Adaptive Backstepping Dynamic Surface Control Research Articles

Distributed Optimization for Fractional-Order Multi-Agent Systems Based on Adaptive Backstepping Dynamic Surface Control Technology

In this article, the distributed optimization problem is studied for a class of fractional-order nonlinear uncertain multi-agent systems (MASs) with unmeasured states. Each agent is represented through a system with unknown nonlinearities, unmeasurable states and a local objective function described by a quadratic polynomial function. A penalty function is constructed by a sum of local objective functions and integrating consensus conditions of the MASs. Radial basis function Neural-networks (RBFNNs) and Neural networks (NN) state observer are applied to approximate the unknown nonlinear dynamics and estimate unmeasured states, respectively. By combining the NN state observer and the penalty function, and the stability theory of the Lyapunov function, the distributed observer-based adaptive optimized backstepping dynamic surface control protocol is proposed to ensure the outputs of all agents asymptotically reach consensus to the optimal solution of the global objective function. Simulations demonstrate the effectiveness of the proposed control scheme.

Dynamic surface control for a class of nonlinearly parameterized systems with input time delay using neural network

By using the radial basis function neural network (RBF NN), this paper presents tracking control problem of the nonlinear systems with the input time delay, in which the unknown continuous functions may be nonlinearly parameterized. Different from the existing results which deal with the nonlinearly parameterized functions by using the separation principle, in this paper, the nonlinearly parameterized functions are lumped into the continuous functions, and then, the neural networks (NNs) are applied to approximate them. Moreover, through a state transformation the system can be easily transformed into a system without the input time delay. Finally, based on the minimal learning parameters (MLP) algorithm and the adaptive backstepping dynamic surface control (DSC) technique, a new adaptive NN backstepping control scheme is developed, and only two parameters need to be adjusted online in the controller design procedure. Thus, the proposed control method cannot only overcome the problem of “explosion of complexity” inherently existing in traditional backstepping design methods, but also reduce the computational burden greatly. It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error can converge to a small neighborhood of the origin with an appropriate choice of design parameters. Finally, three examples are used to show the effectiveness of the proposed approach.

Neural network based adaptive backstepping dynamic surface control of drug dosage regimens in cancer treatment

This manuscript aims at investigating the neural adaptive control of drug dosage regimens in cancer treatment. The goal of the treatment is to get an appropriate scheme for the drug dosage in order to reduce the tumor cells. To obtain a controller presenting good performances, the cancer immunotherapy system is first described by Caputo fractional differential equations. Second, Nussbaum functions and neural networks are introduced to deal with the unknown control directions and the uncertain nonlinear dynamics, respectively. Then, the backstepping dynamic surface control method is deployed to regulate the updating laws and the control signals, simultaneously. Through rigorous analysis based on the Lyapunov stability theory, it is shown that by means of the proposed adaptive controller, the boundedness of all variables in the closed-loop system and the semi-global asymptotic tracking are well ensured for any bounded initial conditions. It is also demonstrated that the performances of the drug treatment based on our proposed adaptive neural control scheme are better than a number of existing schemes. Finally, simulation results are given to demonstrate the feasibility of the proposed control scheme in the diminution of the number of tumor cells in the cancer model.

Design of adaptive backstepping dynamic surface control method with RBF neural network for uncertain nonlinear system

This paper develops an adaptive backstepping dynamic surface control method with RBF Neural Network for a class of nonlinear system under extra disturbances. The considered RBF Neural Network based on adaptive control is applied to approximate the unknown smooth function arbitrarily. The “explosion of the complexity” is eliminated by utilizing the dynamic surface control technique. The Lyapunov function is employed to verify the globally asymptotically stability of the control nonlinear system. Four examples were given to show that the novel control method can not only tracking the expected trajectory very well but also has a better approximation capability for various complex unknown smooth function under disturbances.

(1606-3017) ADAPTIVE FUZZY TRACKING CONTROL FOR A CLASS OF PERTURBED NONLINEARLY PARAMETERIZED SYSTEMS USING MINIMAL LEARNING PARAMETERS ALGORITHM

In this paper, an adaptive fuzzy tracking control approach is proposed for a class of single-inputsingle-output (SISO) nonlinear systems in which the unknown continuous functions may be nonlinearlyparameterized. During the controller design procedure, the fuzzy logic systems (FLS) in Mamdani type are applied to approximate the unknown continuous functions, and then, based on the minimal learning parameters (MLP) algorithm and the adaptive backstepping dynamic surface control (DSC) technique, a new adaptive fuzzy backstepping control scheme is developed. The main advantages of our approach include: (i) unlike the existing results which deal with the nonlinearlyparameterized functions by using the separation principle, the nonlinearly parameterized functions are lumped into the continuous functions which can be approximated by using the FLS, (ii) only one parameter needs to be adjusted online in controller design procedure, which reduces the online computation burden greatly, and our development is able to eliminate the problem of ''explosion of complexity inherent in the existing backstepping-based methods. It is proven thatthe proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound. Finally, two examples are used to show the effectiveness of the proposed approach.

Adaptive‐dynamic‐programming‐based fuzzy control for triangular structure nonlinear uncertain systems with unknown time delay

SummaryThis paper develops a novel fuzzy adaptive backstepping dynamic surface control scheme for a class of strict‐feedback nonlinear systems with unknown time delay based on adaptive dynamic programming. The whole control scheme is composed of 2 parts, ie, feedforward control and feedback optimal control. Fuzzy logic systems are used to identify nonlinear systems. The control design method, which combined the backstepping design technique and the dynamic surface control approach, is applied to convert triangular structure systems to affine nonlinear systems; it not only can solve the problem of “explosion of complexity” but also can avoid the appearance of unknown terms. The closed‐loop system is guaranteed to be uniformly ultimately bounded based on the Lyapunov and optimal control theory, and the system output can track the desired reference signal in an optimal manner. The simulation results of numerical examples are presented to show the effectiveness of the proposed approach.

Composite adaptive fuzzy output feedback dynamic surface control design for stochastic large-scale nonlinear systems with unknown dead zone

In this paper, a composite adaptive fuzzy output feedback decentralized control problem is investigated for a class of nonlinear stochastic large-scale systems. The nonlinear large-scale systems under study have unknown nonlinear functions, unknown dead-zone and immeasurable states. Fuzzy logic systems are used to approximate the unknown nonlinear functions, a fuzzy adaptive state observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy state observer, a serial-parallel estimation model is established. Based on adaptive backstepping dynamic surface control technique and the prediction error between the system states observer model and the serial-parallel estimation model, an adaptive output feedback controller is constructed. The designed fuzzy controller with the composite parameters adaptive laws ensures that all the variables of closed-loop system are bounded in probability, and tracking error converges to a small neighborhood of zero. A numerical example is provided to verify the effectiveness of the proposed approach.

Hybrid adaptive fuzzy control for uncertain MIMO nonlinear systems with unknown dead-zones

In this paper, a hybrid adaptive fuzzy control approach is proposed for a class of uncertain multiple-input and multiple-output (MIMO) strict-feedback nonlinear systems with unknown dead-zones. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a serial-parallel estimation model is established. Based on the adaptive backstepping dynamic surface control (DSC) technique, and utilizing the bounds of the dead-zone slopes and the prediction errors between the system model and the serial-parallel estimation model, a new robust adaptive fuzzy backstepping controller with the composed parameters adaptive laws is developed. The proposed control method can not only overcome the problem of “explosion of complexity” inherently existing in traditional backstepping design methods, but also improve the control performance. It is proved that all the signals of the closed-loop systems are bounded and the system output can follow the given bounded reference signal. A numerical example and simulation comparisons with the existing control methods are provided to show the effectiveness of the proposed approach.

Composite Adaptive Fuzzy Output Feedback Dynamic Surface Control Design for Uncertain Nonlinear Stochastic Systems with Input Quantization

In this paper, a composite adaptive fuzzy output feedback control problem is investigated for a class of single-input and single-output stochastic nonlinear systems, where the input signal takes quantized values. In the control design, by using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy adaptive state observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy state observer, a serial–parallel estimation model is established. Based on adaptive backstepping dynamic surface control technique and the prediction error between the system states observer model and the serial–parallel estimation model, an adaptive output feedback controller is constructed. The designed fuzzy controller with the composite parameters adaptive laws ensures that all the variables of closed-loop system are bounded in probability, and tracking error converges to a small neighborhood of zero. Two examples are provided to verify the effectiveness of the proposed approach.

Composite Adaptive Fuzzy Output Feedback Control Design for Uncertain Nonlinear Strict-Feedback Systems With Input Saturation.

In this paper, a composite adaptive fuzzy output-feedback control approach is proposed for a class of single-input and single-output strict-feedback nonlinear systems with unmeasured states and input saturation. Fuzzy logic systems are utilized to approximate the unknown nonlinear functions, and a fuzzy state observer is designed to estimate the unmeasured states. By utilizing the designed fuzzy state observer, a serial-parallel estimation model is established. Based on adaptive backstepping dynamic surface control technique and utilizing the prediction error between the system states observer model and the serial-parallel estimation model, a new fuzzy controller with the composite parameters adaptive laws are developed. It is proved that all the signals of the closed-loop system are bounded and the system output can follow the given bounded reference signal. A numerical example and simulation comparisons with previous control methods are provided to show the effectiveness of the proposed approach.

Adaptive fuzzy output feedback dynamic surface control of interconnected nonlinear pure-feedback systems.

In this paper, an adaptive fuzzy decentralized output feedback control design is presented for a class of interconnected nonlinear pure-feedback systems. The considered nonlinear systems contain unknown nonlinear uncertainties and the states are not necessary to be measured directly. Fuzzy logic systems are employed to approximate the unknown nonlinear functions, and then a fuzzy state observer is designed and the estimations of the immeasurable state variables are obtained. Based on the adaptive backstepping dynamic surface control design technique, an adaptive fuzzy decentralized output feedback control scheme is developed. It is proved that all the variables of the resulting closed-loop system are semi-globally uniformly ultimately bounded, and also that the observer and tracking errors are guaranteed to converge to a small neighborhood of the origin. Some simulation results and comparisons with the existing results are provided to illustrate the effectiveness and merits of the proposed approach.

Adaptive backstepping dynamic surface control for systems with periodic disturbances using neural networks

This paper addresses the adaptive neural network tracking control problem for a class of strict-feedback systems with unknown non-linearly parameterised and time-varying disturbed function of known periods. Radial basis function neural network and Fourier series expansion are combined into a new function approximator to model each suitable disturbed function in systems. Dynamic surface control approach is used to solve the problem of ‘explosion of complexity’ in backstepping design procedure. The uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. A simulation example is provided to illustrate the effectiveness of the control scheme designed.