Distributed disturbance observer based consensus control for linear multi-agent systems with mismatched disturbances

This paper proposes two kinds of distributed disturbance observer (DO) based consensus control laws for linear multi-agent systems (MAS) with mismatched disturbances. For a linear MAS with mismatched disturbances generated by exosystems, we design relative information based distributed DOs for each agent to obtain information of disturbances. The first method is to utilise the information of disturbances obtained by the distributed DO as a feedforward term to reject influence of exogenous disturbances for consensus results, where the gain matrix of the feedforward term is obtained via solving a matrix equation. The second method is to design an internal model based dynamic compensator to reject influence of exogenous disturbances, where the dynamic compensator is also updated by the distributed DO. The leaderless and leader-follower consensus are both considered in this paper, and rigorous proof of consensus results is also given. Finally, some numerical simulations verify effectiveness of the proposed consensus control laws.     

A modified noise-tolerant ZNN model for solving time-varying Sylvester equation with its application to robot manipulator

Recently, Xiao et al. (2021) proposed an efficient noise-tolerant zeroing neural network (NTZNN) model with fixed-time convergence for solving the time-varying Sylvester equation. In this paper, we propose a modified version of their NTZNN model, named the modified noise-tolerant zeroing neural network (MNTZNN) model. It extends the NTZNN model to a more general form and then we prove that, with appropriate parameter selection, our new MNTZNN model can significantly accelerate the convergence of the NTZNN model. Numerical experiments confirm that the MNTZNN model not only maintains fixed-time convergence and noise-tolerance but also has a faster convergence rate than the NTZNN model under certain conditions. In addition, the design strategy of the MNTZNN is also successfully applied to the path tracking of a 6-link planar robot manipulator under noise disturbance, which demonstrates its applicability and practicality.     

Periodic dynamics for nonlocal Hopfield neural networks with random initial data

In this paper, a class of nonlocal Hopfield neural networks with random initial data is introduced, where the randomness may be of probability uncertainty. Sufficient conditions are derived to ensure the existence and globally exponential convergence of periodic solution for the addressed system in the frame of nonlinear expectation and linear expectation, respectively. Moreover, numerical examples are given to show the effectiveness of the obtained results.     

Zero dynamics and funnel control for linear electrical circuits

We consider electrical circuits containing linear resistances, capacitances and inductances. The circuits can be described by differential-algebraic input–output systems, where the input consists of voltages of voltage sources and currents of current sources and the output consists of currents of voltage sources and voltages of current sources. We generalize a characterization of asymptotic stability of the circuit and give sufficient topological criteria for its invariant zeros being located in the open left half-plane. We show that asymptotic stability of the zero dynamics can be characterized by means of the interconnectivity of the circuit and that it implies that the circuit is high-gain stabilizable with any positive high-gain factor. Thereafter we consider the output regulation problem for electrical circuits by funnel control. We show that for circuits with asymptotically stable zero dynamics, the funnel controller achieves tracking of a class of reference signals within a pre-specified funnel; this means in particular that the transient behavior of the output error can be prescribed and the funnel controller does neither incorporate any internal model for the reference signals nor any identification mechanism, it is simple in its design. The results are illustrated by a simulation of a discretized transmission line.     

Composite anti-disturbance control for uncertain Markovian jump systems with actuator saturation based disturbance observer and adaptive neural network

This paper studies the problem of composite control for a class of uncertain Markovian jump systems (MJSs) with partial known transition rates, multiple disturbances and actuator saturation. Compared with the existing results, a novel robust composite control scheme is put forward by virtue of adaptive neural network technique. For MJSs, the partial unknown information on transition rates and the actuator saturation influence the design of disturbance observer and the robust H_∞ controller. Firstly, without taking account of external disturbances, the network reconstruction error and saturation, a novel robust adaptive control strategy is established to ensure that all the signals of the closed-loop system are asymptotically bounded in mean square. Secondly, the solvability condition for ensuring the robust H_∞ performance is given by using a modified adaptive law, where the saturation is treated as a disturbance-like signal. Finally, the simulations for a numerical example and an application example are performed to validate the effectiveness of the proposed results.     

On “an improved approach for nonlinear system identification using neural networks”

Nonlinear system identification and prediction is a complex task, and often non-parametric models such as neural networks are used in place of intricate mathematics. To that cause, recently an improved approach to nonlinear system identification using neural networks was presented in Gupta and Sinha (J. Franklin Inst. 336 (1999) 721). Therein a learning algorithm was proposed in which both the slope of the activation function at a neuron, β, and the learning rate, η, were made adaptive. The proposed algorithm assumes that η and β are independent variables. Here, we show that the slope and the learning rate are not independent in a general dynamical neural nétwork, and this should be taken into account when designing a learning algorithm. Further, relationships between η and β are developed which helps reduce the number of degrees of freedom and computational complexity in an optimisation task of training a fully adaptive neural network. Simulation results based on Gupta and Sinha (1999) and the proposed approach support the analysis.     

Finite-time stability analysis and stabilization for linear discrete-time system with time-varying delay

The problem of finite-time stability for linear discrete-time systems with time-varying delay is studied in this paper. In order to deal with the time delay, the original system is firstly transformed into two interconnected subsystems. By constructing a delay-dependent Lyapunov–Krasovskii functional and using a two-term approximation of the time-varying delay, sufficient conditions of finite-time stability are derived and expressed in terms of linear matrix inequalities (LMIs). The derived stability conditions can be applied into analyzing the finite-time stability and deriving the maximally tolerable delay. Compared with the existing results on finite-time stability, the derived stability conditions are less conservative. In addition, for the stabilization problem, we design the state-feedback controller. Finally, numerical examples are used to illustrate the effectiveness of the proposed method.     

Active disturbance rejection control for electric power steering system with assist motor variable mode

The steering torque of automobile EPS steering system is significant for driving steering control and good driving feel. Servo motor control and external interference moment are the core factors affecting EPS steering system. With the advancement of automotive technology, the requirements of EPS control technology have been gradually improved, and the driving and handling of vehicles at high speed have become the key issues. For the current EPS steering system at high speed vibration and steering feel, active disturbance rejection EPS torque control method is proposed, EPS variable mode controller was developed. The control of the variable mode is verified by experiment and the vibration torque from the road is controlled, determine the control frequency of 30 KHz, the amount of current fluctuation is the smallest. The ADRC (active disturbance rejection controller) technology is used to suppress the interference of the road surface, finally, the validity of active immunity is verified by bench test. Steering wheel vibration torque can be reduced by an average of 28.5% to 33.3%.     

Composite adaptive disturbance observer based control and back-stepping method for nonlinear system with multiple mismatched disturbances

A novel control scheme combining disturbance observer technique and back-stepping method is proposed for a class of nonlinear system with multiple mismatched disturbances. The uncertain multiple mismatched disturbances contain not only single harmonic or constant disturbances but also another unexpected nonlinear signal presented as a nonlinear function. The composite adaptive disturbance observers are designed to estimate the disturbances with partial known information. By integrating disturbance observer based control with back-stepping method, a composite controller is designed. Here, the disturbance estimations are introduced into the design of virtual control laws in each step to compensate the mismatched disturbances. Rigorous stability analysis for the closed-loop system is established by direct Lyapunov function method. It is shown that the system output asymptotically converges to zero in spite of existing multiple mismatched disturbances. Finally, a simulation example is applied to demonstrate the effectiveness of the proposed method.     

Analysis and robust control of system with uncertainty and disturbance using equivalent-input-disturbance approach

This paper addresses the control problem of an uncertain system suffering from an exogenous disturbance. A new degree of control freedom is developed to handle the problem based on the equivalent-input-disturbance (EID) approach. The effect of the disturbance and uncertainties is equivalent to that of a fictitious disturbance on the control input channel, which is called an EID. A state observer and an improved EID (IEID) estimator are devised to produce an estimate that is used to compensate for the disturbance and uncertainties in a control law. A second-order low-pass filter is employed in the estimator to provide a way to solve a tradeoff between disturbance rejection and noise suppression. The slope of the Bode magnitude curve at high frequencies is two times larger for the IEID estimator than for a conventional one. This makes the IEID estimator less sensitive to measurement noise and more practical. Sufficient analyses reveal the mechanism of disturbance rejection, uncertainty attenuation, and noise suppression of an IEID-based control system. A theorem is derived to guarantee system stability and a procedure is presented for system design. Simulations and experiments of the position control of a magnetic levitation system are carried out to show the validity of the presented method.     

WSVR-based fuzzy neural network with annealing robust algorithm for system identification

This paper proposes a fuzzy neural network (FNN) based on wavelet support vector regression (WSVR) approach for system identification, in which an annealing robust learning algorithm (ARLA) is adopted to adjust the parameters of the WSVR-based FNN (WSVR-FNN). In the WSVR-FNN, first, the WSVR method with a wavelet kernel function is used to determine the number of fuzzy rules and the initial parameters of FNN. After initialization, the adjustment for the parameters of FNNs is performed by the ARLA. Combining the self-learning ability of neural networks, the compact support of wavelet functions, the adaptive ability of fuzzy logic, and the robust learning capability of ARLA, the proposed FNN has the superiority among the several existed FNNs. To demonstrate the performance of the WSVR-FNN, two nonlinear dynamic plants and a chaotic system taken from the extant literature are considered to illustrate the system identification. From the simulation results, it shows that the proposed WSVR-FNN has the superiority over several presented FNNs even the number of training parameters is considerably small.     

Adaptive neural dynamic surface control for full state constrained stochastic nonlinear systems with unmodeled dynamics

This paper solves the problem of adaptive neural dynamic surface control (DSC) for a class of full state constrained stochastic nonlinear systems with unmodeled dynamics. The concept of the state constraints in probability is first proposed and applied to the stability analysis of the system. The full state constrained stochastic nonlinear system is transformed to the system without state constraints through a nonlinear mapping. The unmodeled dynamics is dealt with by introducing a dynamic signal and the adaptive neural dynamic surface control method is explored for the transformed system. It is proved that all signals of the closed-loop system are bounded in probability and the error signals are semi-globally uniformly ultimately bounded(SGUUB) in mean square or the sense of four-moment. At the same time, the full state constraints are not violated in probability. The validity of the proposed control scheme is demonstrated through the simulation examples.     

Time-optimal control problem for a linear parameter varying system with nonlinear item

In this paper, we considered a time-optimal control problem for a new type of linear parameter varying (LPV) system which is obtained through data identification in the process of dealing with actual problems. The addition of non-linear terms is compensation for the method that does not require linear expansion at the equilibrium point. Since the objective function is the terminal time which is an implicit function concerning decision variables, it is a non-standard optimal control problem with uncertain terminal time. To find the global optimal solution to this problem, firstly, the control parameterization method is used to transform it into a nonlinear optimization problem of parameter selection, and then the modifed particle swarm optimization (PSO) algorithm is combined to solve the equivalent nonlinear programming problem. Numerical examples are used to illustrate the effectiveness of the proposed algorithm.     

Distributed data driven control for multi-agent consensus with unknown system dynamics

This study investigates the consensus tracking problem for unknown multi-agent systems (MASs) with time-varying communication topology by using the methods of data-driven control and model predictive control. Under the proposed distributed iterative protocol, sufficient conditions for reducing tracking error are analyzed for both time invariable and time varying desired trajectories. The main feature of the proposed protocol is that the dynamics of the multi-agent systems are not required to be known and only local input-output data are utilized for each agent. Numerical simulations are presented to illustrate the effectiveness of the derived consensus conditions.     

Dynamic modeling and neural network compensation for dual-flexible servo system with an underactuated hand

This paper investigates a difficult problem of nonlinear dynamics and motion control of a dual-flexible servo system with an underactuated hand (DFSS-UH). Variation in grasping mass and nonlinear factors of the DFSS-UH including complex flexible deformation and friction torque aggravate the output speed fluctuation, leading to modeling errors in the dynamics, which in turn affects the underactuated hand motion accuracy. A novel neural network sliding mode control (NNSMC) method is designed to control the DFSS-UH. The strategy utilizes neural networks to compensate for dynamics modeling errors, which takes into account neglected nonlinear factors and inaccurate friction torque. The reaching law with the hyperbolic tangent function is proposed to improve sliding mode control, thereby weakening the chattering phenomenon. First of all, the DFSS-UH mechanical model considering many nonlinear factors is established and a dynamic simplification model which ignores higher-order modes is proposed. Secondly, the adaptive law of weighted coefficients is proposed according to the stability of the DFSS-UH. Finally, the physical control platform of the DFSS-UH is built, and simulation and control experiments are conducted. Experimental results show that the improved NNSMC strategy decreases the tracking error of flexible load, thereby enhancing the control accuracy of the DFSS-UH.     

Adaptive neural control of stochastic nonlinear systems with unmodeled dynamics and time-varying state delays

In this paper, a novel adaptive control scheme is investigated based on the backstepping design for a class of stochastic nonlinear systems with unmodeled dynamics and time-varying state delays. The radial basis function neural networks are used to approximate the unknown nonlinear functions obtained by using Ito differential formula and Young?s inequality. The unknown time-varying delays and the unmodeled dynamics are dealt with by constructing appropriate Lyapunov–Krasovskii functions and introducing available dynamic signal. It is proved that all signals in the closed-loop system are bounded in probability and the error signals are semi-globally uniformly ultimately bounded (SGUUB) in mean square or the sense of four-moment. Simulation results illustrate the effectiveness of the proposed design.