Uniformly convergent sliding mode‐based observation for switched linear systems

The problem of designing an observer capable of reconstructing the continuous and discrete states for a class of switched linear systems is addressed. A stack of dynamical observers based on the super twisting algorithm with finite and uniform‐in‐the‐initial‐condition convergence is considered, which provides an estimate of the continuous state and, at the same time, produces residual signals suitable for reconstructing the discrete state. An appropriate ‘projection’ of the residuals is suggested, which allows to speed up the reconstruction of the discrete state. Formal ‘distinguishability’ conditions guaranteeing that the discrete state can be uniquely reconstructed are derived. Lyapunov‐based proofs of convergence, and numerical simulations, support the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Observability Conditions by Polynomial Ideals

In this paper, we give global and local observability conditions of polynomial systems. Each observability is defined in terms of distinguishability of a pair of initial states. The set of pairs of initial states are represented as an affine variety. By using this affine variety, a global observability condition is derived. Then, a local observability condition is presented based on the minimal decomposition of the affine variety and dimension theory.     

模式转换未知的一类混杂系统的状态估计

Since the state of hybrid systems is determined by interacting continuous and discrete dynamics, the state estimation of hybrid systems becomes a challenging problem. It is more complicated when the discrete mode transition information is not available, and the modes of hybrid systems are nonlinear stochastic dynamic systems. To address this problem, this paper proposes a novel hybrid strong tracking filter (HSTF) for state estimation of a class of hybrid nonlinear stochastic systems with unknown mode transition, the method for designing HSTF is presented. The HSTF can estimate the continuous state and discrete mode accurately with unknown mode transition information, and the estimation of hybrid states is robust against the initial state. Simulation results illustrate the effectiveness of the proposed approach.     

State Estimation of a Class of Hybrid Systems in the Presence of Unknown Mode Transitions

Since the state of hybrid systems is determined by interacting continuous and discrete dynamics,the state estimation of hybrid systems becomes a challenging problem.It is more com- plicated when the discrete mode transition information is not available,and the modes of hybrid systems are nonlinear stochastic dynamic systems.To address this problem,this paper proposes a novel hybrid strong tracking filter (HSTF) for state estimation of a class of hybrid nonlinear stochas- tic systems with unknown mode transition,the method for designing HSTF is presented.The HSTF can estimate the continuous state and discrete mode accurately with unknown mode transition in- formation,and the estimation of hybrid states is robust against the initial state.Simulation results illustrate the effectiveness of the proposed approach.     

Invertibility of switched linear systems

We address the invertibility problem for switched systems, which is the problem of recovering the switching signal and the input uniquely given an output and an initial state. In the context of hybrid systems, this corresponds to recovering the discrete state and the input from partial measurements of the continuous state. In solving the invertibility problem, we introduce the concept of singular pairs for two systems. We give a necessary and sufficient condition for a switched system to be invertible, which says that the individual subsystems should be invertible and there should be no singular pairs. When the individual subsystems are invertible, we present an algorithm for finding switching signals and inputs that generate a given output in a finite interval when there is a finite number of such switching signals and inputs. Detailed examples are included.     

混合动态系统中连续状态系统用离散事件系统描述的一致性

混合动态系统起因于离散事件系统用于监控连续状态系统的行。本文用抽象语言方法描述连续状态系统，研究状态离散事件系统描述的一致性。基于输入输出观点简要地 讨论了离散控制器综合。     

Robust Analytical Redundancy Relations for Fault Diagnosis In Nonlinear Systems

The problem of robust analytical redundancy relations design for fault diagnosis in nonlinear systems is investigated. An approach is proposed to solve this problem through an extension of the system state‐space by means of constant (or slow varying) unknown parameters, followed by designing analytical redundancy relations that are insensitive both to state variables and unknown parameters. To make the design practicable, some problems related to nonlinear transformation of the extended system model into observable one are considered. The quasi‐linear computational form for robust analytical redundancy relations is described. Fault detectability and distinguishability conditions are formulated, and a recommendation for choosing the size of the moving time window is made. The results are demonstrated through an example involving an SISO nonlinear model of an underwater vehicle.     

The complexity of some reachability problems for a system on a finite group

We consider a system defined as the product of a finite set of periodic systems on cyclic groups. It is of interest to determine if certain subgroups and unions of subgroups of the state set are reachable from a specified initial state, and in particular to determine the computational complexity of verifying such reachability. These questions are motivated by certain problems that arise in the modelling and control of discrete event systems and certain forms of periodic scheduling. Our main result is that deciding whether or not the union of a certain set of subgroups is reachable or not is NP-complete.     

Intrinsic robustness of global asymptotic stability

Equivalence is shown for discrete time systems between global asymptotic stability and the so-called integral Input-to-State Stability. The latter is a notion of robust stability with respect to exogenous disturbances which informally translates into the statement “no matter what is the initial condition, if the energy of the inputs is small, then the state must eventually be small”.     

Insensitive observers for discrete time linear systems

This paper considers the problem of designing an observer insensitive to system parameter variations in discrete time linear multivariable systems. A K-insensitive observer is defined as an observer that can reconstruct a linear function of the state vector in spite of the variations of system parameters, provided the initial state of the observer is suitably chosen. A deadbeat observer is defined to be an observer that reconstructs the linear function for an arbitrary initial condition of the observer. Then, the existence of the K-insensitive observer is examined, and the class of K-insensitive observers is characterized. A necessary and sufficient condition is derived under which the K-insensitive deadbeat observer can be designed, and a simple algorithm is proposed to design the observer. The resulting observer is shown to be stable. The order of the observer is evaluated. The condition for generic solvability of the problem is also given.     

基于离散对数的无证书代理签名方案

对已有无证书代理签名方案进行研究发现,基于离散对数知识构造的无证书代理签名方案几乎没有,结合有限域上的离散对数知识和无证书密码体制的优点,提出了一种高效的、基于离散对数的无证书代理签名方案。该方案避免了基于身份密码体制中的密钥托管问题和证书密码体制中的证书存在问题,满足代理签名的不可伪造性、代理密钥的依赖性、代理签名的可区分性和抗滥用性等良好性质。整个方案没有使用双线性对操作,在有限域上离散对数问题难解的条件下证明和讨论了方案的正确性和安全性。     

广义系统稳态Kalman估值器

用现代时间序列分析方法,提出了广义离散线性随机系统稳态Kalman滤波、平滑 和预报的一种统一格式,给出了稳态Kalman估值器增益新算法,避免了求解Riccati方程.为 保证估值器的渐近稳定性,给出了选择初始估值的公式.仿真例子说明了所提出的结果的有 效性.     

Improving continuous–discrete interval observers with application to microalgae-based bioprocesses

Based on intervals bounding the uncertain initial conditions, inputs, model parameters and measurements, interval observers provide guaranteed intervals for the state trajectory. However, most of the published studies focus on methods relying on continuous-time on-line measurements, or at least, relatively fast sampling. In this study, interval state estimation methods are proposed in the situation, quite common in biological systems, where measurements are only available at discrete, and possibly rare, times. The attention is focused on defining predictors preserving the boundedness of the state variables between two measurement times assuming bounded uncertainties. The methods are tested with simulated data from continuous cultures of green algae.     

离散系统状态反馈控制中的跟踪问题

针对离散系统，本文讨论状态调节器的输出跟踪问题，指出了现有的离散状态调节器存在的问题，提出了一种新型的离散状态PI调节器．     

On a method for solving a local boundary problem for a nonlinear stationary system with perturbations in the class of piecewise constant controls

The wide class of nonlinear stationary systems of ordinary differential equations taking into account restrictions on control and external perturbation is considered. An algorithm for constructing a discrete control function that guarantees the transfer of the systems from the initial state to the origin and an arbitrary neighborhood of the origin is proposed. A constructive sufficient condition of the Kalman type, in which the specified translation is possible, is obtained. The problem of robot‐manipulator control is considered and its numerical simulation is carried out.     

Stability bound of discrete multiple time-delay singularly perturbed systems

In this paper, the exact stability bound for discrete multiple time-delay singularly perturbed systems is examined. The obtained results, based on state space approach for the critical stability criterion of discrete systems, are sufficient conditions for the original system and its reduced subsystems about stability problems. Besides, we show that the subsystems are, indeed, zero-order approximations to the original systems. An example is given to illustrate the proposed schemes.     

Some Problems of Analysis of Hybrid Automata

A class of 1-dimensional hybrid automata is defined in which the dynamics at each discrete state for different sets of initial values of a continuous state can be represented by different differential equations, and a finite duration of this dynamics, which can be different for different sets of initial values of such a continuous state, is specified. Algorithms are proposed to solve problems of eliminating contradictions in the objects that define a hybrid automaton, matching these objects with one another, finding the minimum number of switchings, and estimating the minimum time required to reach discrete states from a set of initial discrete states.     

Deterministic and stochastic control of discrete-time bilinear systems

Optimal control of a class of time invariant single-input, discrete bilinear systems is investigated in this paper. Both deterministic and stochastic problems are considered.

In the deterministic problem, for the initial state in a certain set ∑₀, the solution is the same as the solution to the associated linear system. The optimal path may be a regular path or a singular path.

The stochastic control problem is considered with perfect state observation, and additive and multiplicative noise in the state equation. It is demonstrated that the presence of noise simplifies the analysis compared to that in the determinstic case.     

Continuous-discrete gain transformation methods for linear feedback control

The problem of transforming between continuoustime state variable feedback gains and equivalent discrete gains suitable for digital implementation is considered. The concepts of state and control equivalence yield two simple transformation rules, a pseudo-inverse method and an average gain method, respectively. As the sampling interval δ→0, these methods are contrasted with existing Taylor series based approaches. The new transformation rules are also studied numerically using a ship course-keeping example. Transformed optimal continuous gains are compared with optimal discrete gains over a wide range of sampling intervals.     

Mean-square stability for discrete bilinear systems in Hilbert space

A discrete system is uniformly mean-square stable if uniform convergence is preserved between input and state correlation sequences, and if nuclearity is preserved between the input and state correlation limits. This paper supplies a contraction-free condition ensuring mean-square stability for infinite-dimensional bilinear systems evolving in a separable Hilbert space.