Transverse function control with prescribed performance guarantees for underactuated marine surface vehicles

The robotic airship is a unique and promising light-than-air platform, which has attracted worldwide developing interests for its broad applications. This article addresses the control problem of trajectory tracking for robotic airships. A neural network fuzzy sliding mode controller is proposed to steer a robotic airship along a referenced trajectory precisely. First, the dynamics model of a robotic airship is presented, and the problem of trajectory tracking is formulated. Second, a sliding mode controller is designed to track a time-varying trajectory. The neural network is employed to approximate the uncertain model of the airship, with the tracking error and its derivatives and the trajectory and its derivatives as neural network inputs and the approximation of the uncertain model as neural network output. And a fuzzy logic system is adopted to reduce the chattering results from the sliding mode controller. The control gains are tuned synchronously with the sliding surface according to fuzzy rules, with switching sliding surface as fuzzy logic inputs and control gains as fuzzy logic outputs. The stability and convergence of the closed-loop controller are proven using the Lyapunov stability theorem. Finally, the effectiveness and robustness of the proposed controller are demonstrated via simulation results. Contrasting simulation results indicate that the neural network fuzzy sliding mode controller reduces the chattering effectively and has better performance against the sliding mode controller.

PurposeBuilding cost is an important part of construction projects, and its correct estimation has important guiding significance for the follow-up decision-making of construction units.Design/methodology/approachThis study focused on the application of back-propagation (BP) neural network in the estimation of building cost. First, the influencing factors of building cost were analyzed. Six factors were selected as input of the estimation model. Then, a BP neural network estimation model was established and trained by ten samples.FindingsAccording to the experimental results, it was found that the estimation model converged at about 85 times; compared with radial basis function (RBF), the estimation accuracy of the model was higher, and the average error was 5.54 per cent, showing a good reliability in cost estimation.Originality/valueThe results of this study provide a reliable basis for investment decision-making in the construction industry and also contribute to the further application of BP neural network in cost estimation.

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.

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.

A reactor integrated with separation process has been widely proposed and studied to enhance the production of high value added chemicals. An example of such a process is a pervaporative membrane reactor which is the combination of a reactor and a pervaporation part. The inclusive of a pervaporation can shift the chemical equilibrium of esterification by passing water out of reaction mixture and therefore increase the yield of a desired product. In addition, the temperature of the reactor is one of key factors to define the rate of reactions involved. In this work, a neural network inverse models based control (NIMC) has been designed to control an optimal temperature of a pervaporation membrane reactor. Furthermore, a neural network estimator (NNE) has been incorporated to the strategy as an estimator to estimate the amount of heat released of an esterification reaction. The performance of the designed controller has been evaluated in both nominal and plant/model mismatch cases, and compared with GMC coupled with the Kalman Filter. Simulation study has shown that the NIMC with the NNE can successfully control the reactor temperature at a desired set point in nominal cases and plant/model mismatches. The performance of the NIMC with the NNE is equivalent to that of the GMC coupled with the Kalman Filter. As a result, the NIMC with the NNE is applicable to control the pervaporative membrane reactor without first principle models of the reactor is available. This shows the advantage of the NIMC with NNE over the GMC with the Kalman filter.

In theory, recent results in nonparametric regression show that neural network estimates are able to achieve good rates of convergence provided suitable assumptions on the structure of the regression function are imposed. However, these theoretical analyses cannot explain the practical success of neural networks since the theoretically studied estimates are defined by minimizing the empirical L_2 risk over a class of neural networks and in practice, solving this kind of minimization problem is not feasible. Consequently, the neural networks examined in theory cannot be implemented as they are defined. This means that neural network in applications differ from the ones that are analyzed theoretically. In this thesis we narrow the gap between theory and practice. We deal with neural network regression estimates for (p,C)-smooth regression functions m that satisfy a projection pursuit model. We construct three implementable neural network estimates and show that each of them achieve up to a logarithmic factor the optimal univariate rate of convergence. Firstly, for univariate regression functions with p contained in [-1/2,1] we construct a neural network estimate with one hidden layer where the weights are learned via gradient descent. The starting weights are randomly chosen from an interval independently of the data. The interval is large enough to guarantee that the estimate is close to a piecewise constant approximation. Secondly, for multivariate regression functions with p contained in (0,1] we construct a neural network estimate with one hidden layer where the weights are learned via gradient descent. The initial weights are chosen from specific intervals dependently on the data and the projection directions. This choice guarantees that the estimate is close to a piecewise constant approximation. The projection directions are repeatedly chosen randomly. Lastly, for multivariate regression functions with p>0 we construct a multilayer neural network estimate. The value of the inner weights are prescribed dependently on the projection directions by a new approximation result for a projection pursuit model by piecewise polynomials. The outer weights are chosen by solving a linear equation system. The projection directions are repeatedly chosen randomly. Since we are able to show a rate of convergence that is independent of the dimension of the data our second and third estimates are able to circumvent the curse of dimensionality.

Asymptotic tracking control scheme for mechanical systems with external disturbances and friction

Modelling of a bioprocess was developed by combining three neural network estimators (NNEs). The bioprocess was for fed-batch culture of L-lysine production. The NNEs were NNE1, NNE2, and NNE3. NNE1 was applied to estimate the consumed sugar concentration, L-lysine concentration, and cell optical density. NNE2 was utilized to determine the off-gas concentration of O2 and CO2 while NNE3 was employed to predict the agitation speed. These NNEs possessed their own distinct functions and could be used independently. Combination of the NNEs based on neural network gave an easy and significant way for modelling a bioprocess.

This article investigates the problem of attitude tracking control for spacecraft with limited communication, unknown system parameters, and external disturbances. An adaptive control scheme with an event-triggered mechanism (ETM) is proposed to alleviate the communication burden. Radial Basis Function Neural Network (RBFNN) estimation model is developed to provide the input signals for the control module in this control scheme. Estimated attitude information of the spacecraft generated from the estimation model will only be transmitted to the control module at the instants when the ETM is violated. The neural network (NN) and the estimation model will be updated complying with an adaptive algorithm at the discrete triggering instants. It’s substantiated that all the errors of attitude tracking converge towards corresponding residuals and there are no accumulated triggering instants. Numerical simulation also demonstrates the effectiveness of the proposed control method.

This paper investigates the trajectory tracking control problem of an underactuated marine surface vehicle (MSV) with stochastic disturbances, where the tracking errors are required to preserve within the predefined constraint bounds. Since the vehicle system is exposed to the environmental stochastic disturbances, the difficulty arisen from Hessian terms induced by stochastic differentiation rule is overcome by introducing a quartic Lyapunov function. To tackle the difficulties caused by underactuation and nonzero off-diagonal terms in the system matrix, we develop a transverse function control approach to introduce an additional control input in backstepping procedure. A tan-type barrier Lyapunov function is introduced to guarantee the satisfaction of the prescribed tracking error constraints. Based on backstepping procedure, barrier Lyapunov function, transverse function control approach, and Lyapunov synthesis, feedback control laws are proposed to ensure that the tracking errors converge exponentially to a small neighborhood of zero, and the constraint requirements on the tracking errors are not violated in the course of operation in probability despite the presence of stochastic disturbances. Simulation results illustrate the performance of the proposed tracking control.

In this paper, an adaptive sliding mode control algorithm based on friction compensation utilizing neural network (NN) is designed for an opto-electronic tracking system under the circumstance of friction and external disturbance. Since neural networks can approximate any nonlinear function, the developed NN controller can approximate the nonlinear friction which is integrated into the adaptive sliding mode control system in the Lyapunov framework. The adaptive sliding mode controller with friction compensation can effectively reduce the effects of nonlinear friction and external disturbance of the opto-electronic tracking system utilizing neural network approximations. The stability of the proposed method is guaranteed according to Lyapunov criterion. Simulation and experimental validation results for a nonlinear LuGre dynamic model of the opto-electronic tracking system are provided to validate the effectiveness of the proposed control method.

A PID-type controller incorporating neural network elimination scheme and sliding-mode control action for different objectives including H/sub 2/ tracking performance, H/sub /spl infin// tracking performance, and regional pole constraints is developed in robotic systems under plant uncertainties and external disturbances. The adaptive neural networks are used to compensate the plant uncertainties. The sliding-mode control action is included to eliminate the effect of approximation error via neural network approximation. The sufficient conditions are developed for different objectives in terms of linear matrix inequality (LMI) formulations. The interesting combinations of different objectives are considered in this paper, which include H/sub /spl infin// PID tracking control design with regional pole constraints and mixed H/sub 2//H/sub /spl infin// PID tracking control design with regional pole constraints. These multiobjective PID control problems are characterized in terms of eigenvalue problem (EVP). The EVP can be efficiently solved by the LMI toolbox in Matlab. The proposed methods are simple and the PID control gain for different objectives can be obtained systematically.

This paper presents an indirect adaptive neural network control for a class of uncertain non-affine nonlinear switched systems with an unknown control direction. In this method, the unknown non-affine function is firstly converted into an affine-like form using the mean value theorem. Then, an RBF neural network is utilized to approximate the unknown functions. In addition, Nussbaum-gain technique is employed to deal with the issue of not having a priori knowledge about the gain sign. Furthermore, by adding a robustifying term to the control signal, the proposed approach can handle the approximation error in neural network approximation and external disturbance so that the system robustness can be improved. The proposed controller is designed based on Lyapunov stability theory to ensure the asymptotic stability of the closed-loop system. Finally two numerical simulations are given to show the effectiveness of the proposed scheme.

Neural network approximation-based backstepping sliding mode control for spacecraft with input saturation and dynamics uncertainty

Adaptive sliding mode control of maglev system based on RBF neural network minimum parameter learning method