally exponential stability and $H_2/H_{\infty}$ performance problem are discussed. And a sufficient condition for the existence of fuzzy $H_2/H_{\infty}$ controllers is given in terms of linear matrix inequalities(LMIs). The designing fuzzy $H_2/H_{\infty}$ controllers minimize an upper bound on a linear quadratic performance measure. Finally, a design example of fuzzy $H_2/H_{\infty}$ controller for uncertain delayed nonlinear systems with saturating input.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
• /
• v.5B no.1
• /
• pp.70-77
• /
• 2005

This paper presents sensorless speed control of a cylindrical permanent magnet synchronous motor (PMSM) using the adaptive integral binary observer. In view of the composition with a main loop regulator and an auxiliary loop regulator, the normal binary observer has the feature of chattering alleviation in the constant boundary layer. However, the steady state estimation accuracy and robustness are dependent upon the thickness of the constant boundary layer. In order to improve the steady state performance of the binary observer, a new binary observer is formed by the addition of extra integral dynamics to the existing switching hyperplane equation. Also, because the parameters of the dynamic equations such as machine inertia or viscosity friction coefficient are not well known and these values can be changed during normal operations, there are many restrictions in the actual implementation. The proposed adaptive integral binary observer applies an adaptive scheme so that the observer may overcome the problems caused by using dynamic equations. The rotor speed is constructed by using the Lyapunov function. The observer structure and its design method are described. The experimental results of the proposed algorithm are presented to prove the effectiveness of the approach.

• International Journal of Precision Engineering and Manufacturing
• /
• v.1 no.2
• /
• pp.24-34
• /
• 2000

In this paper we propose a controller design method, called Quasi-LQG/$H_{\infty}$/LTR for nonlinear servo systems with hard nonlinearities such as Coulomb friction, dead-zone. Introducing the RIDF method to model Coulomb friction and dead-zone, the statistically linearized system is built. Then, we consider $H_{\infty}$ performance constraint for the optimization of statistically linearized systems, by replacing a covariance Lyapunov equation into a modified Riccati equation of which solution leads to an upper bound of the LQG performance. As a result, the nonlinear correction term is included in coupled Riccati equation, which is generally very difficult to thave a numerical solution. To solve this problem, we use the modified loop shaping technique and show some analytic proofs on LTR condition. Finally, the Quasi-LQG/$H_{\infty}$/LTR controller for a nonlinear system is synthesized by inverse random input describing function techniques (ITIDF). It is shown that the proposed design method has a better performance robustness to the hard nonlinearity than LQG/$H_{\infty}$/LTR method via simulations and experiments for the timing-belt driving servo system that contains the Coulomb friction and dead-zone.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.15 no.2
• /
• pp.463-477
• /
• 1991

This study proposed a new method to design a robot manipulator control system capable of tracking the trajectories of joint angles in a reasonable accuracy to cover with actual situation of varying payload, uncertain parameters, and time delay. The direct adaptive model following control method has been used to improve existing industrial robot manipulator control system design. The proposed robot manipulator controller is operated by adjusting its gains based on the response of the manipulator in such a way that the manipulator closely matches the reference model trajectories predefined by the designer. The manipulator control system studied has two loops: they are an inner loop on adaptive model following controller to compensate nonlinearity in the manipulator dynamic equation and to decouple the coupling terms and an outer loop of state feedback controller with integral action to guarantee the stability of the adaptive scheme. This adaptation algorithm is based on the hyperstability approach with an improved Lyapunov function. The coupling among joints and the nonlinearity in the dynamic equation are explicitly considered. The designed manipulator controller shows good tracking performance in various cases, load variation, parameter uncertainties. and time delay. Since the proposed adaptive control method requires only a small number of parameters to be estimated, the controller has a relatively simple structure compared to the other adaptive manipulator controllers. Therefore, the method used is expected to be well suited for a high performance robot controller under practical operation environments.

• Journal of the Korea Institute of Information and Communication Engineering
• /
• v.25 no.1
• /
• pp.102-107
• /
• 2021

This paper discusses the containment control problem for multi-agent systems with input saturations. The goal of the containment control is to obtain swarming behavior by driving follower agents into the convex hull which is spanned by multiple leader agents. This paper considers multiple leader agents moving at the same constant speed. Then, to solve the containment problem for moving leaders, we propose a PI-based distributed control algorithm. We next analyze the convergence of follower agents to the desired positions. Specifically, we apply the integral-type Lyapunov function to take into account the saturation nonlinearity. Then, based on Lasalle's Invariance Principle, we show that the asymptotic convergence of error states to zero for any positive constant gains. Finally, numerical examples with the static and moving leaders are provided to validate the theoretical results.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.26 no.1
• /
• pp.50-55
• /
• 2016

This paper discusses a sampled-data controller design problem for nonlinear systems including singular perturbation. The concerned system is assumed to be modeled in Takagi--Sugeno (T--S) form. By introducing a novel Lyapunov function and an identity equation, the stability of the sampled-data closed-loop dynamics of the singularly perturbed T--S fuzzy system is analyzed. The design condition is represented in terms of linear matrix inequalities. A few discussions on the development are made that propose future research topics. Numerical simulation shows the effectiveness of the proposed method.

• Proceedings of the KIEE Conference
• /
• 1998.07b
• /
• pp.740-743
• /
• 1998

This paper presents an optimization algorithm for a stable Dynamic Neural Network (DNN) using genetic algorithm. Optimized DNN is applied to a problem of controlling nonlinear dynamical systems. DNN is dynamic mapping and is better suited for dynamical systems than static forward neural network. The real time implementation is very important, and thus the neuro controller also needs to be designed such that it converges with a relatively small number of training cycles. SDNN has considerably fewer weights than DNN. The object of proposed algorithm is to the number of self dynamic neuron node and the gradient of activation functions are simultaneously optimized by genetic algorithms. To guarantee convergence, an analytic method based on the Lyapunov function is used to find a stable learning for the SDNN. The ability and effectiveness of identifying and controlling, a nonlinear dynamic system using the proposed optimized SDNN considering stability' is demonstrated by case studies.