Barrier Function-Based Adaptive Control for Uncertain Strict-Feedback Systems Within Predefined Neural Network Approximation Sets.

SummaryThis paper studies the problem of stabilizing reference trajectories (also called as the trajectory tracking problem) for underactuated marine vehicles under predefined tracking error constraints. The boundary functions of the predefined constraints are asymmetric and time‐varying. The time‐varying boundary functions allow us to quantify prescribed performance of tracking errors on both transient and steady‐state stages. To overcome difficulties raised by underactuation and nonzero off‐diagonal terms in the system matrices, we develop a novel transverse function control approach to introduce an additional control input in backstepping procedure. This approach provides practical stabilization of any smooth reference trajectory, whether this trajectory is feasible or not. By practical stabilization, we mean that the tracking errors of vehicle position and orientation converge to a small neighborhood of zero. With the introduction of an error transformation function, we construct an inverse‐hyperbolic‐tangent‐like barrier Lyapunov function to show practical stability of the closed‐loop systems with prescribed transient and steady‐state performances. To deal with unmodeled dynamic uncertainties and external disturbances, we employ neural network (NN) approximators to estimate uncertain dynamics and present disturbance observers to estimate unknown disturbances. Subsequently, we develop adaptive control, based on NN approximators and disturbance estimates, that guarantees the prescribed performance of tracking errors during the transient stage of on‐line NN weight adaptations and disturbance estimates. Simulation results show the performance of the proposed tracking control.

An improved adaptive neural dynamic surface control for pure-feedback systems with full state constraints and disturbance

In this paper, we deal with the problem of tracking control for a class of uncertain nonlinear systems in strict-feedback form subject to completely unknown system nonlinearities, hard constraints on full states, and unknown time-varying bounded disturbances. Integral barrier Lyapunov functionals are constructed to handle the unknown affine control gains ( $ {g(\cdot )}$ ) with state constraints simultaneously. This removes the need on the knowledge of control gains for control design and avoids the conservative step of transforming original state constraints into new bounds on tracking errors. Neural networks (NNs) are used to approximate the unknown continuous packaged functions. To enhance the robustness, adapting parameters are developed to compensate the unknown bounds on NNs approximations and external disturbances. Design parameters-dependent feasibility conditions are formulated as sufficient conditions for the existence of feasible design parameters to guarantee the state constraints, and an offline constrained optimization step is proposed to obtain the optimal design parameters prior to the implementation of the proposed control. It is proved that the proposed control can guarantee the semiglobal uniform ultimate boundedness of all signals in closed-loop system, all states are ensured to remain in the predefined constrained state space, and tracking error converges to an adjustable neighborhood of the origin by choosing appropriate design parameters. Simulations are performed to validate the proposed control.

An online adaptive optimal control is proposed for continuous-time nonlinear systems with completely unknown dynamics, which is achieved by developing a novel identifier-critic-based approximate dynamic programming algorithm with a dual neural network (NN) approximation structure. First, an adaptive NN identifier is designed to obviate the requirement of complete knowledge of system dynamics, and a critic NN is employed to approximate the optimal value function. Then, the optimal control law is computed based on the information from the identifier NN and the critic NN, so that the actor NN is not needed. In particular, a novel adaptive law design method with the parameter estimation error is proposed to online update the weights of both identifier NN and critic NN simultaneously, which converge to small neighbourhoods around their ideal values. The closed-loop system stability and the convergence to small vicinity around the optimal solution are all proved by means of the Lyapunov theory. The proposed adaptation algorithm is also improved to achieve finite-time convergence of the NN weights. Finally, simulation results are provided to exemplify the efficacy of the proposed methods.

Nonlinear mathematical-programming-based design optimization can be an elegant method. However, the calculations required to generate the merit function, constraints, and their gradients, which are frequently required, can make the process computational intensive. The computational burden can be greatly reduced by using approximating analyzers derived from an original analyzer utilizing neural networks and linear regression methods. The experience gained from using both of these approximation methods in the design optimization of a high speed civil transport aircraft is the subject of this paper. The Langley Research Center's Flight Optimization System was selected for the aircraft analysis. This software was exercised to generate a set of training data with which a neural network and a regression method were trained, thereby producing the two approximating analyzers. The derived analyzers were coupled to the Lewis Research Center's CometBoards test bed to provide the optimization capability. With the combined software, both approximation methods were examined for use in aircraft design optimization, and both performed satisfactorily. The CPU time for solution of the problem, which had been measured in hours, was reduced to minutes with the neural network approximation and to seconds with the regression method. Instability encountered in the aircraft analysis software at certain design points was also eliminated. On the other hand, there were costs and difficulties associated with training the approximating analyzers. The CPU time required to generate the input-output pairs and to train the approximating analyzers was seven times that required for solution of the problem.

This article presents a new command-filtered composite adaptive neural control scheme for uncertain nonlinear systems. Compared with existing works, this approach focuses on achieving finite-time convergent composite adaptive control for the higher-order nonlinear system with unknown nonlinearities, parameter uncertainties, and external disturbances. First, radial basis function neural networks (NNs) are utilized to approximate the unknown functions of the considered uncertain nonlinear system. By constructing the prediction errors from the serial-parallel nonsmooth estimation models, the prediction errors and the tracking errors are fused to update the weights of the NNs. Afterward, the composite adaptive neural backstepping control scheme is proposed via nonsmooth command filter and adaptive disturbance estimation techniques. The proposed control scheme ensures that high-precision tracking performances and NN approximation performances can be achieved simultaneously. Meanwhile, it can avoid the singularity problem in the finite-time backstepping framework. Moreover, it is proved that all signals in the closed-loop control system can be convergent in finite time. Finally, simulation results are given to illustrate the effectiveness of the proposed control scheme.

A novel single fuzzy approximation based adaptive control for a class of uncertain strict-feedback discrete-time nonlinear systems

Considering the unknown nonlinearities and external disturbances for a 2-DOF redundant parallel robot, a novel control method based on adaptive backstepping control and neural network approximation is proposed. In the controller, a RBF NN is used to approximate the uncertain function in order to make the adaptive backstepping control have a strong robustness for the unknown nonlinearities and external disturbances. The simulation results show that the control method has a good performance of tracking and a strong robustness, which can improve the control performance of a parallel robot with a strong coupling and high non-linearity. They also confirm the correctness and effectiveness of the proposed control strategy.

This paper discusses partial state constraint adaptive tracking control problem of switched nonlinear systems with uncertain parameters. In order to ensure boundedness of the outputs and prevent the states from violating the constraints, a barrier Lyapunov function (BLF) is employed. Based on backstepping method, an adaptive controller for the switched system is designed. Furthermore, the state‐constrained asymptotic tracking under arbitrary switching is performed. The closed‐loop signals keep bounded when the initial states and control parameters are given. Finally, examples and simulation results are reported to illustrate the effectiveness of the proposed controller.

An adaptive neural network control scheme is developed for a class of nonlinear systems in the strict-feedback form. Compared with the existing approaches, the main advantage is that the developed scheme can be implemented by utilizing only one neural network approximator. Thus, the designed controller structure is simplified. In addition, less neural network can reduce the running cost in practical application. The developed neural network control scheme can achieve that all the signals of the closed-loop system are uniformly bounded and the tracking errors converge to an arbitrary small neighborhood around zero by selecting suitably design parameters.

An approximation-based adaptive neural controller is constructed for uncertain stochastic nonlinear systems in nonstrict-feedback form appearing dead-zone and output constraint. Neural networks (NNs) are directly utilized to approximate the unknown nonlinear functions existing in systems. A barrier Lyapunov function is introduced to ensure that the trajectory of output is limited within a predetermined range. By integrating NNs into the backstepping technique, an adaptive neural controller is designed to guarantee all variables existing in the considered closed-loop system are semi-globally uniformly ultimately bounded, and by appropriately tuning several design parameters online, the tracking error can be converged to a small neighborhood of the origin. Simulations on a numerical example are given to demonstrate the effectiveness of the method proposed in this paper.

Event-triggered adaptive neural network controller for uncertain nonlinear system

Globally stable direct adaptive backstepping NN control for uncertain nonlinear strict-feedback systems

In this paper, a reinforcement learning-based adaptive control algorithm is proposed to solve the tracking problem of a discrete-time (DT) nonlinear state and input time delayed system of the wheeled mobile robot (WMR). With the typical model of the WMR transformed into an affine nonlinear DT system, a delay matrix function and appropriate Lyapunov-Krasovskii functionals are introduced to overcome the problems caused by the state and input time delays, respectively. Furthermore, with the approximation of the radial basis function neural networks (NNs), the adaptive controller, the critic NN, and action NN adaptive laws are defined to guarantee the uniform ultimate boundedness of all signals in the WMR system, and the tracking errors convergence to a small compact set to zero. Two examples of simulation are given to illustrate the effectiveness of the proposed algorithm.

This paper presents a stable neural network control, scheme for manipulators. Cerebellar model articulation (CMAC) or radial basis function (RBF) neural networks are used. The main contribution of this paper is the stability proof of neural network controllers for manipulators. This distinguishes the paper from other work. The results of this paper also have a closer relation to conventional adaptive control. This means that the neural network controller can either work alone if there is no a priori knowledge or work together with conventional adaptive control. Any a priori knowledge can also easily be used to train the neural networks off-line and, therefore, improve the online performance.