Tracking Convergence Rate Research Articles

Adaptive Learning Based Tracking Control of Marine Vessels with Prescribed Performance

A novel adaptive tracking controller of fully actuated marine vessels is proposed with completely unknown dynamics and external disturbances. The model of dominant dynamic behaviors and unknown disturbances of the vessel are learned by a neural network in real time. The controller is designed and it unifies backstepping and adaptive neural network techniques with predefined tracking performance constraints on the tracking convergence rate and the transient and steady-state tracking error. The stability of the proposed adaptive tracking controller of the vessel is proven with a uniformly bounded tracking error. The proposed adaptive tracking controller is shown to be effective in the tracking control of marine vessels by simulations.

Neural Learning Control of Marine Surface Vessels With Guaranteed Transient Tracking Performance

This paper studies neural learning control with predefined tracking error bound for a marine surface vessel whose accurate dynamics could not be obtained a priori . With the introduction of an error transformation function, the constrained tracking control of the original vessel is transformed into the stabilization of an unconstrained system. A filtered tracking error is introduced based on the error transformation, and radial basis function (RBF) neural networks (NNs) are employed to approximate unknown vessel dynamics. Subsequently, stable adaptive NN control is proposed to ensure ultimate boundedness of all the signals in the closed-loop system and to guarantee prescribed tracking performances. Under persistent excitation (PE) condition, the proposed adaptive NN control is shown to be capable of acquiring knowledge on the vessel dynamics and of storing the learned knowledge in memory. The stored knowledge is reused to develop neural learning control such that the improved control performance with faster tracking convergence rate and less computational burden could be achieved, while prescribed transient and steady-state tracking control performances are guaranteed. Simulation studies are performed to demonstrate the effectiveness of the proposed design techniques.

Neural learning control of pure-feedback nonlinear systems

This paper is concerned with the problem of learning control for a class of pure-feedback systems with unknown non-affine terms in dynamical environments. The implicit function theorem and the mean value theorem are firstly used to transform the closed-loop system into a semi-affine form. By combining the quadratic-type Lyapunov function and the appropriate inequality technology, a concise adaptive neural control scheme is developed to simplify the system stability analysis and guarantee the convergence of the tracking error in a finite time. After the stable control design, we decompose the closed-loop system into a series of linear time-varying perturbed subsystems with the help of the linear state transformation. Using a recursive design, the partial persistent excitation (PE) condition for the radial basis function neural network is satisfied during tracking control to a recurrent reference trajectory. Under the PE condition, accurate approximations of the implicit desired control dynamics are recursively achieved in a local region along recurrent orbits of closed-loop signals. Subsequently, a neural learning control method which effectively utilizes the learned knowledge without re-adapting to the unknown system dynamics is proposed to achieve the closed-loop stability and improved control performance. Simulation studies are performed to demonstrate that the proposed learning control scheme not only can approximate accurately the implicit desired control dynamics, but also can reuse the learned knowledge to achieve the better control performance with the faster tracking convergence rate and the smaller tracking error.

Learning from adaptive neural dynamic surface control of strict-feedback systems.

Learning plays an essential role in autonomous control systems. However, how to achieve learning in the nonstationary environment for nonlinear systems is a challenging problem. In this paper, we present learning method for a class of n th-order strict-feedback systems by adaptive dynamic surface control (DSC) technology, which achieves the human-like ability of learning by doing and doing with learned knowledge. To achieve the learning, this paper first proposes stable adaptive DSC with auxiliary first-order filters, which ensures the boundedness of all the signals in the closed-loop system and the convergence of tracking errors in a finite time. With the help of DSC, the derivative of the filter output variable is used as the neural network (NN) input instead of traditional intermediate variables. As a result, the proposed adaptive DSC method reduces greatly the dimension of NN inputs, especially for high-order systems. After the stable DSC design, we decompose the stable closed-loop system into a series of linear time-varying perturbed subsystems. Using a recursive design, the recurrent property of NN input variables is easily verified since the complexity is overcome using DSC. Subsequently, the partial persistent excitation condition of the radial basis function NN is satisfied. By combining a state transformation, accurate approximations of the closed-loop system dynamics are recursively achieved in a local region along recurrent orbits. Then, the learning control method using the learned knowledge is proposed to achieve the closed-loop stability and the improved control performance. Simulation studies are performed to demonstrate the proposed scheme can not only reuse the learned knowledge to achieve the better control performance with the faster tracking convergence rate and the smaller tracking error but also greatly alleviate the computational burden because of reducing the number and complexity of NN input variables.

Dynamic learning from adaptive neural control with predefined performance for a class of nonlinear systems

In this paper, a neural learning mechanism is presented for a class of single-input–single-output (SISO) uncertain nonlinear systems, which can achieve knowledge acquisition, storage and reuse of the unknown system dynamics as well as the predefined tracking error behavior bound. Using the novel transformed function, the constrained tracking control problem of the original nonlinear system is transformed into the stabilization problem of an augmented system. By combining a filter tracking error with the universal approximation capabilities of radial basis function (RBF) neural networks (NNs), a stable adaptive neural control (ANC) scheme is proposed to guarantee the ultimate boundedness of all the signals in the closed-loop system and the prescribed transient and steady tracking control performance. In the steady control process, a partial persistent excitation (PE) condition of RBF NNs is satisfied during tracking control to recurrent reference orbits. Consequently, it is shown that the proposed ANC scheme can acquire and store knowledge of the unknown system dynamics. The stored knowledge is reused to develop neural learning control, so that the improved control performance with the faster tracking convergence rate and the less computational burden is achieved, while guaranteeing the prescribed transient and steady tracking performance when the initial condition satisfies the prescribed performance bound. Simulation studies are performed to demonstrate and verify the effectiveness of the proposed scheme.