Fixed time event-triggered control for high-order nonlinear uncertain systems with time-varying full state constraints

The fixed time event-triggered control for high-order nonlinear uncertain systems with time-varying full state constraints is investigated in this paper. First, the event-triggered control (ETC) mechanism is introduced to reduce the data transmission in the communication channel. In consideration of the physical constraints and engineering requirements, time-varying barrier Lyapunov function (BLF) is deployed to make all the system states confined in the given time-varying constraints. Then, the radial basis function neural networks (RBF NNs) are used to approximate the unknown nonlinear terms. Further, the fixed time stability strategy is deployed to make the system achieve semiglobal practical fixed time stability (SPFTS) and the convergence time is independent of the initial conditions. Finally, the proposed control scheme is verified by two simulation examples.     

Hybrid threshold strategy‐based adaptive tracking control for nonlinear stochastic systems with full‐state constraints

This article focuses on the adaptive tracking control problem for a class of interconnected nonlinear stochastic systems under full‐state constraints based on the hybrid threshold strategy. Different from the existing works, we propose a novel pre‐constrained tracking control algorithm to deal with the full‐state constraint problem. First, a novel nonlinear transformation function and a new coordinate transformation are developed to constrain state variables, which can directly cope with asymmetric state constraints. Second, the hybrid threshold strategy is constructed to provide a reasonable way in balancing system performance and communication constraints. By the use of dynamic surface control technique and neural network approximate technique, a smooth pre‐constrained tracking controller with adaptive laws is designed for the interconnected nonlinear stochastic systems. Moreover, based on the Lyapunov stability theory, it is proved that all state variables are successfully pre‐constrained within asymmetric boundaries. Finally, a simulation example is presented to verify the effectiveness of proposed control algorithm.     

Adaptive neural control for multiagent systems with asymmetric time‐varying state constraints and input saturation

This article investigates the leader‐follower consensus problem of a class of non‐strict‐feedback nonlinear multiagent systems with asymmetric time‐varying state constraints (ATVSC) and input saturation, and an adaptive neural control scheme is developed. By introducing the distributed sliding‐mode estimator, each follower can obtain the estimation of leader's trajectory and track it directly. Then, with the help of time‐varying asymmetric barrier Lyapunov function and radial basis function neural networks, the controller is designed based on backstepping technique. Furthermore, the mean‐value theorem and Nussbaum function are utilized to address the problems of input saturation and unknown control direction. Moreover, the number of adaptive laws is equal to that of the followers, which reduces the computational complexity. It is proved that the leader‐follower consensus tracking control is achieved without violating the ATVSC, and all closed‐loop signals are semiglobally uniformly ultimately bounded. Finally, the simulation results are provided to verify the effectiveness of the control scheme.     

Finite-time tracking control for strict-feedback nonlinear systems with full state constraints

In this paper, an adaptive finite-time controller is considered for a class of strict-feedback nonlinear systems with parametric uncertainties and full state constraints. Novel tan-type barrier Lyapunov functions are proposed to ensure the boundedness of the fictitious state tracking errors. A new tuning function is constructed to eliminate the effect of uncertainties by using the extended finite-time stability condition. It is shown that under the proposed backstepping control scheme the finite-time convergence of system output tracking error to a small set around zero is realised and the full state constraints are not violated. A numerical example is provided to demonstrate the effectiveness of the proposed finite-time control scheme.     

具有输入和输出约束的高阶随机系统神经网络控制

针对高阶非线性系统,开展自适应神经网络跟踪控制器设计,系统受到随机扰动的影响.首次把输入和输出约束问题引入到高阶系统的跟踪控制中,并假定系统动态是未知.首先借用高斯误差函数表达连续可微的非对称饱和模型以实现输入约束,和障碍Lyapunov函数保证系统输出受限;其次,针对高阶非线性系统,径向基函数(RBF)神经网络用来克服未知系统动态和随机扰动.在每一步的backstepping计算中,仅用到单一的自适应更新参数,从而克服了过参数问题;最后,基于Lyapunov稳定性理论提出自适应神经网络控制策略,并减少了学习参数.最终结果表明设计的控制器能保证所有闭环信号半全局最终一致有界,并能使跟踪误差收敛到零值小的邻域内.仿真研究进一步验证了提出方法的有效性.     

Adaptive dynamic surface control of nonaffine nonlinear system with time‐varying state constraints

This paper investigates the problem of adaptive dynamic surface control for pure‐feedback time‐varying state constrained nonaffine nonlinear system. A continuous and semibounded condition is proposed of nonaffine function to ensure that the system can be controlled, and the invariant set is introduced for this mild condition. By employing the dynamic surface control technique, the “complexity explosion” problem caused by backstepping technique is averted in developed control method. Robust compensators are devised to weaken poor effect of disturbances and uncertainties. The time‐varying barrier Lyapunov functions are adopted to dispose the problem of time‐varying state constrains. Moreover, it is proved that the whole closed‐loop signals are bounded, the tracking error can converge to a small neighborhood of zero, and the system states are insured to maintain in the predefined compact sets. Finally, some simulation results are provided to demonstrate the effectiveness of the proposed method.     

Nussbaum gain adaptive fuzzy control for switched nonlinear systems with predefined output and full time-varying states constraints

In this paper, the problem of adaptive fuzzy tracking control for a class of uncertain switched nonlinear systems with unknown control direction is studied. Aiming at the problem, an adaptive control scheme with Nussbaum gain technology is constructed by using the average dwell time (ADT) method and the backstepping method to overcome the unknown control direction, and time-varying asymmetric barrier Lyapunov functions (ABLFs) are adopted to ensure the full-state constraints satisfaction. The proposed control scheme guarantees that all closed-loop signals remain bounded under a class of switching signals with ADT, while the output tracking error converges to a small neighborhood of the zero. An important innovation of this design method is that the unknown control direction, asymmetric time-varying full state constraints, and predefined time-varying output requirements are simultaneously considered in uncertain switched nonlinear systems for the first time. We set a moment in advance, and make the systems comply with the constraint conditions before running the moment by the shift function nested in the first time-varying ABLF. Finally, a simulation example verifies the effectiveness of the proposed scheme.     

Finite time adaptive filter control of nonlinear systems with actuator faults and state constraints

The finite time adaptive filter control problem is studied for strict-feedback nonlinear systems with actuator faults and state constraints in this paper. First, with the aid of the backstepping technique, the controller and the adaptive laws are designed to compensate the actuator faults and parameter uncertainties. Then, the dynamic surface control is used to establish a first-order filter to alleviate computational burden for the reason of the derivative of virtual control laws. In addition, none of the system states violate predefined constraint boundaries by utilizing a log-type barrier Lyapunov function. Furthermore, the boundedness can be ensured for all the closed-loop signals, and better tracking performance of the system is obtained within a finite-time. Finally, the simulation examples are shown to prove the feasibility and effectiveness of the proposed strategy.     

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 fuzzy dynamic surface control for a class of stochastic MIMO discrete-time nonlinear pure-feedback systems with full state constraints

This paper presents the design of an adaptive fuzzy dynamic surface control for a class of stochastic MIMO discrete-time nonlinear pure-feedback systems with full state constraints using a set of noisy measurements. The design approach is described as follows. The nonlinear uncertainty is approximated by using the fuzzy logic system at the first stage, secondly the proposed adaptive fuzzy dynamic surface control is designed based on a new saturation function for full state constraints, thirdly the number of the adjustable parameters is reduced by using the simplified extended single input rule modules, and finally the simplified weighted least squares estimator is in a simplified structure designed to take the estimates for the un-measurable states and the adjustable parameters. The simulation provides that the proposed approach is effective for the improvement of the system performance.     

时变时滞随机非线性系统的自适应神经网络跟踪控制

针对一类具有时变时滞的不确定随机非线性严格反馈系统的自适应跟踪问题,利用Razumikhin引理和backstepping方法,提出一种新的自适应神经网络跟踪控制器.该控制器可保证闭环系统的所有误差变量皆四阶矩半全局一致最终有界,并且跟踪误差可以稳定在原点附近的邻域内.仿真例子表明所提出控制方案的有效性.     

Adaptive practical preassigned finite‐time stability for a class of pure‐feedback systems with full state constraints

This paper focuses on an adaptive practical preassigned finite‐time control problem for a class of unknown pure‐feedback nonlinear systems with full state constraints. Two new concepts, called preassigned finite‐time function and practical preassigned finite‐time stability, are defined. In order to achieve the main result, the pure‐feedback system is first transformed into an affine strict‐feedback nonlinear system based on the mean value theorem. Then, an adaptive preassigned finite‐time controller is obtained based on a modified barrier Lyapunov function and backstepping technique. Finally, simulation examples are exhibited to demonstrate the effectiveness of the proposed scheme.     

状态与输入受限的二阶多输入多输出非线性系统自适应控制

针对含有状态和输入受限的二阶多输入多输出非线性系统的控制问题,提出了一种自适应控制策略.通过综合利用障碍Lyapunov函数和动态面控制方法的特性,使得系统的状态满足约束条件而且能够减少计算量.此外,为了处理输入约束和系统中的不确定性的影响,分别设计了辅助系统和自适应算法.通过理论分析表明,闭环系统的所有状态都是有界的,而且系统的状态和输入都满足约束条件.最后,通过一个数值仿真算例和一个实际的航天器姿态控制系统的仿真来验证所提出的自适应控制策略的有效性.     

Adaptive finite-time neural network control for nonlinear stochastic systems with state constraints

This paper focuses on the adaptive finite-time neural network control problem for nonlinear stochastic systems with full state constraints. Adaptive controller and adaptive law are designed by backstepping design with log-type barrier Lyapunov function. Radial basis function neural networks are employed to approximate unknown system parameters. It is proved that the tracking error can achieve finite-time convergence to a small region of the origin in probability and the state constraints are confirmed in probability. Different from deterministic nonlinear systems, here the stochastic system is affected by two random terms including continuous Brownian motion and discontinuous Poisson jump process. Therefore, it will bring difficulties to the controller design and the estimations of unknown parameters. A simulation example is given to illustrate the effectiveness of the designed control method.     

Adaptive neural tracking control for nonstrict-feedback stochastic nonlinear time-delay systems with full-state constraints

An adaptive neural tracking control is investigated for a class of nonstrict-feedback stochastic nonlinear time-delay systems with full-state constraints and saturation input. First, the continuous differentiable saturation model is employed to ensure the input constraint, and a barrier Lyapunov function is designed to achieve the full-state constraint. Second, the appropriate Lyapunov–Krasovskii functional and the property of hyperbolic tangent functions are used to deal with the unknown time-delay terms, and neural networks are employed to approximate the unknown nonlinearities. Finally, based on Lyapunov stability theory, an adaptive controller is proposed to guarantee that all the signals in the closed-loop system are 4-Moment (or 2-Moment) semi-globally uniformly ultimately bounded and the tracking error converges to a small neighbourhood of the origin. Two examples are shown to further demonstrate the effectiveness of the proposed control scheme.     

Adaptive state feedback control for switched stochastic high‐order nonlinear systems under arbitrary switchings

This paper studies the adaptive state feedback control for a class of switched time‐varying stochastic high‐order nonlinear systems under arbitrary switchings. Based on the common Lyapunov function and using the inductive method, virtual controllers are designed step by step and the form of the input signal of the system is constructed at the last. The unknown parameters are addressed by the tuning function method. In particular, both the designed state feedback controller and the adaptive law are independent of switching signals. Based on the designed controller, the boundness of the state variables can be guaranteed in probability. Furthermore, without considering the Wiener process or with the known parameter in the assumption, adaptive finite‐time stabilization and finite‐time stabilization in probability can be obtained, respectively. Finally, numerical simulation results are presented to illustrate the effectiveness of the proposed method.     

控制方向未知的全状态约束非线性系统的鲁棒自适应跟踪控制

针对一类控制方向未知的含有时变不确定参数和未知时变有界扰动的全状态约束非线性系统,本文提出了一种基于障碍Lyapunov函数的反步自适应控制方法.障碍Lyapunov函数保证了系统状态在运行过程中始终保持在约束区间内;Nussbaum型函数的引入解决了系统控制方向未知的问题;光滑投影算法确保了不确定时变参数的有界性.障碍Lyapunov函数、Nussbaum型函数及光滑投影算法与反步自适应方法的有效结合首次解决了控制方向未知的全状态约束非线性系统的跟踪控制问题.所设计的自适应鲁棒控制器能在满足状态约束的前提下确保闭环系统的所有信号有界.通过恰当地选取设计参数,系统的跟踪误差将收敛于0的任意小的邻域内.仿真结果表明了控制方案的可行性.     

Distributed fixed‐time consensus for multiagent systems with unknown control directions

This paper investigates the consensus problem for high‐order multiagent systems with unknown control directions and directed communication constraints. To handle the problem of unknown control directions, a logic switching rule is established in the framework of fixed‐time stability. Then, the consensus is achieved in two steps. A group of distributed fixed‐time observers is designed to estimate the reference signals first. Based on these estimates and the designed logic switching rule, a novel control protocol is proposed for each follower system. Different from the existing results, the consensus is achieved with a fixed‐time convergence rate, and the unknown control directions are allowed to be nonidentical for each agent. Finally, simulation results are given to exhibit the validity of the proposed method.     

Data rate for output feedback consensus of uncertain nonlinear multiagent systems

This article considers the data rate problem for output feedback consensus of uncertain nonlinear multiagent systems. Each agent is modeled by an nth order integrator with unknown nonlinear dynamics and unmeasurable states. An (n+2)th order extended state observer (ESO) is first designed to estimate the unmeasurable agent states and the unknown nonlinear dynamics. Based on the output of the ESO and a dynamic encoding and decoding scheme, a distributed consensus protocol is proposed. It is shown that, for a connected undirected network with nth order uncertain nonlinear agents, consensus can be guaranteed with merely one bit information exchange between each pair of adjacent agents at each time step.     

Adaptive mean-square consensus of heterogeneous multiagent systems with stochastic switching topologies

The leader–following consensus of linear heterogeneous multiagent systems is investigated in this paper. To comply with the most practical scenario, the communicating topologies among agents are assumed to switch stochastically and driven by a continuous-time discrete-state Markov process, whose state space corresponds to all the possible topologies. A novel distributed adaptive compensator is designed for the followers to reconstruct the exogenous signals without knowing the Laplacian matrix who is regarded as a global information, and sufficient conditions are given to ensure the compensator converges to the dynamic of the leader asymptotically in the mean square sense. Then, based on the compensator, we solved the consensus problem both by distributed state and measurement output feedback control schemes under output regulation framework, which allow followers to have nonidentical state dimensions. Finally, the theoretical results are demonstrated by a numerical example.