Global stabilization of linear discrete-time systems with bounded feedback

This paper deals with the problem of global stabilization of linear discrete time systems by means of bounded feedback laws. The main result proved is an analog of one proved for the continuous time case by the authors, and shows that such stabilization is possible if and only if the system is stabilizable with arbitrary controls and the transition matrix has spectral radius less than or equal to one. The proof provides in principle an algorithm for the construction of such feedback laws, which can be implemented either as cascades or as parallel connections (“single hidden layer neural networks”) of simple saturation functions.     

State feedback stabilization of linear impulsive systems

We address the fundamental problem of state feedback stabilization for a class of linear impulsive systems featuring arbitrarily-spaced impulse times and possibly singular state transition matrices. Specifically, we show that a strong reachability property enables a state feedback law to be constructed that yields a uniformly exponentially stable closed-loop system. The approach adopts a receding horizon strategy involving a weighted reachability gramian in a manner reminiscent of well-known results for time-varying linear systems for both continuous and discrete-time cases.     

A note on asymptotic stabilization of linear systems by periodic, piecewise constant, output feedback

This note studies the asymptotic stabilization problem for controllable and observable, single-input single-output, linear, time-invariant, continuous-time systems by means of memoryless output feedback of the form u(t)=k(t)y(t), with k(t) periodic and piecewise constant. A necessary and sufficient condition, together with a simpler to test sufficient condition, given in terms of a bilinear matrix inequality, is presented. A few illustrative examples complete the paper.     

空空导弹后射火控截获区仿真

空空导弹后射火控截获区的大小是衡量后射火控系统设计成功的标志。为扩大攻击区,防后方目标的威胁,采用建立空空导弹后射火控模型,给出导弹导引律、导弹后射过零点的判断、推力矢量偏角和攻角及导弹运动学方程,并给出了空空导弹后射火控截获区的仿真方法,通过研究空空导弹后射火控截获区在不同条件下的性能,对影响后射火控截获区的因素进行了仿真,经验证,对比后射与越肩发射的火控截获区,证明后射与越肩发射相结合,可以实现全向攻击的目的。     

Adaptive learning control of linear systems by output error feedback

This paper addresses the problem of designing an output error feedback tracking control for single-input, single-output uncertain linear systems when the reference output signal is smooth and periodic with known period T. The considered systems are required to be observable, minimum phase, with known relative degree and known high frequency gain sign. By developing in Fourier series expansion a suitable unknown periodic input reference signal, an output error feedback adaptive learning control is designed which ‘learns’ the input reference signal by identifying its Fourier coefficients: bounded closed-loop signals and global exponential tracking of both the input and the output reference signals are obtained when the Fourier series expansion is finite, while global exponential convergence of the input and output tracking errors into arbitrarily small residual sets is achieved otherwise. The structure of the proposed controller depends only on the relative degree, the reference signal period, the high frequency gain sign and the number of estimated Fourier coefficients.     

带传输滞后的线性离散系统的状态反馈镇定

针对存在传输滞后的线性离散系统的状态反馈镇定问题,给出了系统可镇定的一个内部限制条件.为克服这一限制条件,提出了两种方法:一种是充分利用滞后状态的信息,另一种是设计带有递推动态的状态反馈控制器.研究结果表明,若系统在没有传输滞后时能通过状态反馈被镇定,则存在传输滞后时一定也能通过设计新的控制器使系统被镇定.     

On pole assignment of linear systems by gain output feedback

In this paper, the Geometric Approach is used to derive in a straightforward way a sufficient condition for pole assignability by gain output feedback. This result leads to a pole assignment procedure which reduces to solving a system of min (n - m, n - p) polynomial equations where n is the number of states, m the number of inputs, p the number of outputs. In the case where m + p > n, this system clearly appears to be linear. The degrees of freedom related to the pole assignment problem are expressed in terms of (right or left) eigenvectors.     

基于LMI 的线性时滞系统输出动态反馈镇定

考虑线性时滞系统的输出动态反馈镇定问题.利用自由参数矩阵对闭环系统进行适当变换,并结合相应的Lyapunov-Krasovskii泛函得到了时滞相关的控制器存在性判据.利用控制器参数化方法,将控制器参数与泛函参数的求解归结为线性矩阵不等式解的形式,从而克服了时滞无关性及求解非凸优化问题所导致的保守性.仿真算例验证了结论的有效性.     

A note on connectivity of multi-agent systems with proximity graphs and linear feedback protocol

In this note, we investigate the possibility of simplifying the connectivity verification for multi-agent systems with proximity graphs and the linear feedback protocol. A Lyapunov-like approach is developed for analyzing the monotonicity of the largest edge length in the network. Based on this approach, we provide an initial-connectivity-based sufficient condition for dynamic connectivity. In particular, when each initial node degree is not less than three fourth of the graph order, initial network connectivity implies dynamic connectivity.     

Output feedback nonlinear control for a linear motor in suspension mode

This work extends an existing model of a permanent magnet linear synchronous motor and proposes a nonlinear controller for it. The motor is assumed to operate without mechanical bearings, so that the airgap length varies and requires regulation; accordingly, the extended model captures both longitudinal and normal dynamics. The output feedback control law mainly relies on the recently proposed power integrator method but also uses the standard techniques of exact feedback linearization and Lyapunov redesign. Uniformly bounded stability of the closed-loop system is achieved in spite of cogging forces and end-effects.     

Output feedback variable structure control for linear systems with uncertainties and disturbances

This paper proposes a dynamic output feedback variable structure controller for linear MIMO systems with mismatched and matched norm-bounded uncertainties and matched nonlinear disturbances. The proposed controller consists of nonlinear and linear parts, similar to the unit vector type of controller. The nonlinear part of the new controller takes care only of matched uncertainties and disturbances and, on the other hand, the linear part with full dynamics completely handles mismatched uncertainties. Designing such a linear part leads to use a Lyapunov function associated with the full states, which achieves the global stability against the mismatched uncertainties. The resulting criteria are, furthermore, converted into solvable ones, by using the so-called cone complementary linearization algorithm for bi-convex problems.     

Observer-based feedback stabilization of linear systems with event-triggered sampling and dynamic quantization

We consider the problem of output feedback stabilization in linear systems when the measured outputs and control inputs are subject to event-triggered sampling and dynamic quantization. A new sampling algorithm is proposed for outputs which does not lead to accumulation of sampling times and results in asymptotic stabilization of the system. The approach for output sampling is based on defining an event function that compares the difference between the current output and the most recently transmitted output sample not only with the current value of the output, but also takes into account a certain number of previously transmitted output samples. This allows us to reconstruct the state using an observer with sample-and-hold measurements. The estimated states are used to generate a control input, which is subjected to a different event-triggered sampling routine; hence the sampling times of inputs and outputs are asynchronous. Using Lyapunov-based approach, we prove the asymptotic stabilization of the closed-loop system and show that there exists a minimum inter-sampling time for control inputs and for outputs. To show that these sampling routines are robust with respect to transmission errors, only the quantized (in space) values of outputs and inputs are transmitted to the controller and the plant, respectively. A dynamic quantizer is adopted for this purpose, and an algorithm is proposed to update the range and the centre of the quantizer that results in an asymptotically stable closed-loop system.     

Output feedback pole placement for linear time-varying systems with application to the control of nonlinear systems

The output feedback pole placement problem is solved in an input-output algebraic formalism for linear time-varying (LTV) systems. The recent extensions of the notions of transfer matrices and poles of the system to the case of LTV systems are exploited here to provide constructive solutions based, as in the linear time-invariant (LTI) case, on the solutions of diophantine equations. Also, differences with the results known in the LTI case are pointed out, especially concerning the possibilities to assign specific dynamics to the closed-loop system and the conditions for tracking and disturbance rejection. This approach is applied to the control of nonlinear systems by linearization around a given trajectory. Several examples are treated in detail to show the computation and implementation issues.     

Piecewise output feedback control for affine systems with disturbances based on linear temporal logic specifications

In the paper,we investigate the problem of finding a piecewise output feedback control law for an uncertain affine system such that the resulting closed-loop output satisfies a desired linear temporal logic (LTL) specification.A two-level hierarchical approach is proposed to solve the problem in a triangularized output space.In the lower level,we explore whether there exists a robust output feedback control law to make the output starting in a simplex either remains in it or leaves via a specific facet.In the higher level,for the triangularization,we construct the transition system according to the reachability relationship obtained in the lower level and search for feasible paths that meet the LTL specification.The control approach is then applied to solve a motion planning problem.     

Robust stabilization and guaranteed cost control for discrete-time linear systems by static output feedback

This paper proposes a systematic approach for the static output feedback control design for discrete-time uncertain linear systems. It is shown that if the open-loop system satisfies some particular structural conditions and the uncertainty has a specific structure, a static output feedback gain can be calculated easily, using a formula only involving the original system matrices. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. Square and nonsquare systems are considered. The performance problem through a quadratic criterion is also discussed (guaranteed cost control).     

Robust output feedback model predictive control using off-line linear matrix inequalities

A fundamental question about model predictive control (MPC) is its robustness to model uncertainty. In this paper, we present a robust constrained output feedback MPC algorithm that can stabilize plants with both polytopic uncertainty and norm-bound uncertainty. The design procedure involves off-line design of a robust constrained state feedback MPC law and a state estimator using linear matrix inequalities (LMIs). Since we employ an off-line approach for the controller design which gives a sequence of explicit control laws, we are able to analyze the robust stabilizability of the combined control laws and estimator, and by adjusting the design parameters, guarantee robust stability of the closed-loop system in the presence of constraints. The algorithm is illustrated with two examples.     

Output feedback robust MPC with one free control move for the linear polytopic uncertain system with bounded disturbance

In this paper a previous approach, for the robust model predictive control (MPC) for a linear polytopic uncertain system, is extended to the case with bounded disturbance and unmeasurable state. The controller on-line optimizes a free control move followed by an output feedback control law based on the pre-specified state estimator. A key technique for this controller is an appropriate formulation of the estimation error bound which accounts for recursive feasibility of the optimization problem. The quadratic boundedness (QB) of the augmented state is guaranteed by the proposed approach. A numerical example is given to illustrate the effectiveness of the proposed controller.     

一种关于反馈Agent的多元线性回归方法

多元线性回归方法常用于数据预测,预测数据和实际数据总会存在误差。为了提高预测精度,采用反馈Agent算法,把误差作为一个新的线性反馈自变量,用在下次的多元线性回归预测中。论文采用实例验证了该方法的有效性。