Natural gradient algorithm for stochastic distribution systems with output feedback

In this paper, we use natural gradient algorithm to control the shape of the conditional output probability density function for the stochastic distribution systems from the viewpoint of information geometry. The considered system here is of multi-input and single output with an output feedback and a stochastic noise. Based on the assumption that the probability density function of the stochastic noise is known, we obtain the conditional output probability density function whose shape is only determined by the control input vector under the condition that the output feedback is known at any sample time. The set of all the conditional output probability density functions forms a statistical manifold (M), and the control input vector and the output feedback are considered as the coordinate system. The Kullback divergence acts as the distance between the conditional output probability density function and the target probability density function. Thus, an iterative formula for the control input vector is proposed in the sense of information geometry. Meanwhile, we consider the convergence of the presented algorithm. At last, an illustrative example is utilized to demonstrate the effectiveness of the algorithm.     

模糊输入时滞系统的输出反馈控制及稳定性分析

针对一类状态不可测的模糊输入时滞系统,应用平行分布补偿算法(PDC),设计了模糊观测器,提出了基于模糊观测器的输出反馈控制方法,给出了保证模糊时滞系统渐近稳定的新的充分条件.应用广义Lyapunov函数和线性矩阵不等式方法,证明了模糊输入时滞系统的渐近稳定性,同时给出了控制和观测增益矩阵的分离设计算法.仿真结果进一步验证了所提出的方法和条件的有效性.     

State-Feedback Stabilization of Well-Posed Linear Systems

A finite-dimensional linear time-invariant system is output-stabilizable if and only if it satisfies the finite cost condition, i.e., if for each initial state there exists at least one L² input that produces an L² output. It is exponentially stabilizable if and only if for each initial state there exists at least one L² input that produces an L² state trajectory. We extend these results to well-posed linear systems with infinite-dimensional input, state and output spaces. Our main contribution is the fact that the stabilizing state feedback is well posed, i.e., the map from an exogenous input (or disturbance) to the feedback, state and output signals is continuous in L_loc² in both open-loop and closed-loop settings. The state feedback can be chosen in such a way that it also stabilizes the I/O map and induces a (quasi) right coprime factorization of the original transfer function. The solution of the LQR problem has these properties.     

Adaptive stabilization and regulator design for distributed-parameter systems in the case of collocated actuators and sensors

In this paper, we consider adaptive stabilization and an adaptiveregulator design for collocated distributed-parameter systemsin the case of the input and output operators being unbounded.Adaptive stabilization is realized by the concept of high-gainoutput feedback. The adaptive regulator is constructed via theconcept of high-gain output feedback, using a mechanism to estimatethe unknown parameters of the bounded disturbances. The stateof the controlled system is shown to converge to zero.     

基于输出反馈的一类非线性不确定互联大系统的分散H∞控制

本文研究基于输出反馈的一类大型互联非线性不确定系统的分散H∞控制问题,通过构造每个子系统收敛的状态观测器,得到分散输出反馈控制器.当反馈控制律作用于该系统时,无扰动输入的闭环系统是全局渐近稳定的,而对允许的不确定性,干扰抑制的大小可以任意小,且控制器的设计也无需解任何的Hamilton-Jacobi方程或不等式.     

Adaptive Predictor-Based Output Feedback Control for a Class of Unknown MIMO Linear Systems

In this paper, the problem of characterizing adaptive output feedback control laws for a general class of unknown MIMO linear systems is considered. Specifically, the presented control approach relies on three components, i.e., a predictor, a reference model and a controller. The predictor is designed to predict the system’s output with arbitrary accuracy, for any admissible control input. Subsequently, a full state feedback control law is designed to control the predictor output to approach the reference system, while the reference system tracks the desired trajectory. Ultimately, the control objective of driving the actual system output to track the desired trajectories is achieved by showing that the system output, the predictor output and the reference system trajectories all converge to each other.     

Modelling,simulation and control of a redundant parallel robotic manipulator based on invariant manifolds

In this article a systematic approach of modelling and control for a parallel robotic manipulator is presented. Regarding the framework of structured analysis of dynamical systems the derivation of a differential-algebraic model of the mechanical system is straightforward. Using some differential-geometric considerations based on invariant manifolds and the definition of fictitious additional input and output variables a suitable state feedback can be constructed which transforms the differential-algebraic representation into a state-space model for the robotic manipulator. On this basis a classical two-degree-of-freedom (2-DOF) control structure has been designed using the well-known input–output linearization and a linear time-variant Kalman filter-based output feedback. Finally, the control structure including a friction compensation is applied to the robotic system in the laboratory which shows the practical applicability of the proposed procedure.     

LMI Approach to Output Feedback Control for Linear Uncertain Systems with D-Stability Constraints

This paper deals with the problem of designing output feedback controllers for linear uncertain continuous-time and discrete-time systems with circular pole constraints. The uncertainty is assumed to be norm bounded and enters into both the system state and input matrices. We focus on the design of a dynamic output feedback controller that, for all admissible parameter uncertainties, assigns all the closed-loop poles inside a specified disk. It is shown that the problem addressed can be recast as a convex optimization problem characterized by linear matrix inequalities (LMI); therefore, an LMI approach is developed to derive the necessary and sufficient conditions for the existence of all desired dynamic output feedback controllers that achieve the specified circular pole constraints. An effective design procedure for the expected controllers is also presented. Finally, a numerical example is provided to show the usefulness and applicability of the present approach.     

Stabilization analysis of time-delay Hamiltonian systems in the presence of saturation

The stabilization of a class of Hamiltonian systems with state time-delay and input saturation is addressed in this paper. Sufficient conditions are derived by using Lyapunov-Krasovskii functional theorem to guarantee the systems as well as the resulted closed-loop systems by output feedback to be asymptotically stable when input saturation effectively occurs. A numerical example is presented to illustrate the effectiveness of the obtained results in this paper.     

Infinite dimensional time varying systems with nonlinear output feedback

This paper deals with time-varying systems on Banach-spaces with unbounded input and output operators and considers nonlinear dynamical perturbations of the output feedback type. We develop an analysis which would establish existence conditions for the perturbed equations and investigate the robustness of stability for this wide class of perturbations.     

Chaos control in lateral oscillations of spinning disks via nonlinear feedback

In this paper the problem of chaos control in single mode lateral oscillations of spinning disks is studied. At first, using the harmonic balance method, one of the periodic orbits of system is evaluated. Then proposing a nonlinear feedback strategy a control law is presented for chaos elimination by tracking the mentioned periodic solution. It is shown that although the system is not input-state feedback linearizable, by defining an output signal and using the input–output linearization method, the objective of complete periodic orbit tracking is achieved. The sufficient condition for this purpose is presented, and the performance of proposed method is examined by numerical simulation.     

飞艇姿态跟踪系统的研究

研究了具有参数不确定和外部干扰的飞艇姿态跟踪控制问题．飞艇姿态运动的数学模型为一个多输入/多输出不确定非线性系统,根据该系统的特点,采用了一个基于不确定项上界的鲁棒输出跟踪控制器设计方法,应用输入/输出反馈线性化法和李雅普诺夫方法,设计了飞艇姿态鲁棒控制律,它可确保系统输出按指数规律跟踪期望输出．该控制器设计简单,易于实现．仿真结果表明:即使系统存在不确定性和外界干扰,仍可在闭环系统中实现精确的姿态控制．     

Triangular configuration of uncertain systems stabilizable by means of feedback controller

The uncertain linear systems with time-varying delays and limited measurable states variables are shown to have special configuration, called triangular configuration, to be stabilizable by means of state variable feedback controller. This configuration indicates the location of uncertainties among system parameters including input and output coefficients.     

Partial pole assignment for the quadratic pencil by output feedback control with feedback designs

In this paper we study the partial pole assignment problem for the quadratic pencil by output feedback control where the output matrix is also a designing parameter. In addition, the input matrix is set to be the transpose of the output matrix. Under certain assumption, we give a solution to this partial pole assignment problem in which the unwanted eigenvalues are moved to desired values and all other eigenpairs remain unchanged. Copyright © 2005 John Wiley & Sons, Ltd.     

Hybrid Impulsive Control of Stochastic Systems with Multiplicative Noise Under Markovian Switching

A problem of state output feedback stabilization of discrete-time stochastic systems with multiplicative noise under Markovian switching is considered. Under some appropriate assumptions, the stability of this system under pure impulsive control is given. Further under hybrid impulsive control, the output feedback stabilization problem is investigated. The hybrid control action is formulated as a combination of the regular control along with an impulsive control action. The jump Markovian switching is modeled by a discrete-time Markov chain. The control input is simultaneously applied to both the stochastic and the deterministic terms. Sufficient conditions based on stochastic semi-definite programming and linear matrix inequalities (LMIs) for both stochastic stability and stabilization are obtained. Such a nonconvex problem is solved using the existing optimization algorithms and the nonconvex CVX package. The robustness of the stability and stabilization concepts against all admissible uncertainties are also investigated. The parameter uncertainties we consider here are norm bounded. Two examples are given to demonstrate the obtained results.     

Adaptive stabilization of infinite-dimensional semilinear second-order systems

In this paper adaptive stabilization of infinite-dimensionalundamped semilinear second-order systems is considered in thecase of the input and output operators being collocated. Theadaptive stabilizer is constructed by the concept of high-gainoutput feedback. An energy-like function and a multiplier functionare introduced and adaptive stabilization of the semilinearsecond-order systems is analysed. The theories are applied toa nonlinear string system and the sine-Gordon system.     

Robust Chaotic Synchronization for a Class of Disturbed Nonlinear Systems with Multiple Equilibria

This study concerns with the robust H _∞ synchronization problem for a class of nonlinear feedback control systems, which are subject to a vector-valued periodic nonlinearity in the feedback path. Under such synchronization configuration, the master system is assumed to be subject to an energy bounded input disturbance, and the slave one is under control. Sufficient conditions for controller design are proposed in terms of linear matrix inequalities by respectively utilizing the output feedback control and the dynamic output control strategies, such that the master system robustly synchronizes the slave one with a guaranteed H _∞ performance. The derived methods can be applied to the robust H _∞ synchronization of many practical systems, and effectiveness of the obtained results are demonstrated through a concrete example of phase-locked loops (PLL).     

Positioning control for a linear actuator with nonlinear friction and input saturation using output‐feedback control

This article deals with the positioning control problem via the output feedback scheme for a linear actuator with nonlinear disturbances. In this study, the proposed controller accounts for not only the nonlinear friction, force ripple, and external disturbance but also the input saturation problem. In detail, the energy consumption for conquering friction and disturbance rejection is estimated and used as compensation based on the hybrid controller including and sliding‐mode‐based adaptive algorithms, which ensures the tracking performance and robustness of electromechanical servo system. Moreover, to confront the input saturation, a saturation observer and an anti‐windup controller are designed. The global robustness of the controller is guaranteed by an output feedback robust law. Theoretically, the designed controller can guarantee a favorable tracking performance in the presence of various disturbance forces and input saturation, which is essential for high accuracy motion plant in industrial application. The simulation results verify the robustness and effectiveness for the motion system with the proposed control strategy under various operation conditions. © 2016 Wiley Periodicals, Inc. Complexity 21: 191–200, 2016     

线性系统最优输出转移问题的反馈解

在适当的条件下讨论如何最佳地施加控制将系统的输出转移至目标点,用来度量控制优劣的指标综合反映了转移时间,转移过程所消耗的输入能量与系统自身运动过程所具有的能量的多少,给出了使此指标达到最小的(状态)反馈控制．     

Stabilization of an Elastic Plate with Viscoelastic Boundary Conditions

The boundary control problem of an elastic thin plate with boundary viscoelasticity is formulated in the standard form of a linear infinite-dimensional systems in the energy Hilbert space. The feedback control is designed so that the input and output are collocated. The frequency-domain approach is adopted in investigating the exponential stability of the closed-loop system. Finally, by considering the boundary viscoelasticity as damping, we establish a strong stability result based on the LaSalle invariance principle and the Hömander uniqueness theorem.