The SDRNN(2, 7, 1) is used in simulation, that is, the input layer has 2 neurons $u(k)$ and $y(k)$, 7 neurons in hidden layer, 1 neuron $y(k +1)$ in output layer. The activation function is sigmoid function in hidden layer: this function is the commonly used bipolar function $\rho(x)=\dfrac{1-e^{-x}}{1+e^{-x}}$, initial weight is random value between -1 and 1, the learning rate $\eta=0.45$, momentum factorγ = 0.1.
In this paper, a kind of second order diagonal recurrent neural network (SDRNN) identification method based on dynamic back propagation(DBP) algorithm with momentum term is proposed. This identification method overcomes the disadvantages such as slow convergent speed and trapping the local minimum. The SDRNN is similar as diagonal recurrent neural network(DRNN) in the structure, two tapped delays are used in the hidden neurons of DRNN, the simple structure of the DRNN is retained, the identification of a nonlinear system is realized with SDRNN. Serial-parallel identification architecture is applied in the modeling. Simulation results show that improved algorithm is effective with advantages the fast convergence, higher identification accuracy, higher adaptability and robustness in system identification. It is suitable for real-time identification of dynamic system.
In this paper, a data-driven model-free adaptive control (MFAC) approach is proposed based on a new dynamic linearization technique (DLT) with a novel concept called pseudo-partial derivative for a class of general multiple-input and multiple-output nonlinear discrete-time systems. The DLT includes compact form dynamic linearization, partial form dynamic linearization, and full form dynamic linearization. The main feature of the approach is that the controller design depends only on the measured input/output data of the controlled plant. Analysis and extensive simulations have shown that MFAC guarantees the bounded-input bounded-output stability and the tracking error convergence.
The present study of tension leg platform is the first commercial application of a revolutionary design of offshore production platform developed by well-known oil company. Intended for oil and gas production in water depths beyond the reach of traditional fixed structures, the tension leg platform was designed as a rectangular shaped floating platform which was connected to the ocean floor by 16 vertical steel tethers or legs, four per corner. The legs were kept in tension so that vertical movement was suppressed, while limited horizontal movement may occur.
The present study is concerned with the identification of the non-linear wave force effects known as 'ringing' on an offshore structure. Ringing is a highly non-linear behaviour in which the motion resonances are outside the region of dominating wave energy. The purpose of this paper is to provide a better prediction of the higher frequency responses of wave forces on the cylinder and to interpret the non-linear effects of 'ringing' using the NARMAX method and the higher order frequency response functions.
A large class of nonlinear phenomena can be described using bilinear systems. Such systems are very attractive since they usually require few parameters, to approximate most nonlinearities (compared to other systems). This paper addresses the problems of bilinear system identicalness using Bayesian inference. The Gibbs sampler is used to estimate the bilinear system parameters, from measurements of the system input and output signals
where $q_1$ and $q_2$ are the angular positions, and $u$ is a torque input. The physical parameters $g, I, J, k, L,$ and $M$ are all positive. Taking $y=q_1$ as the output, it can be verified that $y$ satisfies the fourth-order differential equation
We consider a single-input-single-output nonlinear system which can be represented globally by an input-output model. The system is input-output linearizable by feedback and is required to satisfy a minimum phase condition. The nonlinearities are not required to satisfy any global growth condition. The model depends linearly on unknown parameters which belong to a known compact convex set. We design a semiglobal adaptive output feedback controller which ensures that the output of the system tracks any given reference signal which is bounded and has bounded derivatives up to the nth order, where n is the order of the system. The reference signal and its derivatives are assumed to belong to a known compact set. It is also assumed to be sufficiently rich to satisfy a persistence of excitation condition. The design process is simple. First we assume that the output and its derivatives are available for feedback and design the adaptive controller as a state feedback controller in appropriate coordinates. Then we saturate the controller outside a domain of interest and use a high-gain observer to estimate the derivatives of the output. We prove, via asymptotic analysis, that when the speed of the high-gain observer is sufficiently high, the adaptive output feedback controller recovers the performance achieved under the state feedback one
