Compressive Measurement Identification of Linear Time-Invariant System Application in DC Motor

In traditional system identification (SI), actual values of system parameters are concealed in the input and output data;hence, it is necessary to apply estimation methods to determine the parameters. In signal processing, a signal with N elements must be sampled at least N times. Thus, most SI methods use N or more sample data to identify a model with N parameters;however, this can be improved by a new sampling theory called compressive sensing (CS). Based on CS, an SI method called compressive measurement identification (CMI) is proposed for reducing the data needed for estimation, by measuring the parameters using a series of linear measurements, rather than the measurements in sequence. In addition, the accuracy of the measurement process is guaranteed by a criterion called the restrict isometric principle. Simulations demonstrate the accuracy and robustness of CMI in an underdetermined case. Further, the dynamic process of a DC motor is identified experimentally, establishing that CMI can shorten the identification process and increase the prediction accuracy.

Controllability, Observability and Stability for a Class of Fractional-Order Linear Time-Invariant Control Systems

The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov’s stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems.

The identification algorithm for commensurate order linear time-invariant fractional systems

An efficient identification algorithm is given for commensurate order linear time-invariant fractional systems. This algorithm can identify not only model coefficients of the system, but also its differential order at the same time. The basic idea is to change the system matrix into a diagonal one through basis transformation. This makes it possible to turn the system’s input-output relationships into the summation of several simple subsystems, and after the identification of these subsystems, the whole identification system is obtained which is algebraically equivalent to the former system. Finally an identification example verifies the effectiveness of the method previously mentioned.

Perturbation Analysis of Continuous-Time Linear Time-Invariant Systems

In this paper, we consider the perturbation analysis of linear time-invariant systems, which arise from the linear optimal control in continuous-time. We provide a method to compute condition numbers of continuous-time linear time-invariant systems. It solves the perturbed linear time-invariant systems via Riccati differential equations and continuous-time algebraic Riccati equations in finite and infinite time horizons. We derive the explicit expressions of measuring the perturbation bounds of condition numbers with respect to the solution of the linear time-invariant systems. Furthermore, condition numbers and their upper bounds of Riccati differential equations and continuous-time algebraic Riccati equations are also discussed. Numerical simulations show the sharpness of the perturbation bounds computed via the proposed methods.

COMPREHENSIVE DAMPING COEFFICIENT——A NEW DEFINITION TO DAMPING EFFECT OF LINEAR TIME-INVARIANT SYSTEMS

A new concept is presented to express the damping property of linear time-invariant systems, by the Lyapunov theorem in view of quadratic form-defined energy. Two definitions are introduced: damping energy function D(X_0, X)=Ci∫_(x_0, x) x_idx_(i-1)and comprehensive damping coefficient η-min(Ci/a_(n-i)). It is concluded that (ⅰ) of the Hurwitz determinants, △_(x-1) is proportional to the damping effect of oscillating systems, (ⅱ) the comprehensive damping coefficients of linear time-invariant systems are derived as. piecewise rational fractions which can be easily calculated and (ⅲ) the damping torque coefficient obtained for synchronous machines is independent of ω.

QUALITATIVE BEHAVIORS OF LINEAR TIME-INVARIANT DYNAMIC EQUATIONS ON TIME SCALES

We investigate the type of singularity and qualitative structure of solutions to a time-invariant linear dynamic system on time scales. The results truly unify the qualitative behaviors of the system on the continuous and discrete times with any step size.

Mixed Gl2／GH2 multi-channel multi-objective control synthesis for discrete time systems

This paper proposes a new approach for multi-objective robust control. The approach extends the standard generalized l2 (Gl2) and generalized H2 (GH2) conditions to a set of new linear matrix inequality (LMI) constraints based on a new stability condition. A technique for variable parameterization is introduced to the multi-objective control problem to preserve the linearity of the synthesis variables. Consequently, the multi-channel multi-objective mixed Gl2/GH2 control problem can be solved less conservatively using computationally tractable algorithms developed in the paper.

Low-Storage Runge-Kutta Method for Simulating Time-Dependent Quantum Dynamics

A wide range of quantum systems are time-invariant and the corresponding dynamics is dic- tated by linear differential equations with constant coefficients. Although simple in math- ematical concept, the integration of these equations is usually complicated in practice for complex systems, where both the computational time and the memory storage become limit- ing factors. For this reason, low-storage Runge-Kutta methods become increasingly popular for the time integration. This work suggests a series of s-stage sth-order explicit Runge- Kutta methods specific for autonomous linear equations, which only requires two times of the memory storage for the state vector. We also introduce a 13-stage eighth-order scheme for autonomous linear equations, which has optimized stability region and is reduced to a fifth-order method for general equations. These methods exhibit significant performance improvements over the previous general-purpose low-stage schemes. As an example, we ap- ply the integrator to simulate the non-Markovian exciton dynamics in a 15-site linear chain consisting of perylene-bisimide derivatives.

A Model-free Approach to Fault Detection of Continuous-time Systems Based on Time Domain Data

In this paper, a model-free approach is presented to design an observer-based fault detection system of linear continuoustime systems based on input and output data in the time domain. The core of the approach is to directly identify parameters of the observer-based residual generator based on a numerically reliable data equation obtained by filtering and sampling the input and output signals.

如何在通用人工智能系统中实现“知识锁定标杆浮动效应”——一种基于“时间压力”的简易心智模型

所谓“知识锁定标杆浮动效应”,是指面对同样的信念内容,认知主体会在某些环境下将其判定为“知识”,而在另一些环境下将其判定为“非知识”。该效应的存在,使得人类能够根据环境信息的变化,灵活地改变自身信念,更好地适应环境。人工智能体对于该效应机制的模拟,也能够更好地适应环境。不过,这种模拟必须建立在对于该效应的正确理解上,而西方主流知识论学界对于该效应的解释,如语境主义、比对主义与不变主义提出的解释,要么缺乏足够的普遍性,要么本身建立在一些有待解释的概念上。与之相比较,基于“时间压力”的模型,则将智能体的知识指派倾向的强度视为与其感受的时间压力彼此负相关的一项因素,而“时间压力”本身被视为“主体所预估的问题解决所需要的时间”与其“所愿意付出且能够付出的时间”之间的差值。这样的模型不仅能够对所谓的“银行案例”与“斑马案例”作出简洁的解释,而且在原则上可以被算法化。

知识归赋的实用侵入:异议及其辩护

本文试图为知识归赋中的实用侵入进行辩护。首先,按照对"侵入"界定标准的不同,可分为弱和强两个版本,它们各自受到来自理智主义和实用主义的异议。对于前者,可以从确立论题合理性、证明论证形式成立两方面为其辩护;针对后者,基于直觉和知识模型建构,可诉诸思想案例和实验哲学。其次,本文主张从实用的、可错的、语境的角度来解决知识归赋问题,并以时间约束敏感性和认识的卓越为例,为进行知识分析提供了丰富的可支撑的证据。本文支持实用侵入而不认为它是对传统知识分析路径的背离。

Time-Neutrality of Natural Laws Challenged: Time Is Not an Illusion but Ongoing Energy-Driven Information Loss

It is shown that the time of entropy increase, here called action time, is caused by a dynamically understood energy. It drives time by decreasing its presence per state, that is by abandoning order, information, and creating entropy. This mechanism can be derived from basic principles via the Lagrange-Euler formalism, just considering the properties of really experienced, oriented time and thus abandoning the paradigm of time neutrality. It describes nature driven by a dynamically understood principle of least action, which is identified as manifestation of fundamental irreversibility in nature. This readily explains the second law of thermodynamics and also yields the entropy law for non-linear irreversible thermodynamics: maximum entropy production within the restraints of the system. Dynamic energy-driven time, action time, and time asymmetry is generated via the process of erasing information and liberating its energy irreversibly as heat. It is not an illusion but information-based reality. It is the loss of information to the past and different from clock-time, which is just an artificial scale, using information for tracking real time, action time. Energy-driven fundamental irreversibility of nature can better describe experienced reality and opens the way to understand and finally imitate the self-organizing creativity in nature. It also draws far reaching consequences for understanding quantum physics, gravitation and cosmology as well as biology. From the point of view of irreversibility, nature turns out to be more elegant, simpler and rationally understandable. For the first time, it can be explained in a few words what energy and nature basically represent and why it must have been information, which has started the universe.

Brockett's Second Example:A FAS Approach Treatment

In this paper,several equivalent forms of the well-known Brockett's second example system are firstly presented.The stabilization of the system is then treated in the fully actuated system approach.A simple continuous time-invariant sub-stabilizing controller is designed,and the corresponding region of attraction is characterized.As a result,all trajectories of the system starting from the characterized region of attraction are driven exponentially to the origin.Since the region of attraction is very large,the designed sub-stabilizing controller can be directly useful in many practical situations.In cases where the initial values are indeed needed to be chosen out of the region of attraction,extremely simple pre-controllers can be designed,which drive the system trajectories into the designed region of attraction.A simulation of the designed control system is carried out to show the effect of the proposed approach.

Variable step-size adaptive filtering algorithm based on an exponent sin function

This paper proposes a robust adaptive filter based on the exponent sin cost to improve the capability against Gaussian or multiple types of non-Gaussian noises of the adaptive filtering algorithm when dealing with time-varying/time-invariant linear systems function exponent sin(ExpSin).Then a variable step-size(VSS)-ExpSin algorithm is extended further.Besides,the stepsize,the convergence,and the steady-state performance of the proposed algorithm are validated experimentally.The Monte Carlo simulation results of linear system identification illustrate the principle and efficiency of this proposed adaptive filtering algorithm.Results suggest that the proposed adaptive filtering algorithm has superior performance when estimating the unknown linear systems under multiple-types measurement noises.

ON FORMABILITY OF LINEAR CONTINUOUS-TIME MULTI-AGENT SYSTEMS

This paper is focused on formability of multi-agent systems （MASs）. The problem is concerned with the existence of a protocol that has the ability to drive the MAS involved to the desired formation, and thus, is of essential importance in designing formation protocols. Formability of an MAS depends on several key factors： agents＇ dynamic structures, connectivity topology, properties of the desired formation and the admissible control set. Agents of the MASs considered here are described by a general continuous linear time-invariant （LTI） model. By using the matrix analysis and algebraic graph theory, some necessary and sufficient conditions on formability of LTI-MASs are obtained. These conditions characterize in some sense the relationship of formability, connectivity topology, formation properties and agent dynamics with respect to some typical and widely used admissible protocol sets.

DISTURBANCE ATTENUATION VIA STATE-FEEDBACK CONTROLLERS

This paper focuses on the H optimal control problem in which the wholestate is available for feedback. We show that in attenuating the disturbance, the Hoptimal performance of dynamic state-feedback is no better than that of static state-feedback, which generalizes current results for linear time-invariant systems with no directtransmission from the disturbance and control input to the controlled output.

LS-Based Parameter Estimation of DARMA Systems with Uniformly Quantized Observations

This paper is concerned with the parameter estimation of deterministic autoregressive moving average(DARMA)systems with quantization data.The estimation algorithms adopted here are the least squares(LS)and the forgetting factor LS,and the signal quantizer is of uniform,that is,with uniform quantization error.The authors analyse the properties of the LS and the forgetting factor LS,and establish the boundedness of the estimation errors and a relationship of the estimation errors with the size of quantization error,which implies that the smaller the quantization error is,the smaller the estimation error is.A numerical example is given to demonstrate theorems.

An overview on the designs of distributed observers in LTI multi-agent systems

With the rapid development of information technologies and cloud computing, sensor networks play an increasingly important role in our society. Over the past few decades, distributed observer theory has attracted unprecedented attention due to its wide potential applications in different areas. Meanwhile, various approaches and algorithms have been proposed and investigated. The design of distributed observers is one of the frontier topics of system and control research, which has the significant theoretical values and broad application prospects. This paper attempts to review the representative models and the corresponding approaches for distributed observer design in linear time-invariant(LTI) systems. Firstly, the research backgrounds and main advances of distributed observer designs are briefly reviewed. Then, recent results of distributed observer designs for discrete-time and continuous-time LTI multi-agent systems(MASs) are introduced in detail, respectively. Finally, the prospects and the future work directions of the design of distributed observers are put forward. The main purpose of this paper is to promote the emerging topic on the designs of distributed observers, with focuses on the interdisciplinary interest from technological sciences.