Design of Luenberger function observer with disturbance decoupling for matrix second-order linear systems-a parametric approach

A simple method for disturbance decoupling for matrix second-order linear systems is proposed directly in matrix second-order framework via Luenberger function observers based on complete parametric eigenstructure assignment. By introducing the H2 norm of the transfer function from disturbance to estimation error, sufficient and necessary conditions for disturbance decoupling in matrix second-order linear systems are established and are arranged into constraints on the design parameters via Luenberger function observers in terms of the closed-loop eigenvalues and the group of design parameters provided by the eigenstructure assignment approach. Therefore, the disturbance decoupling problem is converted into an eigenstructure assignment problem with extra parameter constraints. A simple example is investigated to show the effect and simplicity of the approach.

Unified parametric approaches for high-order integral observer design for matrix second-order linear systems

A type of high-order integral observers for matrix second-order linear systems is proposed on the basis of generalized eigenstructure assignment via unified parametric approaches. Through establishing two general parametric solutions to this type of generalized matrix second-order Sylvester matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the fight factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass-dashpot system is utilized to illustrate the design procedure and show the effect of the proposed approach.

Observer design for matrix second-order linear systems: a parametric approach

The issue of designing a type of generalized Luenberger observers for matrix second-order linear (MSOL) systems was addressed in the matrix second-order framework. By introducing the concept of stable matrix pair for MSOL systems, sufficient and necessary conditions for the design of the type of generalized Luenberger observers were given under the assumption of controllability and observability of the MSOL system. Based on the proposed conditions and the right coprime factorization of the system, a parametric approach to the design of such type of observers was presented. The proposed approach provides all the degrees of design freedom, which can be further utilized to achieve additional system specifications. A spring-mass system was utilized to show the effect of the proposed method.

The First Five Years of a Phase Theory for Complex Systems and Networks

In this paper,we review the development of a phase theory for systems and networks in its first five years,represented by a trilogy:Matrix phases and their properties;The MIMO LTI system phase response,its physical interpretations,the small phase theorem,and the sectored real lemma;The synchronization of a multi-agent network using phase alignment.Towards the end,we also summarize a list of ongoing research on the phase theory and speculate what will happen in the next five years.

Cluster consensus of second-order multi-agent systems via pinning control

This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.

Eigenstructure assignment in a class of second-order dynamic systems

Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.

Parametric Approach for the Normal Luenberger Function Observer Design in Second-order Descriptor Linear Systems

In this paper, the normal Luenberger function observer design for second-order descriptor linear systems is considered. It is shown that the main procedure of the design is to solve a so-called second-order generalized Sylvester-observer matrix equation. Based on an explicit parametric solution to this equation, a parametric solution to the normal Luenberger function observer design problem is given. The design degrees of freedom presented by explicit parameters can be further utilized to achieve some additional design requirements.

Distributed Containment Control of Networked Nonlinear Second-order Systems With Unknown Parameters

In this paper, we study the containment control problem for nonlinear second-order systems with unknown parameters and multiple stationary/dynamic leaders. The topologies that characterize the interaction among the leaders and the followers are directed graphs. Necessary and sufficient criteria which guarantee the control objectives are established for both stationary leaders(regulation case) and dynamic leaders(dynamic tracking case) based protocols. The final states of all the followers are exclusively determined by the initial values of the leaders and the topology structures. In the regulation case, all the followers converge into the convex hull spanned by the leaders,while in the dynamic tracking case, not only the positions of the followers converge into the convex hull but also the velocities of the followers converge into the velocity convex hull of the leaders.Finally, all the theoretical results are illustrated by numerical simulations.

Two parametric approaches for eigenstructure assignment in second-order linear systems

This paper considers eigenstructure assignment in second-order linear systems via proportional plus derivative feedback. It is shown that the problem is closely related to a type of so-called second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two complete parametric methods for the proposed eigenstructure assignment problem are presented. Both methods give simple complete parametric expressions for the feedback gains and the closed-loop eigenvector matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows the closed-loop eigenvalues to be set undetermined and sought via certain optimization procedures. An example shows the effectiveness of the proposed approaches. Keywords Second-order linear systems - Eigenstructure assignment - Proportional plus derivative feedback - Parametric solution - Singular value decompoition - Right factorization This work was supported in part by the Chinese Outstanding Youth Foundation (No.69504002).

Distributed event-triggered consensus tracking of second-order multi-agent systems with a virtual leader

This paper investigates the consensus tracking problems of second-order multi-agent systems with a virtual leader via event-triggered control. A novel distributed event-triggered transmission scheme is proposed, which is intermittently examined at constant sampling instants. Only partial neighbor information and local measurements are required for event detection. Then the corresponding event-triggered consensus tracking protocol is presented to guarantee second-order multi-agent systems to achieve consensus tracking. Numerical simulations are given to illustrate the effectiveness of the proposed strategy.

Consensus of Second-order Multi-agent Systems with Nonsymmetric Interconnection and Heterogeneous Delays

In this paper, a consensus algorithm of multi-agent second-order dynamical systems with nonsymmetric interconnection and heterogeneous delays is studied. With the hypothesis of directed weighted topology graph with a globally reachable node, decentralized consensus condition is obtained by applying generalized Nyquist criterion. For the systems with both communication and input delays, it is shown that the consensus condition is dependent on input delays but independent of communication delays.

Reference model based consensus control of second-order multi-agent systems

This paper deals with the consensus problem of multi-agent systems with second-order dynamics. The objective is to design algorithms such that all agents will have same positions and velocities. First, a reference model based consensus algorithm is proposed. It is proved that the consensus can be achieved if the communication graph has a spanning tree. Different from most of the consensus algorithms proposed in the literature, the parameters of the control laws are different among agents. Therefore, each agent can design its control law independently. Secondly, it gives a consensus algorithm for the case that the velocities of the agents are not available. Thirdly, the effectiveness of the input delay and the communication delay is considered. It shows that consensus can be achieved if the input delay of every agent is smaller than a bound related to parameters in its control law. Finally, some numerical examples are given to illustrate the proposed results.

Distributed Fault Detection for Consensus in Second-Order Discrete-Time Multiagent Systems with Adversary

This paper is concerned with distributed fault detection of second-order discrete-time multi-agent systems with adversary,where the adversary is regarded as a slowly time-varying signal.Firstly,a novel intrusion detection scheme based on the theory of unknown input observability( UIO) is proposed. By constructing a bank of UIO,the states of the malicious agents can be directly estimated. Secondly,the faulty-node-removal algorithm is provided.Simulations are also provided to demonstrate the effectiveness of the theoretical results.

H_∞ consensus control of a class of second-order multi-agent systems without relative velocity measurement

This paper studies consensus control problems for a class of second-order multi-agent systems without relative velocity measurement. Some dynamic neighbour-based rules are adopted for the agents in the presence of external disturbances. A sufficient condition is derived to make all agents achieve consensus while satisfying desired H∞ performance. Finally, numerical simulations are provided to show the effectiveness of our theoretical results.

Bounded consensus tracking of second-order multi-agent systems with sampling delay under directed networks

The bounded consensus tracking problems of second-order multi-agent systems under directed networks with sam- pling delay are addressed in this paper. When the sampling delay is more than a sampling period, new protocols based on sampled-data control are proposed so that each agent can track the time-varying reference state of the virtual leader. By using the delay decomposition approach, the augmented matrix method, and the frequency domain analysis, necessary and sufficient conditions are obtained, which guarantee that the bounded consensus tracking is realized. Furthermore, some numerical simulations are presented to demonstrate the effectiveness of the theoretical results.

Intelligent Integrated Control of Underactuated Mechanical Systems with Second-order Nonholonomic Constraints

This paper describes an intelligent integrated control of an acrobot, which is an underactuated mechanical system with second-order nonholonomic constraints. The control combines a model-free fuzzy control, a fuzzy sliding-mode control and a model-based fuzzy control. The model-free fuzzy controller designed for the upswing ensures that the energy of the acrobot increases with each swing. Then the fuzzy sliding-mode controller is employed to control the movement that the acrobot enters the balance area from the swing-up area. The model-based fuzzy controller, which is based on a Takagi-Sugeno fuzzy model, is used to balance the acrobot. The stability of the fuzzy control system for balance control is guaranteed by a common symmetric positive matrix, which satisfies linear matrix inequalities.

Optimal Multiperiodic Control for Inventory Coupled Systems: A Multifrequency Second-Order Test

A complex autonomous inventory coupled system is considered. It can take, for example, the form of a network of chemical or biochemical reactors, where the inventory interactions perform the recycling of by-products between the subsystems. Because of the flexible subsystems interactions, each of them can be operated with their own periods utilizing advantageously their dynamic properties. A multifrequency second-order test generalizing the p-test for single systems is described. It can be used to decide which kind of the operation (the static one, the periodic one or the multiperiodic one) will intensify the productivity of a complex system. An illustrative example of the multiperiodic optimization of a complex chemical production system is presented.

On stabilization for a class of nonlinear stochastic time-delay systems:a matrix inequality approach

This paper treats the feedback stabilization of nonlinear stochastic time-delay systems with state and control-dependent noise. Some locally （globally） robustly stabilizable conditions are given in terms of matrix inequalities that are independent of the delay size. When it is applied to linear stochastic time-delay systems, sufficient conditions for the state-feedback stabilization are presented via linear matrix inequalities. Several previous results are extended to more general systems with both state and control-dependent noise, and easy computation algorithms are also given.

Multiple Regression and Big Data Analysis for Predictive Emission Monitoring Systems

Predictive Emission Monitoring Systems (PEMS) offer a cost-effective and environmentally friendly alternative to Continuous Emission Monitoring Systems (CEMS) for monitoring pollution from industrial sources. Multiple regression is one of the fundamental statistical techniques to describe the relationship between dependent and independent variables. This model can be effectively used to develop a PEMS, to estimate the amount of pollution emitted by industrial sources, where the fuel composition and other process-related parameters are available. It often makes them sufficient to predict the emission discharge with acceptable accuracy. In cases where PEMS are accepted as an alternative method to CEMS, which use gas analyzers, they can provide cost savings and substantial benefits for ongoing system support and maintenance. The described mathematical concept is based on the matrix algebra representation in multiple regression involving multiple precision arithmetic techniques. Challenging numerical examples for statistical big data analysis, are investigated. Numerical examples illustrate computational accuracy and efficiency of statistical analysis due to increasing the precision level. The programming language C++ is used for mathematical model implementation. The data for research and development, including the dependent fuel and independent NOx emissions data, were obtained from CEMS software installed on a petrochemical plant.

Event-Triggered Finite-Time H∞ Filtering for Discrete-Time Nonlinear Stochastic Systems

This paper addresses the problem of event-triggered finite-time H∞ filter design for a class of discrete-time nonlinear stochastic systems with exogenous disturbances. The stochastic Lyapunov-Krasoviskii functional method is adopted to design a filter such that the filtering error system is stochastic finite-time stable (SFTS) and preserves a prescribed performance level according to the pre-defined event-triggered criteria. Based on stochastic differential equations theory, some sufficient conditions for the existence of H∞ filter are obtained for the suggested system by employing linear matrix inequality technique. Finally, the desired H∞ filter gain matrices can be expressed in an explicit form.