Duality Properties of Linear Impulsive Systems

Reachability and observability properties of linear switched, impulsive, and switched/impulsive systems have received a great deal of attention over the past decade. The purpose of this paper is to rigorously establish a duality between reachability and observability for linear impulsive systems both in direct system‐theoretic terms as well as in geometric terms. These connections are established using an appropriately defined adjoint system associated with the original impulsive system. The duality between reachability and observability is then used to leverage recent reachability results in order to tighten the relationship between the set of unobservable states and a certain invariant subspace.     

捷联惯导系统静基座初始对准精度分析及仿真

在利用卡尔曼滤波器对捷联惯导系统（SINS）进行静基座初始对准中,由于系统的不完全可观测性,使得有些状态没有滤波效果,有些状态的估计精度受到限制。对SINS静基座初始对准卡尔曼滤波方程进行了可观测性分析,提出了状态降阶的处理方法,并得到了各状态估计的极限精度公式。最后进行了软件仿真,仿真结果表明：降阶滤波器和全降阶滤波器的估计精度基本相同,但足前者计算量更小,并且在滤波计算中能够消除不可观测状态的不利影响。     

Truncated balanced realization of a stable non-minimal state-space system

In this paper we present a numerically reliable algorithm to compute the balanced realization of a stable state-space system that may be arbitrarily close to being unobservable and/or uncontrollable. The resulting realization, which is known to be a good approximation of the original system, must be minimal and therefore may contain a reduced number of states. Depending on the choice of partitioning of the Hankel singular values, this algorithm can be used either as a form of minimal realization or of model reduction. This illustrates that in finite precision arithmetic these two procedures are closely related. In addition to real matrix multiplication, the algorithm only requires the solution of two Lyapunov equations and one singular value decomposition of an upper-triangular matrix.     

Self‐alignment and calibration of a MEMS IMU: Improving observability and estimability by rotary motions of IMU

The stationary self‐alignment and calibration (SSAC) for a low‐cost MEMS IMU is quite challenging due to the poor observability of an inertial system under static condition and the significant sensor errors of MEMS inertial sensors. This research proposes to employ IMU rotations to improve the system observability and estimability regarding the SSAC of a low‐cost MEMS IMU. IMU rotations about the X, Y, and Z axes are employed in this paper. The analytic estimation algorithm for each error state is derived and the observability of the system with IMU rotation is analyzed. As the observability analysis will not provide clues about how well an error state can be estimated, the estimability analysis is also conducted based on the eigenvalues and eigenvectors from the covariance matrix in the Kalman filter. Tests are conducted with a tri‐axial turntable to verify the improvements on system observability and estimability brought by IMU rotations. Of both theoretical analysis and results indicated with proper IMU rotations, only azimuth error still remains unobservable, and the IMU rotation also significantly improves the estimability of all error states, including the unobservable azimuth.     

Water-quality estimation and control in streams

In this paper a methodology is given for the process of water-quality estimation and control in streams using a systems approach. The proposed procedure is based on the stream water quality model developed by Hassan et at. (1981). A linear observer is designed that can be used to estimate the unobservable states of the system. These states represent the concentration of the water-quality constituents in a given stream that are difficult, time-consuming or costly to measure. Although the system model is non-linear, the application of the developed linear observer in the case of the River Nile showed its stability and convergence to the actual states of the system. The output of this observer can also be used to derive the two-level hierarchical optimization scheme developed for this system in order to maintain water-quality standards in polluted reaches in a given water body with minimum cost.     

对称离散事件系统事件重标记观测器性质研究

当离散事件系统(discrete-event systems,DES)由多组结构相同的组件构成时,则称离散事件系统具有对称性.为了化简对称离散事件系统的状态空间,本文提出事件重标记映射,将完成相同任务的事件标记为同一事件,将与控制无关的不可控事件设为不可观测事件,并将其标记为空字符擦除.为了确保事件重标记前后系统对应的最大监督控制器具有相同的控制效果,本文引入重标记观测器(relabeling observer property,ROP)的概念并给出判断被控对象对应的语言关于事件重标记映射是否具有重标记观测器性质的算法;然后运用重标记观测器性质证明事件重标记前后监督控制器控制效果的等价性,从而可用简化后的监督控制器实现与事件重标记操作前相同的控制任务.最后通过实例验证所提理论的正确性.     

Identification of the unobservable behaviour of industrial automation systems by Petri nets

This paper addresses the problem of identifying the model of the unobservable behaviour of discrete event systems in the industrial automation sector. Assuming that the fault-free system structure and dynamics are known, the paper proposes an algorithm that monitors the system on-line, storing the occurred observable event sequence and the corresponding reached states. At each event observation, the algorithm checks whether some unobservable events have occurred on the basis of the knowledge of the Petri net (PN) modelling the nominal system behaviour and the knowledge of the current PN marking. By defining and solving some integer linear programming problems, the algorithm decides whether it is necessary to introduce some unobservable (silent) transitions in the PN model and provides a PN structure that is consistent with the observed event string. A case study describing an industrial automation system shows the efficiency and the applicability of the proposed algorithm.     

H ∞ model reduction for discrete‐time positive systems with inhomogeneous initial conditions

This paper addresses the H _∞ model reduction problem of discrete‐time positive linear systems with inhomogeneous initial conditions. For an asymptotically stable positive system with non‐zero initial condition, our goal is to approximate it by a reduced‐order initial‐valued positive system without introducing significant error. We establish a necessary and sufficient condition for the existence of a desired reduced‐order model such that the output error between the original system and the reduced‐order one is bounded by a weighted sum of the magnitude of the input and that of the initial condition. Moreover, based on congruent transformation and the dual form of bounded real lemma, several equivalent conditions are derived in terms of LMIs and an iterative convex optimization algorithm is developed accordingly. Finally, an illustrative example is presented to show the effectiveness of the proposed methods. Copyright © 2013 John Wiley & Sons, Ltd.     

Adaptive stabilization for ODE systems via boundary measurement of uncertain diffusion‐dominated actuator dynamics

This paper is concerned with the adaptive stabilization for the ODE systems via boundary measurement of uncertain diffusion‐dominated actuator dynamics. It is worth pointing out that, in the related works, all the states of the diffusion‐dominated actuator are required to be measurable, and this means that an infinite number of sensors are needed to implement the controllers, which is impossible in practice. Quite differently in this paper, only one boundary state of the diffusion‐dominated actuator is measurable and available for feedback design. Moreover, the actuator dynamics contains parameter unknown. Motivated by the existing results, a state observer is first designed to estimate the unmeasurable actuator states, which consists of an input filter and an output filter. Then, by introducing an infinite‐dimensional backstepping transformation, a pivotal target system is obtained from which it is more convenient to design controller and analyze the performance of the original system. Finally, an adaptive controller is constructed by adaptive technique and Lyapunov method, which guarantees that the states of the original system converge to zero, whereas the other states of the closed‐loop system keeping bounded. A simulation example is provided to illustrate the effectiveness of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

FREQUENCY DOMAIN ANALYSIS OF FAST AND SLOW MOTIONS IN SLIDING MODES

A frequency domain approach to analysis of fast and slow motions in sliding modes is proposed in the paper. The proposed approach is based on the construction of a relay system that is equivalent to the original sliding mode control system and on the application of the locus of a perturbed relay system method. A precise model of the fast motions and a non‐reduced order model of the slow motions for the SISO linear time‐invariant case are obtained as a result of the proposed approach.     

基于Petri网结构分析的监控器综合

在基于Petri网建模的离散事件系统中, 提出利用局部关联信息进行约束转换, 并实现Petri网结构监控器综合的方法. 对以Parikh矢量约束形式给出的控制规范, 不可控不可观变迁会导致约束成为非法约束, 分析了不可控变迁的前向关联结构和不可观变迁的后向关联结构, 利用局部关联变迁实现对不可控和不可观变迁的间接控制, 从而将非法矢量约束转换为合法约束, 并保证初始控制规范的实现. 与基于矩阵的监控器综合方法相比, 本文的方法只需利用局部信息, 最后通过实例对该方法进行了说明.     

Reduced Order Robust Gain‐Scheduling Control Of The Diesel Apu For Series Hybrid Vehicles

This paper presents a reduced order robust gain‐scheduling approach for the control of the diesel auxiliary power unit (APU) for series hybrid vehicles. The nonlinear plant dynamics are converted into a linear parameter‐varying (LPV) form with parametric uncertainties, in which only partial information of the plant states is available. For this type of LPV system, a new reduced order robust gain‐scheduling synthesis method is proposed based on partial state feedback. The parametric uncertainties are considered using multipliers to reduce the conservatism. The reduced order synthesis problem is solved offline by means of linear matrix inequalities (LMIs), and the synthesis result requires much simpler online computation than the explicit controller formulas do. The synthesis method is applied to the diesel APU controller design, and simulation results are given to demonstrate the controller performance.     

Global adaptive stabilization for high‐order uncertain time‐varying nonlinear systems with time‐delays

This paper focuses on the adaptive stabilization problem for a class of high‐order nonlinear systems with time‐varying uncertainties and unknown time‐delays. Time‐varying uncertain parameters are compensated by combining a function gain with traditional adaptive technique, and unknown multiple time‐delays are manipulated by the delicate choice of an appropriate Lyapunov function. With the help of homogeneous domination idea and recursive design, a continuous adaptive state‐feedback controller is designed to guarantee that resulting closed‐loop systems are globally uniformly stable and original system states converge to zero. The effectiveness of the proposed control scheme is illustrated by the stabilization of delayed neural network systems. Copyright © 2016 John Wiley & Sons, Ltd.     

Maximally Permissive Petri Net Supervisors for Flexible Manufacturing Systems with Uncontrollable and Unobservable Transitions

This paper presents a deadlock prevention policy to obtain behaviorally optimal supervisors for flexible manufacturing systems with uncontrollable and unobservable transitions. The conditions of uncontrollability and unobservability of transitions are revealed in the sense of the implementation of a Petri net supervisor. Then, integer linear programming models are designed to obtain a Petri net supervisor such that all legal markings are reachable and the number of control places is reduced. We also show that a controllable transition can be unobservable and self‐loops can be used to disable the transition but do not observe its firing. Finally, examples are provided to illustrate the proposed approach.     

State estimation of (otherwise unobservable) linear mechanical systems through the use of non-smooth impacts: the case of two mating gears

In this paper, we consider a particular mechanism, constituted by a pair of infinitely rigid mating gears subject to backlash, where only the position of the actuated gear is measured, so that the system is unobservable if the impacts between the teeth of the gears are ignored. Under the assumption that there is an infinite sequence of non-smooth impacts (which assumption is generally satisfied during a usual task, e.g., when the mechanism is actuated by a constant torque), it is possible to design an observer that asymptotically estimates also the position and the velocity of the non-actuated gear. Simulation results are included to verify the effectiveness of the proposed observer.     

Global decentralized sampled‐data output feedback stabilization for a class of large‐scale nonlinear systems with sensor and actuator failures

In this paper, we investigate global decentralized sampled‐data output feedback stabilization problem for a class of large‐scale nonlinear systems with time‐varying sensor and actuator failures. The considered systems include unknown time‐varying control coefficients and inherently nonlinear terms. Firstly, coordinate transformations are introduced with suitable scaling gains. Next, a reduced‐order observer is designed to estimate unmeasured states. Then, a decentralized sampled‐data fault‐tolerant control scheme is developed with an allowable sampling period. By constructing an appropriate Lyapunov function, it can be shown that all states of the resulting closed‐loop system are globally uniformly ultimately bounded. Finally, the validity of the proposed control approach is verified by using two examples.     

Discrete output feedback sliding‐mode control with integral action

This paper presents a novel approach to the problem of discrete time output feedback sliding‐mode control design. The method described applies to uncertain systems (with matched uncertainties) which are not necessarily minimum phase or relative degree one. A new sliding surface is proposed, which is associated with the equivalent control of the output feedback sliding‐mode controller. Design freedom is available to select the sliding surface parameters to produce an appropriate reduced‐order sliding motion. In order for this to be achieved, a static output feedback condition associated with a certain reduced‐order system obtained from the original plant must be solvable. The practicality of the results are demonstrated through the implementation of the controller on a small DC motor test rig. Copyright © 2005 John Wiley & Sons, Ltd.     

A closed‐loop nonlinear control and sliding mode estimation strategy for fluid flow regulation

Novel sliding mode observer (SMO) and robust nonlinear control methods are presented, which are shown to achieve finite‐time state estimation and asymptotic regulation of a fluid flow system. To facilitate the design and analysis of the closed‐loop active flow control (AFC) system, proper orthogonal decomposition–based model order reduction is utilized to express the Navier‐Stokes partial differential equations as a set of nonlinear ordinary differential equations. The resulting reduced‐order model contains a measurement equation that is in a nonstandard mathematical form. This challenge is mitigated through the detailed design and analysis of an SMO. The observer is shown to achieve finite‐time estimation of the unmeasurable states of the reduced‐order model using direct sensor measurements of the flow field velocity. The estimated states are utilized as feedback measurements in a closed‐loop AFC system. To address the practical challenge of actuator bandwidth limitations, the control law is designed to be continuous. A rigorous Lyapunov‐based stability analysis is presented to prove that the closed‐loop flow estimation and control method achieves asymptotic regulation of a fluid flow field to a prescribed state. Numerical simulation results are also provided to demonstrate the performance of the proposed closed‐loop AFC system, comparing 2 different designs for the SMO.