Analysis on existence of compact set in neural network control for nonlinear systems

Event-triggered controller design of nonlinear discrete-time networked control systems in T-S fuzzy model

The work deals finite frequency H<sub>∞</sub> control design for continuous time nonlinear systems, we provide sufficient conditions, ensuring that the closed-loop model is stable. Simulations will be gifted to show level of attenuation that a H<sub>∞</sub> lower can be by our method obtained developed where further comparison.

It has been a common consensus that general techniques for stabilization of nonlinear systems are available only for some special classes of nonlinear systems. Control design for nonlinear systems with uncertain components is usually carried out on a per system basis, especially when physical control constraints, and certain control performance measures such as optimum time control are imposed. Elegant adaptive control techniques are difficult to apply to this type of problems. A new neural network based control design is proposed and presented in this paper to deal with a special class of uncertain nonlinear systems with multiple inputs. The desired system dynamics are analyzed and utilized in the process of the proposed intelligent control design. The theoretical results are provided to justify the design procedures. The simulation study is conducted on a second-order bilinear system with two inputs and uncertainties on its parameters. The simulation results indicate that the proposed design approach is effective.

In this note, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for such that iterative backstepping design can be carried out. In addition, controller singularity problems are solved by using the integral Lyapunov function and employing practical robust neural network control. The feasibility of neural network approximation of unknown system functions is guaranteed over practical compact sets. It is proved that the proposed systematic backstepping design method is able to guarantee semiglobally uniformly ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin.

Dynamic neural network control for non-linear systems: optimal neural network structure and stability analysis

This paper studies the problem of adaptive eventtriggered dynamic output feedback fuzzy control for nonlinear networked control systems. Two crucial factors, packet dropouts and actuator failure, are taken into consideration simultaneously. Takagi-Sugeno fuzzy model is introduced to describe considered systems. The Bernoulli random distribution process is employed to depict the phenomenon of data missing. The actuator failure model is adopted to depict actuator failure. An innovative adaptive event-triggered strategy is built to save computational resource. In the light of Lyapunov stability theory, a fuzzy dynamic output feedback controller is designed to guarantee the stochastic stability and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance for considered systems. Finally, simulation results are provided to demonstrate the usefulness of the proposed control strategy.

This paper studies the linear feedback control strategies for nonlinear systems. Asymptotic stability of the closed-loop nonlinear system is guaranteed by means of a Lyapunov function, which can clearly be seen to be the solution of the Hamilton-Jacobi-Bellman equation thus guaranteeing both stability and optimality. The formulated Theorem expresses explicitly the form of minimized functional and gives the sufficient conditions that allow using the linear feedback control for nonlinear system. The numerical simulations the Duffing oscillator and the nonlinear automotive active suspension system are provided to show the effectiveness of this method.

This study presents a generalized procedure for designing recurrent neural network enhanced control of time delay nonlinear dynamic systems with non-affine triangle structure and pure-feedback prototype. Under the framework, recurrent neural network is developed to accommodate the on-line approximation, which the weights of the neural network are iteratively and adaptively updated through system state vector. Based on the neural network online approximation model, an indirect adaptive neural network controller is designed by means of dynamic compensation. Indirect control procedure and virtual control law are chosen to deal with the problems encountered in the design of such complex nonlinear control systems. Taking consideration of the correctness, rigorousness, and generality of the new development, Lyapunov stability theory is referred to prove the closed-loop control system uniformly ultimately bounded stable and the output of the system is converged to a small neighborhood of the desired trajectory. A bench mark test is simulated to demonstrate the effectiveness and efficiency of the procedure and furthermore it could be a show case for potential readers/users to digest and/or apply the procedure to their ad hoc problems.

In this paper, a new method is proposed to design a sliding mode controller with variable boundary layer for a nonlinear system. In this method, model predictive control (MPC) is used to predict the future boundary layer thickness. In order to predict the behavior of the nonlinear system, a neural network model is used as an internal model. The simulation results show the supremacy of this method in comparison with the conventional method.

ABSTRACTThis paper focuses on the design of H∞ filter and event-triggered scheme for a class of continuous non-linear networked control systems (NCSs) based on fuzzy system appeared with time delays. First, we consider the discrete event-triggered (ET) scheme to make efficient utilisation of bandwidth. Under this ET-scheme, sensor releases the data only when our sampled-data plant violates the specific event-triggered condition. Second, the T-S fuzzy system is used to model the non-linear NCSs. Another purpose of this paper is to design filters involving delays. Such filters have a more general form than the delay-free filters that have been mostly considered in the traditional studies. By using the time-delay system, co-design of event-triggered scheme and H∞ filter for the delayed NCSs is presented in a unified frame work. To choose the latest data packet and discard the dis-ordered packet logic, zero-order hold is inserted between the fuzzy filter and event generator. Then, by using the novel fuzzy Lyapunov–Krasovskii function approach with free-weighting matrix technique, H∞ filter design of event-triggered delay NCSs is proposed. Finally, to show the effective result of our co-design method, a tunnel-diode example is given.

This paper proposes a wavelet-based cerebellar model arithmetic controller neural network (CMAC NN) and develops a hybrid control scheme, combining supervisory controller, filter, and CMAC, for nonlinear systems. The Gaussian functions of traditional CMAC are replaced by wavelet functions. In addition, properties and advantages of fuzzy TSK- model are used to modify the activation functions of CMAC for obtaining high approximation accuracy and convergent rate. A PD type wavelet-based CMAC controller with pre-filter is constructed for nonlinear affine systems. The corresponding supervisory controller is used to compensate the wavelet-based CMAC controller for better performance. Several simulation results are shown to demonstrate the effectiveness of our approach.

To help along the analysis and design of nonlinear control systems the NONLINCON package, an acronym for nonlinear control, was developed. This note addresses the usefulness of symbolic computation, and of the NONLINCON package in particular, for the symbolic analysis and design of nonlinear control systems. The symbolic computation program MAPLE is used as computing substratum. Textbook problems show that the NONLINCON package can be used successfully. A larger scale problem is too complex, however, to be solved with the current versions of NONLINCON and MAPLE. The conclusion is that symbolic computation is a viable approach for textbook problems, but not yet for more complex ones. >

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Fuzzy control design of nonlinear systems under unreliable communication links: A systematic homogenous polynomial approach

This paper proposes an adaptive sliding mode fault tolerant control design for lipschitz nonlinear system subject to simultaneous actuator and sensor faults. First, in order to estimate the system states, actuator and sensor faults, only one observer with an adaptive nonlinear gain is required where the minimum phase condition is relaxed to delectability and the matching condition is weakened to become a condition related to the system dimensions. Furthermore, our approach is applicable where there are faults greater than outputs. Next, a virtual sensor technique is developed to replace a failed, missing or corrupted sensor to provide a signal having the same effect of the nominal sensor. Then, this study provides an adaptive sliding mode fault tolerant control to achieve an optimal interaction between observer, virtual sensor and controller models. Thus, using the LMI technique with multiobjective optimization performance, sufficient conditions are derived to ensure the closed-loop Lipschitz nonlinear system stability and guarantee that the Lipschitz set of the adaptive sliding mode observer is a subset of the adaptive sliding mode control Lipschitz set. Two illustrative examples the first is the robotic manipulator model and the second is the longitudinal dynamics of the following vehicle system were performed to verify the effectiveness of the proposed approach.