• Transactions on Control, Automation and Systems Engineering
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• v.4 no.2
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• pp.124-129
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• 2002

This paper demonstrates that the largest Lyapunov exponent λ of recurrent neural networks can be controlled efficiently by a stochastic gradient method. An essential core of the proposed method is a novel stochastic approximate formulation of the Lyapunov exponent λ as a function of the network parameters such as connection weights and thresholds of neural activation functions. By a gradient method, a direct calculation to minimize a square error (λ - λ$\^$obj/)$^2$, where λ$\^$obj/ is a desired exponent value, needs gradients collection through time which are given by a recursive calculation from past to present values. The collection is computationally expensive and causes unstable control of the exponent for networks with chaotic dynamics because of chaotic instability. The stochastic formulation derived in this paper gives us an approximation of the gradients collection in a fashion without the recursive calculation. This approximation can realize not only a faster calculation of the gradient, but also stable control for chaotic dynamics. Due to the non-recursive calculation. without respect to the time evolutions, the running times of this approximation grow only about as N$^2$ compared to as N$\^$5/T that is of the direct calculation method. It is also shown by simulation studies that the approximation is a robust formulation for the network size and that proposed method can control the chaos dynamics in recurrent neural networks efficiently.

• 제어로봇시스템학회:학술대회논문집
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• 1988.10a
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• pp.160-163
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• 1988

In this paper, the adaptive controller for the turret gun is discussed which uses model reference adaptive technique based on the Lyapunov direct method. Turret gun can be decomposed into two time-invariant SISO control systems. One is for the elevation angle control and the other is for the azimuth angle control under the assumption of independence each other. Thus we only consider here about the control loop for the elevation angle.

• Journal of Electrical Engineering and Technology
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• v.8 no.6
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• pp.1530-1541
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• 2013

The coexistence and extinction of species are important concepts for biological systems and can be distinguished by an investigation of stability. When determining local stability of nonlinear systems, Lyapunov indirect method based on the Jacobian linearization has been widely employed due to its simplicity. Despite such popularity, it is not applicable to singular systems whose Jacobian has at least one eigenvalue that is equal to zero. In such singular cases, an appropriate Lyapunov function should be sought to determine the stability of systems, which is rather difficult and quite involved. In this paper, we seek for a simple criterion to determine stability of the equilibrium that is located at the boundary of the positive orthant, when one of eigenvalues of the Jacobian is zero. The goal of the paper is to present a generalized condition for the equilibrium to attract all trajectories that starting from initial condition in the positive orthant and near the equilibrium. Unlike the Lyapunov direct method, the proposed method requires just a simple algebraic computation for checking the stability of the critical point. Our approach is applied to various biological systems to show the effectiveness of the proposed method.

• International Journal of Control, Automation, and Systems
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• v.3 no.4
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• pp.552-563
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• 2005

In this paper, we propose a wavelet based fuzzy neural network (WFNN) based direct adaptive control scheme for the solution of the tracking problem of mobile robots. To design a controller, we present a WFNN structure that merges the advantages of the neural network, fuzzy model and wavelet transform. The basic idea of our WFNN structure is to realize the process of fuzzy reasoning of the wavelet fuzzy system by the structure of a neural network and to make the parameters of fuzzy reasoning be expressed by the connection weights of a neural network. In our control system, the control signals are directly obtained to minimize the difference between the reference track and the pose of a mobile robot via the gradient descent (GD) method. In addition, an approach that uses adaptive learning rates for training of the WFNN controller is driven via a Lyapunov stability analysis to guarantee fast convergence, that is, learning rates are adaptively determined to rapidly minimize the state errors of a mobile robot. Finally, to evaluate the performance of the proposed direct adaptive control system using the WFNN controller, we compare the control results of the WFNN controller with those of the FNN, the WNN and the WFM controllers.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.38 no.4
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• pp.335-341
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• 2010

To improve the performance of inner loop based on PD controller for a unmanned helicopter, neural networks are applied. The performance of PD controller designed on the response characteristics of error dynamics decreases because of uncertain nonlinearities of the system. The nonlinearities are decoupled to modified dynamic inversion model(MDIM) and are compensated by the neural networks. For the training of the neural networks, online weight adaptation laws which are derived from Lyapunov's direct method are used to guarantee the stability of the controller. The results of the improved performance of PD controller by neural networks are illustrated in the simulation of unmanned helicopter with nonlinearities,

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.11
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• pp.990-998
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• 2007

Adaptive output feedback control technique using Neural Networks(NN) is proposed for uncertain nonlinear Multi-Input Multi-Output(MIMO) systems. Modified Dynamic Inversion Model(MDIM) is introduced to decouple uncertain nonlinearities from inversion-based control input. MDIM consists of approximated dynamic inversion model and inversion model error. One NN is applied to compensate the MDIM of the system. The output of the NN augments the tracking controller which is based upon a filtered error approximation with online weight adaptation laws which are derived from Lyapunov's direct method to guarantee tracking performance and ultimate boundedness. Several numerical results are illustrated in the simulation of Van der Pol system and unmanned helicopter with model uncertainties.

• Journal of Institute of Control, Robotics and Systems
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• v.3 no.1
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• pp.17-22
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• 1997

The stability robustness problem of linear discrete-time systems with time-varying perturbations is considered. By using Lyapunov direct method, the perturbation bounds for guaranteeing the quadratic stability of the uncertain systems are derived. In the previous results, the perturbation bounds are derived by the quadratic equation stemmed from Lyapunov method. In this paper, the bounds are obtained by a numerical optimization technique. Linear matrix inequalities are proposed to compute the perturbation bounds. It is demonstrated that the suggested bound is less conservative for the uncertain systems with unstructured perturbations and seems to be maximal in many examples. Furthermore, the suggested bound is shown to be maximal for the special classes of structured perturbations.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.37 no.10
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• pp.733-739
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• 1988

Adaptive controllers for linear system whose nominal values of coefficients only are known, that is corrupted by disturbance, are designed by signal synthesis model reference adaptive control (MRAC). This design is stemmed from the Lyapunov direct method. To reduce the model following error and to improve the conrergence rate of the design, an indirect suboptimal control law is de rived using the Hamilton Jacobi Beellman equation. Proper compensaton for the effects of time varying coefficients and plant disturbance are suggested. In the design procedure no complete identification of unknown coefficients are required.

• Journal of Institute of Control, Robotics and Systems
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• v.9 no.2
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• pp.99-106
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• 2003

A new reconfigurable model following flight control method based on direct adaptive scheme is presented. Using the timescale separation principle, both the inner-loop and the outer-loop states are controlled simultaneously. For the timescale separation assumption to be satisfied, the inner-loop model dynamics is set to be fast whereas the outer-loop model dynamics is set to be relatively slow. The stability and convergence of the proposed control law is proved by Lyapunov theorem. One of the merits of the proposed reconfigurable controller is that the FDI process and the persistent input excitation are not necessary, which is suitable for the flight control system. To evaluate the reconfiguration performance of the proposed control method, numerical simulation is performed using six degree-of-freedom nonlinear dynamics.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.37 no.12
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• pp.884-893
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• 1988

Adaptive controllers for linear unknown coefficient system, that is corrupted by disturbance, are designed by parameter adaptation model reference adaptive control(MRAC). This design is stemmed from the Lyapunov direct method. To reduce the model following error and to improve the convergence rate of the design, an indirect-suboptimal control law is derived. Proper compensation for the effects of time-varying coefficients and plant disturbance are suggested. In the design procedure no complete identification of unknown coefficients are required.