Event-triggered optimal tracking control of multiplayer unknown nonlinear systems via adaptive critic designs

In this article, the event-triggered optimal tracking control problem for multiplayer unknown nonlinear systems is investigated by using adaptive critic designs. By constructing a neural network (NN)-based observer with input–output data, the system dynamics of multiplayer unknown nonlinear systems is obtained. Subsequently, the optimal tracking control problem is converted to an optimal regulation problem by establishing a tracking error system. Then, the optimal tracking control policy for each player is derived by solving coupled event-triggered Hamilton-Jacobi (HJ) equation via a critic NN. Meanwhile, a novel weight updating rule is designed by adopting concurrent learning method to relax the persistence of excitation (PE) condition. Moreover, an event-triggering condition is designed by using Lyapunov's direct method to guarantee the uniform ultimate boundedness (UUB) of the closed-loop multiplayer systems. Finally, the effectiveness of the developed method is verified by two different multiplayer nonlinear systems.     

Robust nonovershooting tracking control for fractional‐order systems

A robust tracking control is proposed for the fractional‐order systems (FOSs) to achieve a tracking response with no overshoot, even in the presence of a class of disturbances. The control proposed makes use of a newly designed integral sliding mode technique for FOSs, which is capable of rejecting the bounded disturbances acting through the input channel. The proposed integral sliding mode control design has two components: a nominal control component and a discontinuous control component. The overshoot in the system response is avoided by the nominal control designed with the use of Moore's eigenstructure assignment algorithm. The sliding mode technique is used for the design of discontinuous part of the control that imparts the desired robustness properties.     

Data‐based optimal Denial‐of‐Service attack scheduling against robust control based on Q‐learning

Attack optimization is an important issue in securing cyber‐physical systems. This paper investigates how an attacker should schedule its denial‐of‐service attacks to degrade the robust performance of a closed‐loop system. The measurements of system states are transmitted to a remote controller over a multichannel network. With limited resources, the attacker only has the capacity to jam sparse channels and to decide which channels should be attacked. Under an framework, a data‐based optimal attack strategy that uses Q‐learning is proposed to maximize the effect on the closed‐loop system. The Q‐learning algorithm can adaptively learn the optimal attack using data sniffed over the wireless network without requiring a priori knowledge of system parameters. Simulation results sustain the performance of the proposed attack scenario.     

Robust adaptive tracking of uncertain nonlinear systems by output feedback

We investigate the problem of robust adaptive tracking by output feedback for a class of uncertain nonlinear systems. Based on the high‐gain scaling technique and a new adaptive law, a linear‐like output feedback controller is constructed. Only one dynamic gain is designed, which makes the controller easier to implement. Furthermore, by modifying the update law, the adaptive controller is robust to bounded external disturbance and is able to guarantee the convergence of the output tracking error to an arbitrarily small residual set. A numerical example is used to illustrate the effectiveness of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust consensus tracking for a class of heterogeneous second‐order nonlinear multi‐agent systems

This paper deals with the robust consensus tracking problem for a class of heterogeneous second‐order nonlinear multi‐agent systems with bounded external disturbances. First, a distributed adaptive control law is proposed based on the relative position and velocity information. It is shown that for any connected undirected communication graph, the proposed control law solves the robust consensus tracking problem. Then, by introducing a novel distributed observer and employing backstepping design techniques, a distributed adaptive control law is constructed based only on the relative position information. Compared with the existing results, the proposed adaptive consensus protocols are in a distributed fashion, and the nonlinear functions are not required to satisfy any globally Lipschitz or Lipschitz‐like condition. Numerical examples are given to verify our proposed protocols. Copyright © 2014 John Wiley & Sons, Ltd.     

Robust practical output regulation for a class of uncertain linear minimum‐phase systems by output‐based event‐triggered control

In this paper, we consider the robust practical output regulation problem for a class of SISO uncertain linear minimum‐phase systems subject to external disturbances by an output‐based event‐triggered control law, where the reference inputs and the external disturbances are both generated by a so‐called exosystem with known dynamics. Our approach consists of two steps. First, on the basis of the internal model principle, we convert the problem into the robust practical stabilization problem of a well‐defined augmented system. Second, we design an output‐based event‐triggered mechanism and an output‐based event‐triggered control law to solve the stabilization problem, which in turn leads to the solvability of the original problem. What is more, we show that the event‐triggered mechanism prevents the Zeno behavior from happening. A numerical example is given to illustrate the design. Copyright © 2017 John Wiley & Sons, Ltd.     

Robust trajectory tracking: differential game/cheap control approach

A robust trajectory tracking problem is treated in the framework of a zero-sum linear-quadratic differential game of a general type. For the cheap control version of this game, a novel solvability condition is derived. The sufficient condition, guaranteeing that the tracking problem is solved by the optimal strategy of the minimiser in the cheap control game, is established. The boundedness of the time realisations of this strategy is analysed. An illustrative example is presented.     

An optimal control approach to robust tracking of linear systems

In our early work, we show that one way to solve a robust control problem of an uncertain system is to translate the robust control problem into an optimal control problem. If the system is linear, then the optimal control problem becomes a linear quadratic regulator (LQR) problem, which can be solved by solving an algebraic Riccati equation. In this article, we extend the optimal control approach to robust tracking of linear systems. We assume that the control objective is not simply to drive the state to zero but rather to track a non-zero reference signal. We assume that the reference signal to be tracked is a polynomial function of time. We first investigated the tracking problem under the conditions that all state variables are available for feedback and show that the robust tracking problem can be solved by solving an algebraic Riccati equation. Because the state feedback is not always available in practice, we also investigated the output feedback. We show that if we place the poles of the observer sufficiently left of the imaginary axis, the robust tracking problem can be solved. As in the case of the state feedback, the observer and feedback can be obtained by solving two algebraic Riccati equations.     

Output‐feedback adaptive consensus tracking control for a class of high‐order nonlinear multi‐agent systems

In this paper, an output‐feedback adaptive consensus tracking control scheme is proposed for a class of high‐order nonlinear multi‐agent systems. The agents are allowed to have unknown parameters, unknown nonlinearities, and input quantization simultaneously. The desired trajectory to be tracked is available for only a subset of agents, and only the relative outputs and the quantized inputs need to be measured or transmitted as signal exchange among neighbors regardless of the system order. By introducing a kind of high‐gain K‐filters and a smooth function, the effect among agents caused by the unknown nonlinearities is successfully counteracted, and all closed‐loop signals are proved to be globally uniformly bounded. Moreover, it is shown that the tracking errors converge to a residual set that can be made arbitrarily small. Simulation results on robot manipulators are presented to illustrate the effectiveness of the proposed scheme. Copyright © 2017 John Wiley & Sons, Ltd.     

Data‐driven optimal event‐triggered consensus control for unknown nonlinear multiagent systems with control constraints

This paper considers optimal consensus control problem for unknown nonlinear multiagent systems (MASs) subjected to control constraints by utilizing event‐triggered adaptive dynamic programming (ETADP) technique. To deal with the control constraints, we introduce nonquadratic energy consumption functions into performance indices and formulate the Hamilton‐Jacobi‐Bellman (HJB) equations. Then, based on the Bellman's optimality principle, constrained optimal consensus control policies are designed from the HJB equations. In order to implement the ETADP algorithm, the critic networks and action networks are developed to approximate the value functions and consensus control policies respectively based on the measurable system data. Under the event‐triggered control framework, the weights of the critic networks and action networks are only updated at the triggering instants which are decided by the designed adaptive triggered conditions. The Lyapunov method is used to prove that the local neighbor consensus errors and the weight estimation errors of the critic networks and action networks are ultimately bounded. Finally, a numerical example is provided to show the effectiveness of the proposed ETADP method.     

Adaptive output‐feedback tracking for nonlinear systems with rather general control coefficients

This paper studies the problem of global practical tracking by output feedback for a class of uncertain nonlinear systems with unmeasured state‐dependent growth and unknown time‐varying control coefficients. Compared with the closely related works, the remarkableness of this paper is that the upper and lower bounds of unknown control coefficients are not required to be known a priori. Motivated by our recent works, by combining the methods of universal control and deadzone with the backstepping technique and skillfully constructing a novel Lyapunov function, we propose a new adaptive tracking control scheme with appropriate design parameters. The new scheme guarantees that the state of the resulting closed‐loop system is globally bounded while the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time. Two examples, including a practical example, are given to illustrate the effectiveness of the theoretical results.     

Robust adaptive fault‐tolerant tracking control for uncertain linear systems with time‐varying performance bounds

In this paper, the problem of robust adaptive fault‐tolerant tracking control with time‐varying performance bounds is investigated for a class of linear systems subject to parameter uncertainties, external disturbances and actuator failures. In order to ensure the norm of the tracking error less than the user‐defined time‐varying performance bounds, we propose a new control strategy which is predicated on the generalized restricted potential function. Compared with the existing result, a novel method which provides two design freedoms is developed to reduce the tracking error. According to the online estimation information provided by adaptive mechanism, a fault‐tolerant tracking control method guaranteeing time‐varying performance bounds is developed for robust tracking of reference model. It is shown that the closed‐loop signals are bounded and the tracking error within an a priori given, time‐varying performance bounds. A simulation result is provided to demonstrate the efficacy of the proposed fault‐tolerant tracking control method.     

Robust output feedback learning control for induction motor servo drives

This paper addresses the output feedback tracking control problem for induction motor servo drives with mechanical uncertainties: rotor angle, rotor speed and stator currents are assumed to be available for feedback. A robust adaptive learning control is designed under the assumption that the reference profile for the rotor angle is periodic with known period: it ‘learns’ the periodic disturbance signal by identifying the Fourier coefficients of any truncated approximation; ??₂ and ??_∞ transient performances are guaranteed in the ‘learning phase’. It is shown that, for any motor initial condition belonging to an arbitrary given compact set, by properly setting the control parameters: (i) the rotor position and flux modulus tracking errors exponentially converge to residual sets, which may be arbitrarily reduced by increasing the number of terms in the truncated Fourier series; (ii) when the unknown periodic disturbance can be represented by a finite Fourier series, the rotor position and flux modulus tracking errors exponentially converge to zero. As in field oriented‐control, the control algorithm generates references for the magnetizing flux component and for the torque component of the stator current leading to significant simplifications for current‐fed motors. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust adaptive fault‐tolerant tracking control of multiple time‐delays systems with mismatched parameter uncertainties and actuator failures

This study deals with the problem of robust adaptive fault‐tolerant tracking for uncertain systems with multiple delayed state perturbations, mismatched parameter uncertainties, external disturbances, and actuator faults including loss of effectiveness, outage, and stuck. It is assumed that the upper bounds of the delayed state perturbations, the external disturbances and the unparameterizable time‐varying stuck faults are unknown. Then, by estimating online such unknown bounds and on the basis of the updated values of these unknown bounds from the adaptive mechanism, a class of memoryless state feedback fault‐tolerant controller with switching signal function is constructed for robust tracking of dynamical signals. Furthermore, by making use of the proposed adaptive robust tracking controller, the tracking error can be guaranteed to be asymptotically zero in spite of multiple delayed state perturbations, mismatched parameter uncertainties, external disturbances, and actuator faults. In addition, it is also proved that the solutions with tracking error of resulting adaptive closed‐loop system are uniformly bounded. Finally, a simulation example for B747‐100/200 aircraft system is provided to illustrate the efficiency of the proposed fault‐tolerant design approach. Copyright © 2014 John Wiley & Sons, Ltd.     

离散非线性零和博弈的事件驱动最优控制方案

在求解离散非线性零和博弈问题时,为了在有效降低网络通讯和控制器执行次数的同时保证良好的控制效果,本文提出了一种基于事件驱动机制的最优控制方案.首先,设计了一个采用新型事件驱动阈值的事件驱动条件,并根据贝尔曼最优性原理获得了最优控制对的表达式.为了求解该表达式中的最优值函数,提出了一种单网络值迭代算法.利用一个神经网络构建评价网.设计了新的评价网权值更新规则.通过在评价网、控制策略及扰动策略之间不断迭代,最终获得零和博弈问题的最优值函数和最优控制对.然后,利用Lyapunov稳定性理论证明了闭环系统的稳定性.最后,将该事件驱动最优控制方案应用到了两个仿真例子中,验证了所提方法的有效性.     

Event‐triggered optimal tracking control of nonlinear systems

We propose a novel event‐triggered optimal tracking control algorithm for nonlinear systems with an infinite horizon discounted cost. The problem is formulated by appropriately augmenting the system and the reference dynamics and then using ideas from reinforcement learning to provide a solution. Namely, a critic network is used to estimate the optimal cost while an actor network is used to approximate the optimal event‐triggered controller. Because the actor network updates only when an event occurs, we shall use a zero‐order hold along with appropriate tuning laws to encounter for this behavior. Because we have dynamics that evolve in continuous and discrete time, we write the closed‐loop system as an impulsive model and prove asymptotic stability of the equilibrium point and Zeno behavior exclusion. Simulation results of a helicopter, a one‐link rigid robot under gravitation field, and a controlled Van‐der‐Pol oscillator are presented to show the efficacy of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

Robust plant by plant control design using model‐error tracking sets

This paper presents a method for designing a robust two‐degree‐of‐freedom control scheme, capable of satisfying multiple model‐error specifications on a plant by plant basis. Traditional quantitative feedback theory methods generally use a single model‐error or above‐below magnitude tracking specification, which can result in overdesign for plants located away from the bounding conditions. The performance specifications are also generally hand‐tuned, or iteratively adjusted to keep the underlying time‐domain signals within permissible levels. Our method aims to perform a model‐error design on a per‐plant basis, such that each plant's corresponding model tracking has equal weighting given the plant's inherent feedback requirements and capability. The quantitative feedback theory method allows this per‐plant approach to be undertaken with ease. Additionally, sufficiently low‐order model specifications are designed using simple optimisation, which take into account performance limiting effects, such as non‐minimum phase behaviour and signal constraints. A worked example is presented, showing the viability and transparency of the proposed method.     

Adaptive optimal dynamic surface control of strict‐feedback nonlinear systems with output constraints

In this paper, an adaptive optimal control strategy is proposed for a class of strict‐feedback nonlinear systems with output constraints by using dynamic surface control. The controller design procedure is divided into two parts. One is the design of feedforward controller and the other is the design of optimal controller. To guarantee the satisfaction of output constraints in feedforward controller, nonlinear mapping is utilized to transform the constrained system into an unconstrained system. Neural‐network based adaptive dynamic programming algorithm is employed to approximate the optimal cost function and the optimal control law. By theoretical analysis, all the signals in the closed‐loop system are proved to be semi‐globally uniformly ultimately bounded and the output constraints are not violated. A numerical example illustrates the effectiveness of the proposed scheme.