RBF neural networks-based robust adaptive tracking control for switched uncertain nonlinear systems

In this paper, a robust adaptive H∞ control scheme is presented for a class of switched uncertain nonlinear systems. Radical basis function neural networks (RBF NNs) are employed to approximate unknown nonlinear functions and uncertain terms. A robust H∞ controller is designed to enhance robustness due to the existence of the compound disturbance which consists of approximation errors of the neural networks and external disturbance. Adaptive neural updated laws and switching signals are deducted from multiple Lyapunov function approach. It is proved that with the proposed control scheme, the resulting closed-loop switched system is robustly stable and uniformly ultimately bounded (UUB) such that good capabilities of tracking performance is attained and H∞ tracking error performance index is achieved. A practical example shows the effectiveness of the proposed control scheme.     

Robustifying nonlinear systems using high-order neural networkcontrollers

A robust control methodology for affine control of nonlinear dynamical systems is developed in this paper. A correction control signal is added to a nominal controller (designed to guarantee a desired performance for the corresponding nominal system), to render the actual system uniformly and ultimately bounded. The control signal is smooth and does not require a priori knowledge of an upper bound on the modeling error and/or optimal weight values. Simulations performed on a simple nonlinear system illustrate the approach     

Numerical solution of static and dynamic nonlinear multi-degree-of-freedom systems

The performance of a dynamic algorithm is demonstrated on a series of nonlinear multi-degree-of-freedom systems. Nonlinear dynamics, large deflections and postbuckling behaviour are dealt with. In highly nonlinear problems of a prevailing static nature it is shown that, due to its clear physical interpretation, the dynamic approach allows easier guessing of initial conditions assuring convergence.     

Output regulation of nonaffine nonlinear systems using singular perturbation theory

A control synthesis method for output regulation based on singular perturbation theory combined with inverting design is considered for a class of nonaffine nonlinear systems. The resulting control signal is defined as a solution to ＂fast＂ dynamics which inverts a series error model, whose state is exponentially stable. It is shown that, under sufficient conditions being consistent with the assumptions of singular perturbation theory, this problem is solvable with （ε） tracking error if and only if a set of first-order nonlinear partial differential equations are solvable. The control law can be easily constructed and the simulations show the feasibility and effectiveness of the controller.     

Stabilization of unknown nonlinear systems using neural networks

This paper deals with stabilization of unknown nonlinear systems using a nonlinear controller made with a backpropagation neural network. Control strategies based on an inverse state neural model built from an off-line learning step are proposed. The proposed strategies can be implemented following two approaches. The first one consists on computing control horizon based on actual state vector and desired one at a future instant. The second approach applies control action in the sense of a receding horizon. Adaptive control has been considered where the updating of the neural controller is accomplished to optimize different control objectives.     

Stable control of nonlinear systems using neural networks

A neural-network-based direct control architecture is presented that achieves output tracking for a class of continuous-time nonlinear plants, for which the nonlinearities are unknown. The controller employs neural networks to perform approximate input/output plant linearization. The network parameters are adapted according to a stability principle. The architecture is based on a modification of a method previously proposed by the authors, where the modification comprises adding a sliding control term to the controller. This modification serves two purposes: first, as suggested by Sanner and Slotine,¹ sliding control compensates for plant uncertainties outside the state region where the networks are used, thus providing global stability; second, the sliding control compensates for inherent network approximation errors, hence improving tracking performance. A complete stability and tracking error convergence proof is given and the setting of the controller parameters is discussed. It is demonstrated that as a result of using sliding control, better use of the network's approximation ability can be achieved, and the asymptotic tracking error can be made dependent only on inherent network approximation errors and the frequency range of unmodelled dynamical modes. Two simulations are provided to demonstrate the features of the control method.     

Cognitive computing for intelligent multimedia systems

Multimedia Tools and Applications -     

Numerical solution of singular perturbation problems

A finite difference method for Second Order Singular Perturbation Problems is presented. It is based on a mesh selection strategy derived by using sufficient conditions which ensure the well conditioning of tridiagonal matrices. In particular the implementation aspects of the method are discussed. Numerical tests are reported to evidence the effectiveness of this method and its competitiveness with respect to known solvers for BVPs. Work performed within the activities of the project ‘Matematica Computazionale’ supported by MURST 40%.     

Event-triggered neural intelligent control for uncertain nonlinear systems with specified-time guaranteed behaviors

Neural Computing and Applications - In this paper, an event-triggered neural intelligent control for uncertain nonlinear systems with specified-time guaranteed behaviors is proposed. To cope with...     

Disturbance rejection in nonlinear systems using neural networks

Neural networks with different architectures have been successfully used for the identification and control of a wide class of nonlinear systems. The problem of rejection of input disturbances, when such networks are used in practical problems is considered. A large class of disturbances, which can be modeled as the outputs of unforced linear or nonlinear dynamic systems, is treated. The objective is to determine the identification model and the control law to minimize the effect of the disturbance at the output. In all cases, the method used involves expansion of the state space of the disturbance-free plant in an attempt to eliminate the effect of the disturbance. Several stages of increasing complexity of the problem are discussed in detail. Theoretical justification is provided for the existence of solutions to the problem of complete rejection of the disturbance in special cases. This provides the rationale for using similar techniques in situations where such theoretical analysis is not available.     

Numerical solution of nonlinear differential equations using computer algebra

This paper describes a numerical method for finding periodic solutions to nonlinear ordinary differential equations. The solution is approximated by a trigonometric series. The series is substituted into the differential equation using the FORMAC computer algebra system for the resulting lengthy algebraic manipulations. This lead to a set of nonlinear algebraic equations for the series coefficients. Modern search methods are used to solve for the coefficients. The method is illustrated by application to Duffing’ equation.     

Identification of nonlinear dynamical systems using multilayered neural networks

A novel multilayer discrete-time neural net paradigm is presented for the identification of multi-input multi-output (MIMO) nonlinear dynamical systems. The major novelty of this approach is a rigorous proof of identification error convergence that reveals a requirement for a new identifier structure and nonstandard weight tuning algorithms. The NN identifier includes modified delta rule weight tuning and exhibits a learning-while-functioning feature instead of learning-then-functioning, so that the identification is on-line with no explicit off-line learning phase needed. The structure of the neural net (NN) identifier is derived using a passivity aproach. Linearity in the parameters is not required and certainty equivalence is not used. The notion of persistency of excitation (PE) and passivity properties of the multilayer NN are defined and used in the convergence analysis of both the identification error and the weight estimates.     

Observer‐based adaptive neural control for a class of nonlinear singular systems

The problem of observer‐based adaptive neural control via output feedback for a class of uncertain nonlinear singular systems is studied in this article. The nonlinear singular systems can be regarded as two subsystems that are coupled with each other: differential subsystem and algebraic subsystem. The differential systems can be nonstrict feedback structures. To guarantee that the singular system is regular and impulse‐free, two new conditions are proposed. By the conditions, the linear controller and observer, which are used to estimate the immeasurable state variables, are obtained. Then, an output feedback scheme through adaptive neural backstepping is proposed to ensure that all states of the closed‐loop system are semiglobally uniformly ultimately bounded and converge to a small neighborhood of the origin. Simulation examples illustrate the effectiveness of the presented method.     

Numerical solution of singular boundary value problems using advanced Adomian decomposition method

Engineering with Computers - In this work, we present a powerful method for the numerical solution of non-linear singular boundary value problems, namely the advanced Adomian decomposition method...     

State observer design for nonlinear systems using neural network

In this paper, an observer design is proposed for nonlinear systems. The Hamilton–Jacobi–Bellman (HJB) equation based formulation has been developed. The HJB equation is formulated using a suitable non-quadratic term in the performance functional to tackle magnitude constraints on the observer gain. Utilizing Lyapunov's direct method, observer is proved to be optimal with respect to meaningful cost. In the present algorithm, neural network (NN) is used to approximate value function to find approximate solution of HJB equation using least squares method. With time-varying HJB solution, we proposed a dynamic optimal observer for the nonlinear system. Proposed algorithm has been applied on nonlinear systems with finite-time-horizon and infinite-time-horizon. Necessary theoretical and simulation results are presented to validate proposed algorithm.     

仿射非线性奇异系统的受控分布

研究非线性奇异系统的受控不变分布问题.讨论了非线性奇异系统的受控不变分布算法与该系统经过状态反馈转化为正常非线性系统的受控不变分布算法的关系.得到了在一定条件下,正则非线性奇异系统的受控不变分布算法与该系统经过状态反馈转化为正常非线性系统的受控不变分布算法的一致性.并给出一个例子说明本文的结果.     

Numerical solution of fully fuzzy linear systems by fuzzy neural network

In this paper, a new hybrid method based on fuzzy neural network (FNN) for approximate solution of fuzzy linear systems of the form Ax=d,Ax=d, where AA is a square matrix of fuzzy coefficients, xx and dd are fuzzy number vectors, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate solution of an n×nn\times n system of fuzzy linear equations that supposedly has a unique fuzzy solution, a simple algorithm from the cost function of the FNN is proposed. Finally, we illustrate our approach by some numerical examples.     

A neural network solution for fixed-final time optimal control of nonlinear systems

In this paper, fixed-final time optimal control laws using neural networks and HJB equations for general affine in the input nonlinear systems are proposed. The method utilizes Kronecker matrix methods along with neural network approximation over a compact set to solve a time-varying HJB equation. The result is a neural network feedback controller that has time-varying coefficients found by a priori offline tuning. Convergence results are shown. The results of this paper are demonstrated on an example.     

Adaptive L_2 control of nonlinear systems using neural networks

An adaptive neural network controller is developed to achieve output-tracking of a class of nonlinear systems. The global L2 stability of the closed-loop system is established. The proposed control design overcomes the limitation of the conventional adaptive neural control design where the modeling error brought by neural networks is assumed to be bounded over a compact set. Moreover,the generalized matching conditions are also relaxed in the proposed L2 control design as the gains for the external disturbances entering the system are allowed to have unknown upper bounds.