FAULT TOLERANT CONTROL OF FLEXIBLE SMART STRUCTURES USING ROBUST DECENTRALIZED FAST OUTPUT SAMPLING FEEDBACK TECHNIQUE

This paper presents the modeling, design and simulation of a Robust Decentralized Fast Output Sampling (RDFOS) feedback controller for the vibration control of a smart structure (flexible cantilever beam) when there is actuator failure. The beam is divided into 8 finite elements and the sensors / actuators are placed at finite element positions 2, 4, 6, and 8 as collocated pairs. The smart structure is modeled using the concepts of piezoelectric theory, Euler‐Bernoulli beam theory, Finite Element Method (FEM) techniques and the state space techniques. Four multi‐variable state‐space models of the smart structure plant are obtained when there is a failure of one of the four actuators to function. The effect of failure of one of the piezo actuators to function during the vibration of the beam is observed. The tip displacements, open and closed loop responses with and without the controller are observed. For all of these models, a common stabilizing state feedback gain F is obtained. A robust decentralized fast output sampling feedback gain L which realizes this state feedback gain is obtained using the LMI approach. In this designed control law, the control inputs to each actuator of the multi‐model representation of the smart structure is a function of the output of that corresponding sensor only and the gain matrix has got all off‐diagonal terms zero and this makes the control design a robust decentralized one. Then, the performance of the designed smart system is evaluated for Active Vibration Control (AVC). The robust decentralized FOS controller obtained by the designed method requires only constant gains and hence may be easier to implement in real time.     

Simultaneous LQ control of a set of LTI systems using constrained generalized sampled-data hold functions

In this paper, sampled-data control of a set of continuous-time LTI systems is considered. It is assumed that a predefined guaranteed continuous-time quadratic cost function, which is, in fact, the sum of the performance indices for all systems, is given. The main objective here is to design a decentralized periodic output feedback controller with a prespecified form, e.g., polynomial, piecewise constant, exponential, etc., which minimizes the above mentioned guaranteed cost function. This problem is first formulated as a set of matrix inequalities, and then by using a well-known technique, it is reformulated as a LMI problem. The set of linear matrix inequalities obtained provides necessary and sufficient conditions for the existence of a decentralized optimal simultaneous stabilizing controller with the prespecified form (rather than a general form). Moreover, an algorithm is presented to solve the resultant LMI problem. Finally, the efficiency of the proposed method is demonstrated in two numerical examples.     

An algorithm for synthesis of the suboptimal control law for quasi-linear stochastic dynamical systems

We consider the information constrained optimization problem for stochastic dynamical systems governed by quasi-linear Ito equations. Let us describe the information constraints. We suppose that each control vector component depends on a prespecified set of precisely measured state vector components. In this article we present an algorithm for synthesis of the suboptimal control law. This control law is the linear feedback regulator. The linear parameter and the constant term of the regulator are polynomial functions of time. The algorithm is successfully applied to the problem of two-link robotic arm optimal control. These manipulators may be effectively used at space stations, e.g. for moving cargo in outer space.     

基于BMI的一类不确定分段线性系统的最优控制设计

将不确定分段线性系统的最优控制问题转化成最优控制性能界的优化问题．其中性能上界的优化是以反馈增益为寻优参数的一组双线性矩阵不等式(BMI)问题，对此将遗传算法和内点法结合， 设计了一种混合算法进行求解．最后的算例表明控制律的设计及其求解算法的有效性．     

2D system approach based output feedback repetitive control for uncertain discrete-time systems

This paper presents a two-dimensional (2D)-based approach to the problem of output feedback repetitive control for uncertain discrete-time systems. It is shown first how the proposed repetitive control scheme can be equivalently formulated in the form of a distinct class of 2D system. Then sufficient conditions for the existence of output feedback control law are derived in terms of linear matrix inequality (LMI), and the control law matrices are characterized by the feasible solutions to this LMI. Moreover, an optimization problem is introduced to efficiently solve the optimal output feedback control law by minimizing the upper bound of a given cost function. Compared with the commonly used 1D-based method, the proposed approach increases the degree of freedom of controller design by not only including in the scheme an output feedback gain but also a feed forward one which can be simultaneously solved using the 2D-based procedures presented in the paper. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.     

跳变双线性随机离散组合系统的保成本分散控制

研究一类跳变双线性随机离散组合系统的保成本分散控制问题．首先给出问题可解的充分条件,然后基于线性矩阵不等式方法设计保成本分散状态反馈控制律．理想的保成本分散状态反馈控制器可通过应用现有的软件，求解一组线性矩阵不等式而得到．仿真例子说明了该方法的有效性.     

A technique for suboptimal feedback control of nonlinear systems

A simple easily implemented method is developed for obtaining a suboptimal control law for the optimization problem associated with minimizing a quadratic cost functional for nonlinear systems. The suboptimal control law is derived using a Taylor's series representation for the feedback gain matrix after modeling the nonlinear system by a linear system at each instant of time. The resultant control law is of feedback form and is nonlinear in state. The suboptimal control is obtained without using iterative techniques or any true optimal solutions. A second-order numerical example illustrates the effectiveness of the method and gives a comparison to the results of previous methods.     

随机非线性时滞大系统的输出反馈分散镇定

针对具有严格反馈形式的随机非线性时滞大系统,设计了含有时滞项的随机控制Lyapunov函数,运用Backstepping技术,构造出一类输出反馈无记忆控制器.在此控制器作用下,所考虑的闭环系统实现概率意义上的时滞无关全局渐近稳定.并在无限时区优化指标函数的约束下,对控制器进行逆优再设计,以满足一定的性能要求.     

Output feedback decentralized stabilization: ILMI approach

In this paper, the static output feedback decentralized stabilization problem is addressed using a linear matrix inequality approach. A necessary and sufficient condition for static output feedback decentralized stabilizability is derived for linear time-invariant large-scale systems. It is proven that the existence of a stabilizing decentralized gain is equivalent to that of the solution of a quadratic matrix inequality. The extension of the result to control is studied. An iterative LMI algorithm based on the linear matrix inequality technique is proposed to obtain the decentralized feedback gain. Examples show the effectiveness of the algorithm.     

Decentralized control and state estimation of linear time-periodic systems

The main contributions of this article are the design of a decentralized controller and state estimator for linear time-periodic systems with fixed network topologies. The proposed method to tackle both problems consists of reformulating the linear periodic dynamics as a linear time-invariant system by applying a time-lifting technique and designing a discrete-time decentralized controller and state estimator for the time-lifted formulation. The problem of designing the decentralized estimator is formulated as a discrete-time Kalman filter subject to sparsity constraints on the gains. Two different algorithms for the computation of steady-state observer gains are tested and compared. The control problem is posed as a state feedback gain optimization problem over an infinite-horizon quadratic cost, subject to a sparsity constraint on the gains. An equivalent formulation that consists in the optimization of the steady-state solution of a matrix difference equation is presented and an algorithm for the computation of the decentralized gain is detailed. Simulation results for the practical cases of the quadruple-tank process and an extended 40-tank process are presented that illustrate the performance of the proposed solutions, complemented with numerical simulations using the Monte Carlo method.     

一类关联不确定离散系统的分散保性能控制

结合一个给定的二次型性能指标, 研究一类关联不确定离散大系统的分散保性能状态反馈控制器设计问题. 采用线性矩阵不等式处理方法, 导出了分散控制器存在的条件, 并给出了一组分散保性能控制器的参数化表示, 据此, 通过建立和求解一个凸优化问题给出了使得闭环性能指标的上界最小化的最优分散保性能控制器设计方法.     

A computational method for simultaneous LQ optimal control designvia piecewise constant output feedback

The paper is concerned with simultaneous linear-quadratic (LQ) optimal control design for a set of LTI systems via piecewise constant output feedback. First, the discrete-time simultaneous LQ optimal control design problem is reduced to solving a set of coupled matrix inequalities and an iterative LMI algorithm is presented to compute the feedback gain. Then, simultaneous stabilization and simultaneous LQ optimal control design of a set of LTI continuous-time systems are considered via periodic piecewise constant feedback gain. It is shown that the design of a periodic piecewise constant feedback gain simultaneously minimizing a set of given continuous-time performance indexes can be reduced to that of a constant feedback gain minimizing a set of equivalent discrete-time performance indexes. Explicit formulas for computing the equivalent discrete-time systems and performance indexes are derived. Examples are used to demonstrate the effectiveness of the proposed method.     

一类线性离散时滞大系统的分散镇定

用一组线性矩阵不等式给出一类线性离散时滞大系统分散能镇定的一个充分条件,进而,通过建立和求解一个凸优化问题,提出了具有较反馈增益参数的分散稳定化状态反馈控制律的设计方法,所得到的控制器不仅使得闭环境系统是稳定的,而且还可以使得闭环系统状态具有给定的衰减度。     

参数不确定广义大系统的保性能分散控制

对一类范数有界时不变参数不确定的连续广义大系统和一个二次型性能指标,研究了其保性能分散控制问题.目的是设计一状态反馈分散控制器,使得对所有容许的不确定性,闭环系统不仅是鲁棒稳定的,而且性能指标有一上界.应用线性矩阵不等式方法,给出了一个用线性矩阵不等式表达的保性能分散控制器存在的充分条件;在此条件可解时,给出了保性能分散控制律的表达式.最后,举例说明了该方法的应用.     

An optimal control based approach to designing plantwide control system architectures

An approach to designing decentralized plantwide control system architectures is presented. The approach is based on splitting the optimal controller gain matrix that results from solving an output optimal control problem into feedback and feedforward parts. These two parts are then used to design and evaluate decentralized control systems. Results for the application of the methodology to a realistic, 4 by 4 reactor with recycle process are given. For this system, the optimal control based approach suggests feedback pairings that are significantly different than those suggested by the steady state RGA. The approach presented can give an indication if MPC is preferred over a decentralized approach to plantwide control. Comparison of the results produced by the best decentralized plantwide system and a model predictive control system are presented.     

Decentralized spatial partitioning for multi-vehicle systems in spatiotemporal flow-field

We consider the problem of characterizing a generalized Voronoi diagram/partition of a convex polygon in a two-dimensional Euclidean space that encodes information about the proximity relations between a team of aerial/marine vehicles and arbitrary points in the partition space. These proximity relations are determined by the time required for each vehicle to reach an arbitrary point (time-to-go) in the partition space when driven by a locally optimal feedback control law in the presence of a spatiotemporal drift field. The main contribution of this work is the presentation of a partitioning algorithm, which is decentralized, in the sense that each vehicle can independently compute its corresponding cell from the generalized Voronoi partition without computing or receiving information about the cells of the other vehicles. Finally, we present numerical simulations using data from real drift fields to illustrate the key features of the decentralized solution to the proposed class of spatial partitioning problems.     

一类离散非线性不确定互联系统的模糊分散控制

利用模糊控制方法研究一类离散非线性互联系统的分散控制问题.首先采用模糊(T-S)模型对离散非线性不确定互联系统进行模糊建模,应用并行分布补偿算法(PDC)给出状态反馈分散模糊控制方案,并基于李亚普诺夫函数方法证明了闭环系统的稳定性.然后当系统的状态不完全可测时,设计模糊分散观测器来估计各子系统的状态,从而给出基于观测器的状态反馈分散模糊控制设计的方法.因为该分散模糊控制设计问题是以线性矩阵不等式的形式给出,所以很容易用凸优化方法求解.仿真结果验证了所提出控制方法的有效性.     

Optimization of formation for multi-agent systems based on LQR

In this paper, three optimal linear formation control algorithms are proposed for first-order linear multiagent systems from a linear quadratic regulator (LQR) perspective with cost functions consisting of both interaction energy cost and individual energy cost, because both the collective object (such as formation or consensus) and the individual goal of each agent are very important for the overall system. First, we propose the optimal formation algorithm for first-order multi-agent systems without initial physical couplings. The optimal control parameter matrix of the algorithm is the solution to an algebraic Riccati equation (ARE). It is shown that the matrix is the sum of a Laplacian matrix and a positive definite diagonal matrix. Next, for physically interconnected multi-agent systems, the optimal formation algorithm is presented, and the corresponding parameter matrix is given from the solution to a group of quadratic equations with one unknown. Finally, if the communication topology between agents is fixed, the local feedback gain is obtained from the solution to a quadratic equation with one unknown. The equation is derived from the derivative of the cost function with respect to the local feedback gain. Numerical examples are provided to validate the effectiveness of the proposed approaches and to illustrate the geometrical performances of multi-agent systems.     

On decentralized linear stochastic control problems with quadratic cost

A decentralized stochastic optimal control problem is considered where agents have different a priori information on the system initial state. Agents are assumed to exchange their control values but not their state vector observation values. It is shown that this leads to a suboptimal control law, with correction terms being added to the well-known optimal proportional feedback control signal obtainable under the information centralization assumption of linear dynamics with quadratic cost, when person-by-person satisfactory team decisions are considered.