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.     

Output feedback regulation of upper triangular nonlinear systems with uncertain time‐varying delays in states and input

In this paper, an output feedback controller is studied to regulate a class of upper triangular nonlinear systems with uncertain time‐varying delays. The key features of our considered system are that there are uncertain time‐varying delays in both states and input and the high‐order nonlinearity is in a more relaxed form over the previous results. Theoretical analysis and numerical example are presented to show the benefits of our controller. Copyright © 2017 John Wiley & Sons, Ltd.     

An Intelligent Robust Tracking Control for a Class of Electrically Driven Mobile Robots

This paper addresses the problem of designing robust tracking control for a class of uncertain wheeled mobile robots actuated by brushed direct current motors. This class of electrically‐driven mechanical systems consists of the robot kinematics, the robot dynamics, and the wheel actuator dynamics. Via the backstepping technique, an intelligent robust tracking control scheme that integrates a kinematic controller and an adaptive neural network‐based (or fuzzy‐based) controller is developed such that all of the states and signals of the closed‐loop system are bounded and the tracking error can be made as small as possible. Two adaptive approximation systems are constructed to learn the behaviors of unknown mechanical and electrical dynamics. The effects of both the approximation errors and the unmodeled time‐varying perturbations in the input and virtual‐input weighting matrices are counteracted by suitably tuning the control gains. Consequently, the robust control scheme developed here can be employed to handle a broader class of electrically‐driven wheeled mobile robots in the presence of high‐degree time‐varying uncertainties. Finally, a simulation example is given to demonstrate the effectiveness of the developed control scheme.     

Application of nonlinear time–scaling for robust controller design of reaction systems

Even though the basic mechanisms of operation of reaction systems are relatively simple the dynamical models obtained from first principles are complex and contain highly uncertain terms. To develop reliable model‐based controllers it is therefore necessary to simplify the system dynamics preserving the features which are essential for control. Towards this end, co‐ordinate transformations identifying the states which are dependent/independent of the reactions and flows have been reported in the literature. This has allowed, for instance, the design of observers which are insensitive to the (usually unknown) reaction functions. The main contribution of this paper is to show the utility of nonlinear state‐dependent time‐scaling to simplify the system dynamics, and consequently the controller design. In particular, we show that with time‐scaling and an input transformation we can reveal the existence of attractive invariant manifolds, which allows us to reduce the dimension of the system. As an application we study the well‐known fourth order baker's yeast fed‐batch fermentation process model, whose essential dynamics is captured by a planar system perturbed by an exponentially decaying term. We then exploit this particular structure to design, with reduced control authority, a nonlinear asymptotically stabilizing control law which is robust with respect to the reaction function. Copyright © 2001 John Wiley & Sons, Ltd.     

Global finite‐time stabilization via time‐varying output‐feedback for uncertain nonlinear systems with unknown growth rate

This paper considers the global finite‐time output‐feedback stabilization for a class of uncertain nonlinear systems. Comparing with the existing related literature, two essential obstacles exist: On the one hand, the systems in question allow serious parametric unknowns and serious time variations coupling to the unmeasurable states, which is reflected in that the systems have the unmeasurable states dependent growth with the rate being an unknown constant multiplying a known continuous function of time. On the other hand, the systems possess remarkably inherent nonlinearities, whose growth allows to be not only low‐order but especially high‐order with respect to the unmeasurable states. To effectively cope with these obstacles, we established a time‐varying output‐feedback strategy to achieve the finite‐time stabilization for the systems under investigation. First, a time‐varying state‐feedback controller is constructed by adding an integrator method, and by homogeneous domination approach, a time‐varying reduced‐order observer is designed to precisely rebuild the unmeasurable states. Then, by certainty equivalence principle, a desired time‐varying output‐feedback controller is constructed for the systems. It is shown that, as long as the involved time‐varying gain is chosen fast enough to overtake the serious parametric unknowns and the serious time variations, the output‐feedback controller renders that the closed‐loop system states converge to zero in finite time. Copyright © 2017 John Wiley & Sons, Ltd.     

A robust constrained model predictive control scheme for norm‐bounded uncertain systems with partial state measurements

A robust model predictive control scheme for a class of constrained norm‐bounded uncertain discrete‐time linear systems is developed under the hypothesis that only partial state measurements are available for feedback. The proposed strategy involves a two‐phase procedure. Initialization phase is devoted to determining an admissible, though not optimal, linear memoryless controller capable to formally address the input rate constraint; then, during on‐line phase, predictive capabilities complement the designed controller by means of N steps free control actions in a receding horizon fashion. These additive control actions are obtained by solving semidefinite programming problems subject to linear matrix inequalities constraints. As computational burden grows linearly with the control horizon length, an example is developed to show the effectiveness of the proposed approach for realistic control problems: the design of a flight control law for a flexible unmanned over‐actuated aircraft, where the states of the flexibility dynamics are not measurable, is discussed, and a numerical implementation of the controller within a nonlinear simulation environment testifies the validity of the proposed approach and the possibility to implement the algorithm on an onboard computer.     

Robust flow control in data‐communication networks with multiple time‐delays

Robust controller design for a flow control problem where uncertain multiple time‐varying time‐delays exist is considered. Although primarily data‐communication networks are considered, the presented approach can also be applied to other flow control problems and can even be extended to other control problems where uncertain multiple time‐varying time‐delays exist. Besides robustness, tracking and fairness requirements are also considered. To solve this problem, an ??^∞ optimization problem is set up and solved. Unlike previous approaches, where only a suboptimal solution could be found, the present approach allows to design an optimal controller. Simulation studies are carried out in order to illustrate the time‐domain performance of the designed controllers. The obtained results are also compared to the results of a suboptimal controller obtained by an earlier approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Robust H∞ control of uncertain linear impulsive stochastic systems

This paper develops robust stability theorems and robust H_∞ control theory for uncertain impulsive stochastic systems. The parametric uncertainties are assumed to be time varying and norm bounded. Impulsive stochastic systems can be divided into three cases, namely, the systems with stable/stabilizable continuous‐time stochastic dynamics and unstable/unstabilizable discrete‐time dynamics, the systems with unstable/unstabilizable continuous dynamics and stable/stabilizable discrete‐time dynamics, and the systems in which both the continuous‐time stochastic dynamics and the discrete‐time dynamics are stable/stabilizable. Sufficient conditions for robust exponential stability and robust stabilization for uncertain impulsive stochastic systems are derived in terms of an average dwell‐time condition. Then, a linear matrix inequality‐based approach to the design of a robust H_∞ controller for each system is presented. Finally, the numerical examples are provided to demonstrate the effectiveness of the proposed approach. Copyright © 2007 John Wiley & Sons, Ltd.     

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.     

NETWORK‐INDUCED DELAY‐DEPENDENT H∞ CONTROLLER DESIGN FOR A CLASS OF NETWORKED CONTROL SYSTEMS

This paper is concerned with the problem of robust H_∞ controller design for a class of uncertain networked control systems (NCSs). The network‐induced delay is of an interval‐like time‐varying type integer, which means that both lower and upper bounds for such a kind of delay are available. The parameter uncertainties are assumed to be normbounded and possibly time‐varying. Based on Lyapunov‐Krasovskii functional approach, a robust H_∞ controller for uncertain NCSs is designed by using a sum inequality which is first introduced and plays an important role in deriving the controller. A delay‐dependent condition for the existence of a state feedback controller, which ensures internal asymptotic stability and a prescribed H_∞ performance level of the closed‐loop system for all admissible uncertainties, is proposed in terms of a nonlinear matrix inequality which can be solved by a linearization algorithm, and no parameters need to be adjusted. A numerical example about a balancing problem of an inverted pendulum on a cart is given to show the effectiveness of the proposed design method.     

Trigger‐based tracking control for a class of uncertain nonlinear systems via an event‐triggered extended state observer

An event‐triggered observer‐based output feedback control issue together with triggered input is investigated for a class of uncertain nonlinear systems subject to unknown external disturbances. Two separate event‐triggered conditions are located on the measurement channel and control channel, respectively. An event‐triggered extended state observer (ETESO) is employed to estimate unmeasurable states and compensate uncertainties and disturbances in real time while it is not required for real‐time output measurement. Then, combined with backstepping method and active disturbance rejection control, an output feedback control scheme is proposed, where an event‐triggered input is developed for reducing the communication rate between the controller and the actuator. The triggered instants are determined by a time‐varying event‐triggered condition. Two simulations, including a numerical example and an permanent‐magnet motor, are illustrated to verify the effectiveness of the proposed schemes.     

Global adaptive stabilization for high‐order uncertain time‐varying nonlinear systems with time‐delays

This paper focuses on the adaptive stabilization problem for a class of high‐order nonlinear systems with time‐varying uncertainties and unknown time‐delays. Time‐varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time‐delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state‐feedback controller is designed to guarantee that resulting closed‐loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Tracking control for sampled‐data systems with uncertain time‐varying sampling intervals and delays

In this paper, a solution to the approximate tracking problem of sampled‐data systems with uncertain, time‐varying sampling intervals and delays is presented. Such time‐varying sampling intervals and delays can typically occur in the field of networked control systems. The uncertain, time‐varying sampling and network delays cause inexact feedforward, which induces a perturbation on the tracking error dynamics, for which a model is presented in this paper. Sufficient conditions for the input‐to‐state stability (ISS) of the tracking error dynamics with respect to this perturbation are given. Hereto, two analysis approaches are developed: a discrete‐time approach and an approach in terms of delay impulsive differential equations. These ISS results provide bounds on the steady‐state tracking error as a function of the plant properties, the control design and the network properties. Moreover, it is shown that feedforward preview can significantly improve the tracking performance and an online extremum seeking (nonlinear programming) algorithm is proposed to online estimate the optimal preview time. The results are illustrated on a mechanical motion control example showing the effectiveness of the proposed strategy and providing insight into the differences and commonalities between the two analysis approaches. Copyright © 2009 John Wiley & Sons, Ltd.     

Global stabilization of uncertain stochastic nonlinear time‐delay systems by output feedback

Constructive control techniques have been proposed for controlling strict feedback (lower triangular form) stochastic nonlinear systems with a time‐varying time delay in the state. The uncertain nonlinearities are assumed to be bounded by polynomial functions of the outputs multiplied by unmeasured states or delayed states. The delay‐independent output feedback controller making the closed‐loop system globally asymptotically stable is explicitly constructed by using a linear dynamic high‐gain observer in combination with a linear dynamic high‐gain controller. A simulation example is given to demonstrate the effectiveness of the proposed design procedure. Copyright © 2007 John Wiley & Sons, Ltd.     

Observer‐based controller for constrained uncertain stochastic nonlinear discrete‐time systems

In this paper, an observer‐based control approach is proposed for uncertain stochastic nonlinear discrete‐time systems with input constraints. The widely used extended Kalman filter (EKF) is well known to be inadequate for estimating the states of uncertain nonlinear dynamical systems with strong nonlinearities especially if the time horizon of the estimation process is relatively long. Instead, a modified version of the EKF with improved stability and robustness is proposed for estimating the states of such systems. A constrained observer‐based controller is then developed using the state‐dependent Riccati equation approach. Rigorous analysis of the stability of the developed stochastically controlled system is presented. The developed approach is applied to control the performance of a synchronous generator connected to an infinite bus and chaos in permanent magnet synchronous motor. Simulation results of the synchronous generator show that the estimated states resulting from the proposed estimator are stable, whereas those resulting from the EKF diverge. Moreover, satisfactory performance is achieved by applying the developed observer‐based control strategy on the two practical problems. Copyright © 2015 John Wiley & Sons, Ltd.     

Synchronized adaptive control for coordinating manipulators with time‐varying actuator constraint and uncertain dynamics

This paper addresses the control issue for cooperative visual servoing manipulators on strongly connected graph with communication delays, in which case that the uncertain robot dynamics and kinematics, uncalibrated camera model, and actuator constraint are simultaneously considered. An adaptive cooperative image‐based approach is established to overcome the control difficulty arising from nonlinear coupling between visual model and robot agents. To estimate the coupled camera‐robot parameters, a novel adaptive strategy is developed and its superiority mainly lies in the containment of both individual image‐space errors and the synchronous errors among networked robots; thus, the cooperative performance is significantly strengthened. Moreover, the proposed cooperative controller with a Nussbaum‐type gain is implemented to both globally stabilize the closed‐loop systems and realize the synchronization control objective under the existence of unknown and time‐varying actuator constraint. Finally, simulations are carried out to validate the developed approach.     

Adaptive Robust Output Tracking Control of Uncertain Nonlinear Cascade Systems with Disturbance and Multiple Unknown Time‐Varying Delays

In this paper, an adaptive robust controller is designed for a class of uncertain nonlinear cascade systems with multiple time‐varying delays under external disturbance. It is assumed that multiple time‐varying delays are not exactly known and, therefore, the delayed terms must not appear in the adaptation and control laws. Accordingly, by using a Lyapunov‐Krasovskii function, delays are deleted from the adaptation and control laws. A controller based on an adaptive backstepping approach is designed to assure the global asymptotic tracking of the desired output and boundedness of the other states. The proposed controller is proved to be robust against unknown time‐varying delays and external disturbances applying to the system. Simulation results are provided to show the effectiveness of the proposed approach.     

Robust control of a family of uncertain nonminimum‐phase systems via continuous‐time and sampled‐data output feedback

The problem of global robust stabilization is studied by both continuous‐time and sampled‐data output feedback for a family of nonminimum‐phase nonlinear systems with uncertainty. The uncertain nonlinear system considered in this paper has an interconnect structure consisting of a driving system and a possibly unstable zero dynamics with uncertainty, ie, the uncertain driven system. Under a linear growth condition on the uncertain zero dynamics and a Lipschitz condition on the driving system, we show that it is possible to globally robustly stabilize the family of uncertain nonminimum‐phase systems by a single continuous‐time or a sampled‐data output feedback controller. The sampled‐data output feedback controller is designed by using the emulated versions of a continuous‐time observer and a state feedback controller, ie, by holding the input/output signals constant over each sampling interval. The design of either continuous‐time or sampled‐data output compensator uses only the information of the nominal system of the uncertain controlled plant. In the case of sampled‐data control, global robust stability of the hybrid closed‐loop system with uncertainty is established by means of a feedback domination method together with the robustness of the nominal closed‐loop system if the sampling time is small enough.     

Parameterizing robust manipulator controllers under approximate inverse dynamics: A double‐Youla approach

We consider the goal of ensuring robust stability when a given manipulator feedback control law is modified online, for example, to safely improve the performance by a learning module. To this end, the factorization approach is applied to both the plant and controller models to characterize robustly stabilizing controllers for rigid‐body manipulators under approximate inverse dynamics control. Outer‐loop controllers to stabilize the nonlinear uncertain loop that results from approximate inverse dynamics are often derived by lumping uncertainty in a single term and subsequent analysis of the error system. Here, by contrast, the well‐known norm bounds of these uncertain dynamics are first recast into a generalized plant configuration that preserves the characteristic uncertainty structure. Then, the overall loop uncertainty is expressed with respect to the nominal outer‐loop feedback controller by means of an uncertain dual‐Youla operator. Therefore, using the dual‐Youla parameterization, we provide a novel way to rigorously quantify permissible perturbations of robot manipulator feedforward/feedback controllers. The method proposed in this paper does not constitute another robust control law for rigid‐body manipulators, but rather a characterization of a set of robustly stabilizing controllers. The resulting double‐Youla parameterization for the control of robot manipulators is amenable to numerous advanced design methods. The result is thoroughly discussed by a planar elbow manipulator and exemplified with a six‐degree‐of‐freedom robot scenario with varying payload.