Cooperative adaptive control for synchronization of second‐order systems with unknown nonlinearities

This paper studies synchronization to a desired trajectory for multi‐agent systems with second‐order integrator dynamics and unknown nonlinearities and disturbances. The agents can have different dynamics and the treatment is for directed graphs with fixed communication topologies. The command generator or leader node dynamics is also nonlinear and unknown. Cooperative tracking adaptive controllers are designed based on each node maintaining a neural network parametric approximator and suitably tuning it to guarantee stability and performance. A Lyapunov‐based proof shows the ultimate boundedness of the tracking error. A simulation example with nodes having second‐order Lagrangian dynamics verifies the performance of the cooperative tracking adaptive controller. Copyright © 2010 John Wiley & Sons, Ltd.     

Adaptive consensus protocol for networks of multiple agents with nonlinear dynamics using neural networks

In this paper, an adaptive protocol is proposed to solve the consensus problem of multi‐agent systems with high‐order nonlinear dynamics by using neural networks (NNs) to approximate the unknown nonlinear system functions. It is derived that all agents achieve consensus if the undirected interaction graph is connected, and the transient performance of the multi‐agent system is also investigated. It shows that the adaptive protocol and the consensus analysis can be easily extended to switching networks by the existing LaSalle's Invariance Principle of switched systems. A numerical simulation illustrates the effectiveness of the proposed consensus protocol. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

神经网络工况识别的混合动力电动汽车模糊控制策略

采用模糊控制可以改进混合动力电动汽车(HEV)的燃油经济性和排放性,但是对模糊控制器进行优化时通常只针对某一典型工况.不同的城市的行驶工况有一定差别,影响了模糊控制改善混合动力电动汽车性能的效果.研究中以广州和上海市主干道行驶工况为例,首先建立了一个模糊控制策略,并采用遗传算法,以汽车燃油经济性和排放性为优化目标,分别针对广州和上海主干道行驶工况对模糊控制器中隶属度函数进行优化.然后建立了一个基于模糊神经网络的行驶工况识别方法,通过识别广州和上海的主干道行驶工况,对控制策略中模糊控制器的隶属度参数进行相应调整,结果证明采用模糊神经网络识别行驶工况的HEV模糊控制策略可以进一步提高汽车的燃油经济性和排放性能.     

Razumikhin–Nussbaum‐lemma‐based adaptive neural control for uncertain stochastic pure‐feedback nonlinear systems with time‐varying delays

This paper addresses the problem of adaptive neural control for a class of uncertain stochastic pure‐feedback nonlinear systems with time‐varying delays. Major technical difficulties for this class of systems lie in: (1) the unknown control direction embedded in the unknown control gain function; and (2) the unknown system functions with unknown time‐varying delays. Based on a novel combination of the Razumikhin–Nussbaum lemma, the backstepping technique and the NN parameterization, an adaptive neural control scheme, which contains only one adaptive parameter is presented for this class of systems. All closed‐loop signals are shown to be 4‐Moment semi‐globally uniformly ultimately bounded in a compact set, and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed control schemes. Copyright © 2012 John Wiley & Sons, Ltd.     

Distributed control of uncertain multiagent systems for tracking a leader with unknown fractional‐order dynamics

This paper proposes distributed adaptive cooperative control algorithms for second‐order agents to track a leader with unknown dynamics. The models of the followers and the leader are composed of uncertain nonlinear components. The order of the leader's dynamics is unknown and can be fractional. Only the single output information is shared among neighbored agents. To simplify the control design, linearly parameterized neural networks are used to approximate the unknown functions. We first present an adaptive control for leaderless consensus and then extend the method to the tracking problem. Thorough theoretical proofs as well as numerical simulation are included to verify the results. Compared with relevant literature, the new approach applies to a larger variety of systems because (i) knowledge about the structure of leader's model is unnecessary; (ii) the unknown functions in different agents' dynamics can be diverse and arbitrary, in other words, the algorithms apply to heterogeneous agents; (iii) the results can be simply used without parameter calculations.     

Robust adaptive output‐feedback control for nonlinear systems with output unmodeled dynamics

In this paper, for a class of uncertain nonlinear systems in the presence of inverse dynamics, output unmodeled dynamics and nonlinear uncertainties, a robust adaptive output‐feedback controller design is proposed by combining small‐gain theorem, changing supply function techniques with backstepping methods. It is shown that all the signals of the closed‐loop system are uniformly bounded in biased case, and the output can be regulated to a small neighborhood of the origin in unbiased case. Furthermore, under some additional assumptions, an asymptotical result is obtained. Copyright © 2007 John Wiley & Sons, Ltd.     

Adaptive neural network control for a nonlinear Euler‐Bernoulli beam in three‐dimensional space with unknown control direction

In this paper, an adaptive neural network control system is developed for a nonlinear three‐dimensional Euler‐Bernoulli beam with unknown control direction. The Euler‐Bernoulli beam is modeled as a combination of partial differential equations (PDEs) and ordinary differential equations (ODEs). Adaptive radial basis function–based neural network control laws are designed to determine approximation of disturbances. A projection mapping operator is adopted to realize bounded approximation of disturbances. A Nussbaum function is introduced to compensate for the unknown control direction. The goal of this study is to suppress the vibrations of the Euler‐Bernoulli beam in three‐dimensional space. In addition, unknown control direction problem and bounded disturbances are considered to guarantee that the signals of the system are uniformly bounded. Numerical simulations demonstrate the effectiveness of the proposed method.     

Model‐free adaptive formation control for unknown multiinput‐multioutput nonlinear heterogeneous discrete‐time multiagent systems with bounded disturbance

Based on the model‐free adaptive control, the distributed formation control problem is investigated for a class of unknown heterogeneous nonlinear discrete‐time multiagent systems with bounded disturbance. Two equivalent data models to the unknown multiagent systems are established through the dynamic linearization technique considering the circumstances with measurable and unmeasurable disturbances. Based on the obtained data models, two distributed controllers are designed with only using the input/output and disturbance data of the neighbor agents system. The tracking error of the closed‐loop system driven by the proposed controllers is shown to be bounded by the contraction mapping principle and inductive methods. An example illustrates the effectiveness of the proposed two distributed controllers.     

Robust approximation‐based adaptive control of multiple state delayed nonlinear systems with unmodeled dynamics

This paper addresses the problem of tracking control for a class of uncertain nonstrict‐feedback nonlinear systems subject to multiple state time‐varying delays and unmodeled dynamics. To overcome the design difficulty in system dynamical uncertainties, radial basis function neural networks are employed to approximate the black‐box functions. Novel continuous functions that deal with whole states uncertainties are introduced in each step of the adaptive backstepping to make the controller design feasible. The robust problem caused by unmodeled dynamics when constructing a stable controller is solved by employing an auxiliary signal to regulate its boundedness. A novel Lyapunov‐Krasovskii functional is developed to compensate for the delayed nonlinearity without requiring the priori knowledge of its upper bound functions. On the basis of the proposed robust adaptive neural controller, all the closed‐loop signals are semiglobal uniformly ultimately bounded with good tracking performance.     

Direct adaptive control for a class of discrete‐time unknown nonaffine nonlinear systems using neural networks

In this paper, a direct adaptive state‐feedback control approach is developed for a class of nonlinear systems in discrete‐time (DT) domain. We study MIMO unknown nonaffine nonlinear DT systems and employ a two‐layer NN to design the controller. By using the presented method, the NN approximation is able to cancel the nonlinearity of the unknown DT plant. Meanwhile, pretraining is not required, and the weights of NNs used in adaptive control are directly updated online. Moreover, unlike standard NN adaptive controllers yielding uniform ultimate boundedness results, the tracking error is guaranteed to be uniformly asymptotically stable by utilizing Lyapunov's direct method. Two illustrative examples are provided to demonstrate the effectiveness and the applicability of the theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.     

Global output‐feedback stabilization for nonlinear systems with unknown relative degree

This paper is devoted to the global stabilization via output feedback for a class of nonlinear systems with unknown relative degree, dynamics uncertainties, unknown control direction, and nonparametric uncertain nonlinearities. In particular, the unknown relative degree is without known upper bound, which renders us to research for a filter with varying dimension rather than the ones with over dimensions in the existing literature. In comparison with more popular but a bit stronger input‐to‐state stable or input‐to‐state practically stable requirement, only bounded‐input bounded‐state stable requirement is imposed on the dynamics uncertainties, which affect the systems in a persistent intensity rather than in a decaying one. In this paper, to compensate multiple serious system uncertainties and realize global output‐feedback stabilization, a design scheme via switching logic together with varying dimensional filter is developed. In this scheme, 2 switching sequences, which separately generate the gains of the controller and act as the varying dimensions of the filter, are designed to overcome unknown control direction, dynamics uncertainties and nonparametric uncertain nonlinearities, and unknown relative degree, respectively. A 2‐mass lumped‐parameter structure is provided to show the effectiveness of the proposed method in this paper.     

Adaptive event‐triggered neural control for nonlinear uncertain system with input constraint

In this article, the issue of developing an adaptive event‐triggered neural control for nonlinear uncertain system with input delay is investigated. The radial basis function neural networks (RBFNNs) are adopted to approximate the uncertain terms, where the time‐varying approximation errors are considered into the approximation system. However, the RBFNNs' weight vector is extended, which may cause the computing burdens. To save network resource, the computing burden caused by the weight vector is handled with the developed adaptive control strategy. Furthermore, in order to compensate the effect of input delay, an auxiliary system is introduced into codesign. With the help of adaptive backstepping technique, an adaptive event‐triggered control approach is established. Under the proposed control approach, the effect of input delay can be compensated effectively while the considered system suffered network resource constraint, and all signals in the close‐loop system can be guarantee bounded. Finally, two simulation examples are given to verify the proposed control method's effectiveness.     

Multidimensional Taylor network adaptive control for MIMO time‐varying uncertain nonlinear systems with noises

In this paper, an adaptive control approach based on the multidimensional Taylor network (MTN) is proposed here for the real‐time tracking control of multiple‐input–multiple‐output (MIMO) time‐varying uncertain nonlinear systems with noises. Two MTNs are used to formulate the optimum control and adaptive filtering approaches. The feed‐forward MTN controller (MTNC) is developed to realize the precise tracking control. The closed‐loop errors between the filtered outputs and expected values are directly chosen as the MTNC's inputs. A valid initial value selection scheme for the weights of the MTNC, which can ensure the initial stability of adaptive process, is introduced. The proposed MTNC can update its weights online according to errors caused by system's uncertain factors, based on stable learning rate. The resilient backpropagation algorithm and the adaptive variable step size algorithm via linear reinforcement are utilized to update the MTNC's weights. The MTN filter (MTNF) is developed to eliminate measurement noises and other stochastic factors. The proposed adaptive MTN filtering system possesses the distinctive properties of the Lyapunov theory–based adaptive filtering system and MTN. Lyapunov function of the filtering errors between the measured values and MTNF's outputs is defined. By properly choosing the weights update law in the Lyapunov sense, the MTNF's outputs can asymptotically converge to the desired signals. The design is independent of the stochastic properties of the input disturbances. Simulation of the MTN‐based control is conducted to test the effectiveness of the presented results.     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.     

Distributed consensus control for multi‐agent systems using terminal sliding mode and Chebyshev neural networks

This paper investigates the problem of consensus tracking control for second‐order multi‐agent systems in the presence of uncertain dynamics and bounded external disturbances. The communication ?ow among neighbor agents is described by an undirected connected graph. A fast terminal sliding manifold based on lumped state errors that include absolute and relative state errors is proposed, and then a distributed finite‐time consensus tracking controller is developed by using terminal sliding mode and Chebyshev neural networks. In the proposed control scheme, Chebyshev neural networks are used as universal approximators to learn unknown nonlinear functions in the agent dynamics online, and a robust control term using the hyperbolic tangent function is applied to counteract neural‐network approximation errors and external disturbances, which makes the proposed controller be continuous and hence chattering‐free. Meanwhile, a smooth projection algorithm is employed to guarantee that estimated parameters remain within some known bounded sets. Furthermore, the proposed control scheme for each agent only employs the information of its neighbor agents and guarantees a group of agents to track a time‐varying reference trajectory even when the reference signals are available to only a subset of the group members. Most importantly, finite‐time stability in both the reaching phase and the sliding phase is guaranteed by a Lyapunov‐based approach. Finally, numerical simulations are presented to demonstrate the performance of the proposed controller and show that the proposed controller exceeds to a linear hyperplane‐based sliding mode controller. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive neural control for a class of stochastic nonlinear time‐delay systems with unknown dead zone using dynamic surface technique

This paper investigates the problem of adaptive control for a class of stochastic nonlinear time‐delay systems with unknown dead zone. A neural network‐based adaptive control scheme is developed by using the dynamic surface control (DSC) technique and the minimal learning parameters algorithm. The dynamic surface control technique, which can avoid the problem of ‘explosion of complexity’ inherent in the conventional backstepping design procedure, is first extended to the stochastic nonlinear time‐delay system with unknown dead zone. The unknown nonlinearities are approximated by the function approximation technique using the radial basis function neural network. For the purpose of reducing the numbers of parameters, which are updated online for each subsystem in the process of approximating the unknown functions, the minimal learning parameters algorithm is then introduced. Also, the adverse effects of unknown time‐delay are removed by using the appropriate Lyapunov–Krasovskii functionals. In addition, the proposed control scheme is systematically derived without requiring any information on the boundedness of the dead zone parameters and avoids the possible controller singularity problem in the approximation‐based adaptive control schemes with feedback linearization technique. It is shown that the proposed control approach can guarantee that all the signals of the closed‐loop system are bounded in probability, and the tracking errors can be made arbitrary small by choosing the suitable design parameters. Finally, a simulation example is provided to illustrate the performance of the proposed control scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust adaptive backstepping sliding mode control for motion mode decoupling of two‐axle vehicles with active kinetic dynamic suspension systems

A mode decoupling control strategy is proposed for the active Kinetic Dynamic Suspension Systems (KDSS) with electrohydrostatic actuator (EHA) to improve the roll and warp mode performances. A matrix transfer method is employed to derive the modes of body and wheel station motions for full vehicle with active KDSS. The additional mode stiffness produced by the active KDSS is obtained and quantitatively described with the typical physical parameters. A new hierarchical feedback control strategy is proposed for the active KDSS to improve the roll and warp motion performances and simultaneously accounting for nonlinear dynamics of the actuators with hydraulic uncertainties. H∞ static output‐feedback control is employed to obtain the desirable mode forces, and a new projection‐based adaptive backstepping sliding mode tracking controller is designed for EHA to deal with address the nonlinearity and parameters uncertainty. This controller is used to realize the desirable pressure difference of EHA required from the target mode forces. Numerical simulations are presented to compare the roll and warp performances between the active KDSS, conventional spring‐damper suspension, and suspension with antiroll bar under typical excitation conditions. The evaluation indices are normalized and compared with radar chart. The obtained results illustrate that the proposed active KDSS with proposed controller does not produce additional warp motion for vehicle body, and has achieved more reasonable tire force distribution among wheel stations, the roll stability, road holding, and significantly improved ride comfort simultaneously.     

Neural adaptive global stability control for robot manipulators with time‐varying output constraints

In this paper, a novel adaptive control scheme is proposed based on radial basis function neural network (RBFNN). The considered system is deduced by the structure of RBFNN with nonzero time‐varying parameter that installed in the fore‐end and terminal of RBFNN. With this structure and the Taylor expansion of any smooth continuous nonlinear function, a universal approximation of RBFNN is addressed according to the analysis of the character of continuous homogenous function and the Euler's theorem. The approximation accuracies can be adjusted online by the nonzero time‐varying parameter in the device with the degree of continuous homogenous function, which expand the semiglobally stability to global stability over conventional neural controller design approaches. Based on the theory analysis of barrier Lyapunov function, the violation of time‐varying constraints can be subjugated without wrecked. Finally, simulation results are carried out to verify the effectiveness by the design methods.