Adaptive output feedback dynamic surface control of stochastic nonlinear systems with state and input unmodeled dynamics

In this paper, an adaptive neural output feedback control scheme is investigated for a class of stochastic nonlinear systems with unmeasured states and four kinds of uncertainties including uncertain nonlinear function, dynamic disturbance, input unmodeled dynamics, and stochastic inverse dynamics. The unmeasured states are estimated by K‐filters, and stochastic inverse dynamics is dealt with by constructing a changing supply function. The considered input unmodeled dynamic subsystem possesses nonlinear feature, and a dynamic normalization signal is introduced to counteract the unstable effect produced by the input unmodeled dynamics. Combining dynamic surface control technique with stochastic input‐to‐state stability, small‐gain condition, and Chebyshev's inequality, the designed robust adaptive controller can guarantee that all the signals in the closed‐loop system are bounded in probability, and the error signals are semi‐globally uniformly ultimately bounded in mean square or the sense of four‐moment. Simulation results are provided to verify the effectiveness of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

离散时间非线性系统的观测器设计

针对离散时间Lipschitz非线性系统的观测器设计问题,依据离散时间系统的Lyapunov稳定性理论,研究了保证观测误差渐近稳定的充分条件,并依据该条件应用线性矩阵不等式方法,得到了观测器增益矩阵的设计方法。所得方法计算简便,并通过算例说明该方法的应用。     

Global output‐feedback control of systems with dynamic nonlinear input uncertainties through singular perturbation‐based dynamic scaling

A general class of uncertain nonlinear systems with dynamic input nonlinearities is considered. The system structure includes a core nominal subsystem of triangular structure with additive uncertain nonlinear functions, coupled uncertain nonlinear appended dynamics, and uncertain nonlinear input unmodeled dynamics. The control design is based on dual controller/observer dynamic high‐gain scaling with an additional dynamic scaling based on a singular perturbation‐like redesign to address the non‐affine and uncertain nature of the input appearance in the system dynamics. The proposed approach yields a constructive global robust adaptive output‐feedback control design that is robust to the dynamic input uncertainties and to uncertain nonlinear functions allowed throughout the system structure. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive backstepping neural control of state‐delayed nonlinear systems with full‐state constraints and unmodeled dynamics

In this paper, the problem of adaptive neural control is discussed for a class of strict‐feedback time‐varying delays nonlinear systems with full‐state constraints and unmodeled dynamics, as well as distributed time‐varying delays. The considered nonlinear system with full‐state constraints is transformed into a nonlinear system without state constraints by introducing a one‐to‐one asymmetric nonlinear mapping. Based on modified backstepping design and using radial basis function neural networks to approximate the unknown smooth nonlinear function and using a dynamic signal to handle dynamic uncertainties, a novel adaptive backstepping control is developed for the transformed system without state constraints. The uncertain terms produced by state time delays and distributed time delays are compensated for by constructing appropriate Lyapunov‐Krasovskii functionals. All signals in the closed‐loop system are proved to be semiglobally uniformly ultimately bounded. A numerical example is provided to illustrate the effectiveness of the proposed design scheme.     

Robust adaptive tracking control of uncertain discrete time systems

In this paper, the problem of robust adaptive tracking for uncertain discrete‐time systems is considered from the slowly varying systems point of view. The class of uncertain discrete‐time systems considered is subjected to both 𝓁_∞ to 𝓁_∞ bounded unstructured uncertainty and external additive bounded disturbances. A priori knowledge of the dynamic model of the reference signal to be tracked is not completely known. For such problem, an indirect adaptive tracking controller is obtained by frozen‐time controllers that at each time optimally robustly stabilize the estimated models of the plant and minimize the worst‐case steady‐state absolute value of the tracking error of the estimated model over the model uncertainty. Based on 𝓁_∞ to 𝓁_∞ stability and performance of slowly varying system found in the literature, the proposed adaptive tracking scheme is shown to have good robust stability. Moreover, a computable upper bound on the size of the unstructured uncertainty permitted by the adaptive system and a computable tight upper bound on asymptotic robust steady‐state tracking performance are provided. Copyright © 2005 John Wiley & Sons, Ltd.     

A convex optimization approach to adaptive stabilization of discrete‐time LTI systems with polytopic uncertainties

This paper suggests a simple convex optimization approach to state‐feedback adaptive stabilization problem for a class of discrete‐time LTI systems subject to polytopic uncertainties. The proposed method relies on estimating the uncertain parameters by solving an online optimization at each time step, such as a linear or quadratic programming, and then, on tuning the control law with that information, which can be conceptually viewed as a kind of gain‐scheduling or indirect adaptive control. Specifically, an admissible domain of stabilizing state‐feedback gain matrices is designed offline by means of linear matrix inequality problems, and based on the online estimation of the uncertain parameters, the state‐feedback gain matrix is calculated over the set of stabilizing feedback gains. The proposed stabilization algorithm guarantees the asymptotic stability of the overall closed‐loop control system. An example is given to show the effectiveness of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Fault estimation and accommodation for networked control systems with nonuniform sampling periods

This paper deals with the problem of fault estimation and accommodation for a class of networked control systems with nonuniform uncertain sampling periods. Firstly, the reason why the adaptive fault diagnosis observer cannot be applied to networked control systems is analyzed. Based on this analysis, a novel robust fault estimation observer is constructed to estimate both continuous‐time fault and system states by using nonuniformly discrete‐time sampled outputs. Furthermore, using the obtained states and fault information, a nonuniformly sampled‐data fault tolerant control law is designed to preserve the stability of the closed‐loop system. The proposed scheme can not only guarantee the impact of continuous‐time uncertainties and discrete‐time sampled estimation errors on the faulty system to satisfy a H _∞ performance index but also repress the negative effect of the unknown intersample behavior of continuous‐time fault by use of an inequality technique. Finally, simulation results are included to demonstrate the feasibility of the proposed method. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust adaptive MPC for constrained uncertain nonlinear systems

In this paper, we consider the problem of adaptive model predictive control subject to exogenous disturbances. Using a novel set‐based adaptive estimation, the problem of robust adaptive MPC is proposed and solved for a class of linearly parameterized uncertain nonlinear systems subject to state and input constraints. Two formulations of the adaptive MPC routine are proposed. A general minmax approach is considered. A Lipschitz‐based formulation is also proposed. The closed‐loop robust stability of both approaches is demonstrated. The Lipschitz‐based approach avoids the need for a minmax optimization problem and is amenable to real‐time computation. A simple chemical reactor simulation example is presented that demonstrates the effectiveness of the technique. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust input‐output finite‐time filtering for uncertain Markovian jump nonlinear systems with partially known transition probabilities

In this paper, the robust input‐output finite‐time filtering problem is addressed for a class of uncertain Markovian jump nonlinear systems with partially known transition probabilities. Here, the disturbances, uncertainties, state delay, and distributed delays are all taken into account. Both the stochastic finite‐time boundedness and the stochastic input‐output finite‐time stability are introduced to the Markovian jump nonlinear systems with partially known transition probabilities. By constructing a reasonable stochastic Lyapunov functional and using linear matrix inequality techniques, sufficient conditions are established to guarantee the filtering error systems are stochastic finite‐time bounded and stochastic input‐output finite‐time stable, respectively. Finally, 2 examples are provided to illustrate the effectiveness of the proposed methods.     

Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation

A decentralized prescribed performance adaptive tracking control problem is investigated for Markovian jump uncertain nonlinear interconnected large‐scale systems. The considered interconnected large‐scale systems contain unknown nonlinear uncertainties, unknown control gains, actuator saturation, and Markovian jump signals, and the Markovian jump subsystems are in the form of triangular structure. First, by defining a novel state transformation with the performance function, the prescribed performance control problem is transformed to stabilization problem. Then, introducing an intermediate control signal into the control design, employing neural network to approximate the unknown composite nonlinear function, and based on the framework of the backstepping control design and adaptive estimation method, a corresponding decentralized prescribed performance adaptive tracking controller is designed. It is proved that all the signals in the closed‐loop system are bounded, and the prescribed tracking performances are guaranteed. A numerical example is provided to illustrate the effectiveness of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive control for nonlinear uncertain systems with actuator amplitude and rate saturation constraints

A direct adaptive nonlinear tracking control framework for multivariable nonlinear uncertain systems with actuator amplitude and rate saturation constraints is developed. To guarantee asymptotic stability of the closed‐loop tracking error dynamics in the face of amplitude and rate saturation constraints, the control signal to a given reference (governor or supervisor) system is modified to effectively robustify the error dynamics to the saturation constraints. Illustrative numerical examples are provided to demonstrate the efficacy of the proposed approach. Copyright © 2008 John Wiley & Sons, Ltd.     

Adaptive set‐point regulation of discrete‐time nonlinear systems

In this paper, adaptive set‐point regulation controllers for discrete‐time nonlinear systems are constructed. The system to be controlled is assumed to have a parametric uncertainty, and an excitation signal is used in order to obtain the parameter estimate. The proposed controller belongs to the category of indirect adaptive controllers, and its construction is based on the policy of calculating the control input rather than that of obtaining a control law. The proposed method solves the adaptive set‐point regulation problem under the assumption that the target state is reachable for each fixed parameter value. Additional feature of the proposed method is that Lyapunov‐like functions have not been used in the construction of the controllers. Copyright © 2015 John Wiley & Sons, Ltd.     

Predictor‐based adaptive dynamic surface control for consensus of uncertain nonlinear systems in strict‐feedback form

This paper investigates the leader–follower consensus problem of uncertain nonlinear systems in strict‐feedback form. By parameterizations of unknown nonlinear dynamics of the agents, an adaptive dynamic surface control with the aid of predictors, tracking differentiators is proposed to realize output consensus of the multi‐agent systems. Unlike the existing adaptive consensus methods, the predictor errors are used to learn the unknown parameters, which can achieve fast learning without high‐frequency signals in control inputs. As a fast precise signal filter, the tracking differentiator is used in the control design instead of first‐order filters, which can further improve the control performance. Based on graph theory and Lyapunov stability theory, it is shown that the outputs of all followers ultimately synchronize to that of the leader with bounded tracking errors. Simulation results are provided to validate the effectiveness and advantage of the proposed consensus algorithm. Copyright © 2016 John Wiley & Sons, Ltd.     

Neural network based terminal iterative learning control for uncertain nonlinear non‐affine systems

In this paper, a novel neural network based terminal iterative learning control method is proposed for a class of uncertain nonlinear non‐affine systems to track run‐varying reference point with initial state variance. In this new control scheme, the non‐affine terminal dynamics are converted affine, and the unrealisable recurrent network is simplified into realisable static network. As a result, the effect of initial state and control signal on terminal output can be estimated by neural network. With this estimation, the proposed control scheme can drive nonlinear non‐affine systems to track run‐varying reference point in the presence of initial state variance. Stability and convergence of this approach are proven, and numerical simulation results are provided to verify its effectiveness.     

An adaptive switching scheme for uncertain discrete time‐delay systems

In this paper, an adaptive switching control algorithm is proposed for the stabilization of uncertain discrete‐time systems with time‐varying delay. It is assumed that the time delay is unknown and time varying, nonetheless bounded with a known bound. It is supposed that the system is highly uncertain, and that a set of controllers are designed (off‐line) to stabilize the system in the whole uncertain parameter space; subsequently, a switching scheme is developed to stabilize the uncertain time‐delay system. A thorough stability analysis for the uncertain time‐delay system under the mentioned control scheme is provided. Furthermore, an upper bound on the allowable rate of change of the system parameters and delay is obtained. Simulation results are presented to show the efficacy of the proposed switching scheme. Copyright © 2008 John Wiley & Sons, Ltd.     

A 3D finite element analysis of large‐scale nonlinear dynamic electromagnetic problems by harmonic balancing and domain decomposition

The dual–primal finite element tearing and interconnecting (FETI‐DP) method is applied together with the harmonic balance method and the fixed‐point (FP) method to improve the efficiency of three‐dimensional finite element analysis of large‐scale nonlinear dynamic electromagnetic problems. The FETI‐DP method decomposes the original problem into smaller subdomains problems. Combined with parallel computing techniques, the total computation time can be reduced significantly. To account for nonlinear B‐H characteristics, the FP method is applied together with the polarization formulation. Because the FP method assumes a constant reluctivity, it decouples the systems of different harmonics. The FETI‐DP method can then be applied to speed up the simulation of each harmonic in each FP iteration. Two benchmark problems and a three‐phase inductor are simulated by the proposed method to validate the formulation and demonstrate its performance. Copyright © 2015 John Wiley & Sons, Ltd.     

Threshold computation for fault detection in linear discrete‐time Markov jump systems

This paper proposes a threshold computation scheme for an observer‐based fault detection (FD) in linear discrete‐time Markovian jump systems. An observer‐based FD scheme typically consists of two stages known as residual generation and residual evaluation. Even information of faults is contained inside a residual signal, a decision of faults occurrence is consequently made by a residual evaluation stage, which consists of residual evaluation function and threshold setting. For this reason, a successful FD strongly depends on a threshold setting for a given residual evaluation function. In this paper, Kalman filter (KF) is used as a residual generator. Based on an accessibility of Markov chain to KF, two types of residual generations are considered, namely mode‐dependent and mode‐independent residual generation. After that threshold is computed in a residual evaluation stage such that a maximum fault detection rate is achieved, for a given false alarm rate. Without any knowledge of a probability density function of residual signal before and after fault occurrence, a threshold is computed by using an estimation of residual evaluation function variance in a fault‐free case. Finally, a detection performance is demonstrated by a numerical example. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive observer for a class of nonlinear systems with time‐varying delays

The adaptive observer design problems have been extensively studied in literature for both linear and nonlinear systems. Some researches have also been carried out on adaptive observer design for linear time‐delay systems, but there is no significant work on adaptive observer design for nonlinear time‐delay systems. In this work, the adaptive observer design problem for a class of nonlinear time‐delay systems is considered. The observer is designed for the nonlinear systems whose nonlinear functions satisfy Lipschitz condition. Like conventional adaptive observers for the systems without time delays, this observer also estimates both states and unknown parameters simultaneously. For this property, it will be very much useful for many real‐time systems where time delays cannot be avoided. The sufficient conditions for existence of the observer are derived using the linear matrix inequality approach. With the help of a numerical example, effectiveness of the proposed observer is demonstrated. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive control for high‐order time‐delay uncertain nonlinear system and application to chemical reactor system

This paper focuses on global adaptive state‐feedback stabilization for a class of high‐order uncertain nonlinear systems with multiple delays. Restriction on system growth is relaxed. Two dynamic gains are introduced to deal with uncertainty and nonlinear growth rate of the system. Without precise information about time‐delay being needed and only by like Lyapunov function, a new control strategy is presented based on homogeneous domination idea and two necessary transformations. As an application, the developed scheme is utilized to control design of a two‐stage chemical reactor with delayed recycle streams. Copyright © 2014 John Wiley & Sons, Ltd.     

Adaptive neural network control for stochastic constrained block structure nonlinear systems with dynamical uncertainties

Stochastic adaptive dynamic surface control is presented for a class of uncertain multiple‐input–multiple‐output (MIMO) nonlinear systems with unmodeled dynamics and full state constraints in this paper. The controller is constructed by combining the dynamic surface control with radial basis function neural networks for the MIMO stochastic nonlinear systems. The nonlinear mapping is applied to guarantee the state constraints being not violated. The unmodeled dynamics is disposed through introducing an available dynamic signal. It is proved that all signals in the closed‐loop system are bounded in probability and the error signals are semiglobally uniformly ultimately bounded in mean square or the sense of four‐moment and the state constraints are confirmed in probability. Simulation results are offered to further illustrate the effectiveness of the control scheme.