Design of state estimators for uncertain linear systems using quadratic boundedness

The notion of quadratic boundedness, which allows one to address the stability of a dynamic system in the presence of bounded disturbances, is applied to the design of state estimators for discrete-time linear systems with polytopic uncertainties. Necessary and sufficient stability conditions are stated and upper bounding sequences on the estimation error are derived. For the purpose of design, such conditions can be expressed in terms of linear matrix inequalities (LMIs), thus guaranteeing the numerical tractability. Simulation results are reported to show the effectiveness of the approach.     

Decentralized adaptive output-feedback control for a class of nonlinear large-scale systems with unknown time-varying delayed interactions

In this paper, the authors investigate a decentralized adaptive output-feedback controller design for large-scale nonlinear systems with input saturations and time-delayed interconnections unmatched in control inputs. The interaction terms with unknown time-varying delays are bounded by unknown nonlinear bounding functions including all states of subsystems. This point is a main contribution of this paper compared with previous output-feedback control approaches which assume that the time-delayed bounding functions only depend on measurable output variables. The bounding functions are compensated by using appropriate Lyapunov–Krasovskii functionals and the function approximation technique based on neural networks. The observer dynamic surface design technique is employed to design the proposed memoryless local controller for each subsystem. In addition, we prove that all signals in the closed-loop system are semiglobally uniformly bounded and control errors converge to an adjustable neighborhood of the origin. Finally, an example is provided to illustrate the effectiveness of the proposed control system.     

Robust adaptive neural control for a class of perturbed strict feedback nonlinear systems

This paper presents a robust adaptive neural control design for a class of perturbed strict feedback nonlinear system with both completely unknown virtual control coefficients and unknown nonlinearities. The unknown nonlinearities comprise two types of nonlinear functions: one naturally satisfies the "triangularity condition" and can be approximated by linearly parameterized neural networks, while the other is assumed to be partially known and consists of parametric uncertainties and known "bounding functions." With the utilization of iterative Lyapunov design and neural networks, the proposed design procedure expands the class of nonlinear systems for which robust adaptive control approaches have been studied. The design method does not require a priori knowledge of the signs of the unknown virtual control coefficients. Leakage terms are incorporated into the adaptive laws to prevent parameter drifts due to the inherent neural-network approximation errors. It is proved that the proposed robust adaptive scheme can guarantee the uniform ultimate boundedness of the closed-loop system signals.. The control performance can be guaranteed by an appropriate choice of the design parameters. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

Adaptive output-feedback regulation for nonlinear delayed systems using neural network

A novel adaptive neural network （NN） output-feedback regulation algorithm for a class of nonlinear time-varying timedelay systems is proposed. Both the designed observer and controller are independent of time delay. Different from the existing results, where the upper bounding functions of time-delay terms are assumed to be known, we only use an NN to compensate for all unknown upper bounding functions without that assumption. The proposed design method is proved to be able to guarantee semi-global uniform ultimate boundedness of all the signals in the closed system, and the system output is proved to converge to a small neighborhood of the origin. The simulation results verify the effectiveness of the control scheme.     

Adaptive and robust controls of uncertain systems with nonlinear parameterization

Two classes of partially known systems are considered in this note; both of them have a fractional parameterization of the unknowns. The first class consists of nonlinear systems whose uncertainties are bounded by a function of fractional parameterization, and the second class compromises those systems whose unknown dynamics can directly, but nonlinearly, be parameterized. It is shown that adaptive robust control can be extended to accommodate nonlinearly parameterized bounding functions and that, with the aid of a robust auxiliary system, new adaptation laws and a simple adaptive control can be designed for the unknowns in the fractional parameterization. Practical stability (in terms of uniform boundedness and ultimate boundedness) is shown; global for adaptive robust control and semiglobal for the new adaptive control.     

Adaptive neural control of uncertain MIMO nonlinear systems

In this paper, adaptive neural control schemes are proposed for two classes of uncertain multi-input/multi-output (MIMO) nonlinear systems in block-triangular forms. The MIMO systems consist of interconnected subsystems, with couplings in the forms of unknown nonlinearities and/or parametric uncertainties in the input matrices, as well as in the system interconnections without any bounding restrictions. Using the block-triangular structure properties, the stability analyses of the closed-loop MIMO systems are shown in a nested iterative manner for all the states. By exploiting the special properties of the affine terms of the two classes of MIMO systems, the developed neural control schemes avoid the controller singularity problem completely without using projection algorithms. Semiglobal uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop of MIMO nonlinear systems is achieved. The outputs of the systems are proven to converge to a small neighborhood of the desired trajectories. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. The proposed schemes offer systematic design procedures for the control of the two classes of uncertain MIMO nonlinear systems. Simulation results are presented to show the effectiveness of the approach.     

Output Feedback Regulation of Stochastic Nonlinear Systems With Stochastic iISS Inverse Dynamics

This paper develops a unifying framework for output feedback regulation of stochastic nonlinear systems with more general stochastic inverse dynamics. The contributions of this work are characterized by the following novel features: 1) Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) using Lyapunov function in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov function is first introduced, two important properties of SiISS are obtained: (i) SiISS is strictly weaker than SISS using Lyapunov function; (ii) SiISS is stronger than the minimum-phase property. However, only under the minimum-phase assumption, there is no dynamic output feedback control law for global stabilization in probability. 2) Almost sure boundedness, a reasonable and stronger concept than boundedness in probability, is introduced. The purpose of introducing the concept is to prove the boundedness and convergence of some signals in the closed-loop control system. 3) Some important mathematical tools which play an essential role in the boundedness and convergence analysis of the closed-loop system are established. 4) A unifying framework is proposed to design a dynamic output feedback control law, which drives the states to the origin almost surely while maintaining all the closed-loop signals bounded almost surely.      

Adaptive regulation of uncertain nonlinear systems by output feedback: A universal control approach

The problem of global state regulation via output feedback is investigated for uncertain nonlinear systems. The class of uncertain systems under consideration is assumed to be dominated by a bounding system which is linear growth in the unmeasurable states but can be a polynomial function of the system output, with unknown growth rates. To achieve global state regulation in the presence of parametric uncertainty, we propose a non-identifier based output feedback control scheme by employing the idea of universal control integrated with the design of a linear high-gain observer, whose gains are composed of two components, both of them are not constant and need to be dynamically updated. In particular, we explicitly design a universal output feedback controller which globally regulates all the states of the uncertain system while maintaining global boundedness of the closed-loop system.     

A Novel Robust Constraint Force Servo Control for Under‐actuated Manipulator Systems: Fuzzy and Optimal

We consider the control design for under‐actuated manipulator systems. The task is to drive the system to be close to a prescribed constraint. The system contains uncertainty. It is bounded where the bounding information is prescribed by a fuzzy set (e.g., the bound is close to 1). The initial condition is also prescribed by a fuzzy set. A class of robust control is proposed, which guarantees a deterministic performance. On top of that, the choice of a control design parameter is cast into a fuzzy‐theoretic setting. A performance index, consisting of accumulated fuzzy‐based system performance and control cost, is proposed. The optimal control design parameters, which minimize the performance index, can be obtained by solving two algebraic quartic (fourth‐order) equations. As a result, the control design problem, which addresses both fuzzy and optimal characteristics, is completely solved.     

Adaptive fuzzy control for unknown nonlinear time-delay systems with virtual control functions

In this paper, adaptive fuzzy control is presented for a class of unknown nonlinear timedelay systems with virtual control functions. By employing fuzzy logic systems and the technique of delay replacement, dynamic surface control (DSC) design approach can be carried out with both unknown delay signals and nonlinearities. This is different from the existing results, which are used to make limitations on the time-delays. It is proved that the proposed design method is able to guarantee semiglobal uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system, with arbitrary small tracking error by appropriately choosing design constants.     

A riccati equation approach to the stabilization of uncertain linear systems

This paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems. The systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set. Furthermore, these uncertain parameters may be time-varying. The method used to establish asymptotic stability of the closed loop system (obtained when the feedback control is applied) involves the use of a quadratic Lyapunov function. The main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic Lyapunov function. Once the Lyapunov function has been obtained, it is used to construct the stabilizing feedback control law. The fundamental idea behind the algorithm presented involves constructing an upper bound for the Lyapunov derivative corresponding to the closed loop system. This upper bound is a quadratic form. By using this upper bounding procedure, a suitable Lyapunov function can be found by solving a certain matrix Riccati equation. Another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic Lyapunov function.     

带有干扰的时变系统的变结构鲁棒控制

对含有未知时变参数和外界干扰的单输入单输出线性时变系统,给出了一种变结构鲁棒输出跟踪控制器.系统参数不限定为慢时变或者结构已知的,只要求光滑有界且所需高阶导数有界.通过引入辅助信号和带有记忆功能的正规化信号,以及适当选择控制器参数,该变结构控制器能保证闭环系统所有信号的有界性,跟踪误差能被调整到任意小的范围内.     

A robust adaptive dynamic surface control for a class of nonlinear systems with unknown Prandtl–Ishilinskii hysteresis

In this paper, a robust adaptive dynamic surface control for a class of uncertain perturbed strict‐feedback nonlinear systems preceded by unknown Prandtl–Ishlinskii hysteresis is proposed. The main advantages of our scheme are that the explosion of complexity problem can be eliminated when the hysteresis is fused with backstepping design and, by introducing an initialization technique, the ??_∞ performance of system tracking error can be achieved. It is proved that the new scheme can guarantee semi‐global uniform ultimate boundedness of all closed‐loop signals and make the convergence of the tracking error to an arbitrarily small residual set. Simulation results are presented to demonstrate the efficiency of the proposed scheme. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust redesign of a neural network controller in the presence of unmodeled dynamics

This work presents a neural network control redesign, which achieves robust stabilization in the presence of unmodeled dynamics restricted to be input to output practically stable (IOpS), without requiring any prior knowledge on any bounding function. Moreover, the state of the unmodeled dynamics is permitted to go unbounded provided that the nominal system state and/or the control input also go unbounded. The neural network controller is equipped with a resetting strategy to deal with the problem of possible division by zero, which may appear since we consider unknown input vector fields with unknown signs. The uniform ultimate boundedness of the system output to an arbitrarily small set, plus the boundedness of all other signals in the closed-loop is guaranteed.     

Robust adaptive control of nonlinearly parametrized multivariable systems with unmatched disturbances

A new robust adaptive control scheme is developed for nonlinearly parametrized multivariable systems in the presence of parameter uncertainties and unmatched disturbances. The developed control scheme employs a new integrated framework of a functional bounding technique for handling nonlinearly parametrized system dynamics, an adaptive parameter estimation algorithm for dealing with parameter uncertainties, a nonlinear feedback controller structure for stabilization of interconnected system states, and a robust adaptive control design for accommodating unmatched disturbances. It is proved that such a new robust adaptive control scheme is capable of ensuring the global boundedness and mean convergence of all closed‐loop system signals. A complete simulation study on an air vehicle system with nonlinear parametrization in the presence of an unmatched wind disturbance is conducted, and its results verify the effectiveness of the proposed robust adaptive control scheme.     

未知输出反馈非线性时滞系统自适应神经网络跟踪控制

An adaptive output feedback neural network tracking controller is designed for a class of unknown output feedback nonlinear time-delay systems by using backstepping technique. Neural networks are used to approximate unknown time-delay functions. Delay-dependent filters are introduced for state estimation. The domination method is used to deal with the smooth time-delay basis functions. The adaptive bounding technique is employed to estimate the upper bound of the neural network reconstruction error. Based on Lyapunov-Krasoviskii functional, the semi-global uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop system is proved. The arbitrary output tracking accuracy is achieved by tuning the design parameters and the neural node number. The feasibility is investigated by an illustrative simulation example.     

Adaptive Neural Tracking Control for Unknown Output Feedback Nonlinear Time-delay Systems

An adaptive output feedback neural network tracking controller is designed for a class of unknown output feedback nonlinear time-delay systems by using backstepping technique.Neural networks are used to approximate unknown time-delay functions.Delay-dependent filters are intro- duced for state estimation.The domination method is used to deal with the smooth time-delay basis functions.The adaptive bounding technique is employed to estimate the upper bound of the neural network reconstruction error.Based on Lyapunov-Krasoviskii functional,the semi-global uniform ultimate boundedness(SGUUB)of all the signals in the closed-loop system is proved.The arbitrary output tracking accuracy is achieved by tuning the design parameters and the neural node number. The feasibility is investigated by an illustrative simulation example.     

Adaptive synchronisation of unknown nonlinear networked systems with prescribed performance

This paper proposes an adaptive tracking control with prescribed performance function for distributive cooperative control of highly nonlinear multi-agent systems. The use of such approach confines the tracking error within a large predefined set to a predefined smaller set. The key idea is to transform the constrained system into unconstrained one through the transformation of the output error. Agents’ dynamics are assumed unknown, and the controller is developed for a strongly connected structured network. The proposed controller allows all agents to follow the trajectory of the leader node, while satisfying the necessary dynamic requirements. The proposed approach guarantees uniform ultimate boundedness for the transformed error as well as a bounded adaptive estimate of the unknown parameters and dynamics. Simulations include two examples to validate the robustness and smoothness of the proposed controller against highly nonlinear heterogeneous multi-agent system with uncertain time-variant parameters and external disturbances.     

线性系统的事件触发输出反馈有限时间有界控制

本文研究了线性系统的事件触发输出反馈有限时间有界控制问题. 与渐近稳定只定性地要求系统在采样间隔 有界不同, 有限时间有界需要估计系统轨迹的上界以保证满足动态系统的定量要求. 本文基于类李雅普诺夫函数给出了 保证闭环系统的有限时间有界性和避免芝诺现象的充分条件. 这些充分条件可以转化为线性矩阵不等式, 便于验证和实 际应用. 此外, 为了节约资源, 提出了一种可变参数的事件触发规则, 提高了设计灵活性. 仿真结果验证了本文的主要结 论.