Adaptive architectures for control of uncertain dynamical systems with actuator and unmodeled dynamics

In adaptive control of uncertain dynamical systems, it is well known that the presence of actuator and/or unmodeled dynamics in feedback loops can yield to unstable closed‐loop system trajectories. Motivated by this standpoint, this paper focuses on the analysis and synthesis of multiple adaptive architectures for control of uncertain dynamical systems with both actuator and unmodeled dynamics. Specifically, we first analyze model reference adaptive control architectures with standard, hedging‐based, and expanded reference models for this class of uncertain dynamical systems and develop sufficient stability conditions. We then synthesize a robustifying term for the latter architecture and analytically show that this term can allow for a relaxed sufficient stability condition. The proposed theoretical treatments involve Lyapunov stability theory, linear matrix inequalities, and matrix mathematics. Finally, we compare the resulting sufficient stability conditions of the considered adaptive control architectures on a benchmark mechanical system subject to actuator and unmodeled dynamics.     

Centralized sliding mode frequency regulation approach for an uncertain islanded micro grid integrated with disturbance observer

This paper proposes a novel secondary frequency regulation technique for an uncertain islanded micro grid (MG). The major motivation of the work is to integrate the intrinsic robustness of the sliding mode control scheme with the disturbance observer to estimate and alleviate the unknown mismatched uncertainties caused by renewable resources and load variations. To this end, a dynamical sliding manifold is first utilized and then a control law is derived with Lyapunov's method which stabilizes the MG dynamics. Moreover, in order to ensure faster time domain responses of the closed‐loop system, we employ a power rate reaching law in our proposed control design. Thereafter, the performances of the introduced control strategy are tested on an islanded MG using MATLAB/Simulink, and robustness analysis is also carried out by considering five different case studies. Further, in contrast to the existing approaches such as robust H _∞ and robust PID control, the proposed strategy renders appealing time domain characteristics such as settling time, peak overshoot, and integral absolute frequency error.     

Quadratic Stabilization of Switched Uncertain Linear Systems: A Convex Combination Approach

We consider quadratic stabilization for a class of switched systems which are composed of a finite set of continuoustime linear subsystems with norm bounded uncertainties. Under the assumption that there is no single quadratically stable subsystem, if a convex combination of subsystems is quadratically stable, then we propose a state-dependent switching law, based on the convex combination of subsystems, such that the entire switched linear system is quadratically stable. When the state information is not available, we extend the discussion to designing an output-dependent switching law by constructing a robust Luenberger observer for each subsystem.      

A novel reliability-based topology optimization framework for the concurrent design of solid and truss-like material structures with unknown-but-bounded uncertainties

A new nonprobabilistic reliability-based topology optimization method for continuum structures with displacement constraints is proposed in this paper, in which the optimal layout consists of solid material and truss-like microstructure material simultaneously. The unknown-but-bounded uncertainties that exist in material properties, external loads, and safety displacements are considered. By utilizing the representative volume element analysis, rules of macro-micro stiffness performance equivalence can be confirmed. A solid material and truss-like microstructure material structure integrated design interpolation model is firstly constructed, in which design domain elements can be conducted to select solid material or truss-like microstructure material by a combination of the finite element method in the topology optimization process. Moreover, a new nonprobabilistic reliability measuring index, namely, the optimization feature distance is defined by making use of the area-ratio ideas. Furthermore, the adjoint vector method is employed to obtain the sensitivity information between the reliability measure and design variables. By utilizing the method of moving asymptotes, the investigated optimization problem can be iteratively solved. The effectiveness of the developed methodology is eventually demonstrated by two examples.     

Supervisory switching‐based prescribed performance control of unknown nonlinear systems against actuator failures

This article studies the fault‐tolerant control problem for unknown nonlinear strict‐feedback systems subject to actuator failures yet with dynamic redundancies. The prescribed performance control methodology is newly combined with a modification‐based supervisory switching strategy to solve the problem. To implement failure detection, the performance function is properly modified to synthesize a monitoring function to supervise the behavior of an error variable. Once a failure is detected, the current actuator is shut down and the backup actuator is switched in to execute the reconfigured control command. Compared with the existing results, (1) the postfailure and postswitching tracking performance is improved, other than uniform ultimate boundedness and (2) the dependence on extra robust control schemes (eg, adaptive or approximating structures) to deal with model uncertainties or the need to compute analytic derivatives of virtual control signals in the backstepping design is eliminated.     

Filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties

This paper synthesizes a filtering adaptive neural network controller for multivariable nonlinear systems with mismatched uncertainties. The multivariable nonlinear systems under consideration have both matched and mismatched uncertainties, which satisfy the semiglobal Lipschitz condition. The nonlinear uncertainties are approximated by a Gaussian radial basis function (GRBF)‐based neural network incorporated with a piecewise constant adaptive law, where the adaptive law will generate adaptive parameters by solving the error dynamics between the real system and the state predictor with the neglection of unknowns. The combination of GRBF‐based neural network and piecewise constant adaptive law relaxes hardware limitations (CPU). A filtering control law is designed to handle the nonlinear uncertainties and deliver a good tracking performance with guaranteed robustness. The matched uncertainties are cancelled directly by adopting their opposite in the control signal, whereas a dynamic inversion of the system is required to eliminate the effect of the mismatched uncertainties on the output. Since the virtual reference system defines the best performance that can be achieved by the closed‐loop system, the uniform performance bounds are derived for the states and control signals via comparison. To validate the theoretical findings, comparisons between the model reference adaptive control method and the proposed filtering adaptive neural network control architecture with the implementation of different sampling time are carried out.     

显式抑制测量误差的改进滑模控制

反馈控制系统中模型不确定性和测量误差的同时出现, 给高精度控制器的设计带来挑战. 经典滑模控制能抵抗一定程度的模型不确定性和输入干扰, 但引入的高增益使得其性能对测量噪声极为敏感, 也容易引起系统强烈抖振. 为此, 本文针对一种典型的角度和角速率测量分别包含高频和低频测量误差条件, 提出了一种改进的基于趋近律的角度跟踪控制方案. 本方案采用低通滤波器来应对高频测量噪声, 同时采用一种新颖的基于模型的测量误差估计器, 来补偿低频测量漂移. 采用Quanser Aero平台进行两自由度角轨迹跟踪控制仿真和实验验证, 并与自抗扰控制等几种典型鲁棒控制方案进行了全面对比, 证实了本文方案性能上的优越性和调参的便捷性.     

事件触发下随机非确定线性多智能体的指数同步

研究随机非确定线性多智能体系统在有向拓扑连接下的指数同步问题,为减少不必要的网络带宽资源的浪费,提出一种基于事件触发控制的协议。根据组合测量对系统中的所有节点设计相应的事件触发函数,使得节点之间的控制信号更新仅在事件触发时刻进行。基于Lyapunov稳定性理论和M矩阵理论,得到了多智能体系统指数同步结论,并给出了同步的收敛速度。同时,理论排除了事件触发控制过程中的芝诺（Zeno）现象。数值仿真结果进一步验证了理论分析的有效性。     

FTESO‐Based Finite Time Control for Underactuated System Within a Bounded Input

Finite time control problem is investigated for a class of underactuated systems with uncertainties and external disturbances. For the sake of expanding control region furthest within a bound input, finite time extended state observer (FTESO) and a novel adaptive terminal sliding mode (ATSM) controller are applied to improve the stability performance of system. Compared to the general extended state observer (ESO), FTESO makes use of fractional powers to reduce the estimation errors to zero in finite time. The coordinate transformation is made for more degrees of design freedom. Rigorous analysis of finite time convergence results has been performed through Lyapunov theory and sufficient conditions are provided for the observer/controller‐design. Finally, simulation results on the Rotating Inverted Pendulum are given to demonstrate the effectiveness of the proposed controller and observer.     

Global output‐feedback stabilization for nonlinear systems with unknown relative degree

This paper is devoted to the global stabilization via output feedback for a class of nonlinear systems with unknown relative degree, dynamics uncertainties, unknown control direction, and nonparametric uncertain nonlinearities. In particular, the unknown relative degree is without known upper bound, which renders us to research for a filter with varying dimension rather than the ones with over dimensions in the existing literature. In comparison with more popular but a bit stronger input‐to‐state stable or input‐to‐state practically stable requirement, only bounded‐input bounded‐state stable requirement is imposed on the dynamics uncertainties, which affect the systems in a persistent intensity rather than in a decaying one. In this paper, to compensate multiple serious system uncertainties and realize global output‐feedback stabilization, a design scheme via switching logic together with varying dimensional filter is developed. In this scheme, 2 switching sequences, which separately generate the gains of the controller and act as the varying dimensions of the filter, are designed to overcome unknown control direction, dynamics uncertainties and nonparametric uncertain nonlinearities, and unknown relative degree, respectively. A 2‐mass lumped‐parameter structure is provided to show the effectiveness of the proposed method in this paper.