Reduced-order functional observers with application to partial state estimation of linear systems with input-delays

Reduced-order multi-functional observer design for multi-input multi-output linear timeinvariant(LTI)systems with constant delayed-inputs is studied.This research is useful in the input estimation of LTI systems with actuator delay,as well as system monitoring and fault detection of these systems.Two approaches for designing an asymptotically stable functional observer for the system are proposed:delay-dependent and delay-free.The delay-dependent observer is infinite-dimensional,while the delay-free structure is finite-dimensional.Moreover,since the delay-free observer does not require any information on the time delay,it is more practical in real applications.However,the delay-dependent observer contains less restrictive assumptions and covers more variety of systems.The proposed observer design schemes are novel,simple to implement,and have improved numerical features compared to some of the other available approaches to design(unknown-input)functional observers.In addition,the proposed observers usually possess lower order than ordinary Luenberger observers,and the design schemes do not need the observability or detectability requirements of the system.The necessary and sufficient conditions of the existence of an asymptotic observer in each scenario are explored.The extensions of the proposed observers to systemswith multiple delayed-inputs are also discussed.Several numerical examples and simulation results are employed to support our theories.

Observer design and output feedback stabilization for linear singular time-delay systems with unknown inputs

The design of a functional observer and reduced-order observer with internal delay for linear singular timedelay systems with unknown inputs is discussed. The sufficient conditions of the existence of observers, which are normal linear time-delay systems, and the corresponding design steps are presented via linear matrix inequality（LMI）. Moreover, the observer-based feedback stabilizing controller is obtained. Three examples are given to show the effectiveness of the proposed methods.

Target layer state estimation in multi-layer complex dynamical networks considering nonlinear node dynamics

In many engineering networks, only a part of target state variables are required to be estimated.On the other hand,multi-layer complex network exists widely in practical situations.In this paper, the state estimation of target state variables in multi-layer complex dynamical networks with nonlinear node dynamics is studied.A suitable functional state observer is constructed with the limited measurement.The parameters of the designed functional observer are obtained from the algebraic method and the stability of the functional observer is proven by the Lyapunov theorem.Some necessary conditions that need to be satisfied for the design of the functional state observer are obtained.Different from previous studies, in the multi-layer complex dynamical network with nonlinear node dynamics, the proposed method can estimate the state of target variables on some layers directly instead of estimating all the individual states.Thus, it can greatly reduce the placement of observers and computational cost.Numerical simulations with the three-layer complex dynamical network composed of three-dimensional nonlinear dynamical nodes are developed to verify the effectiveness of the method.

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.

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.

Function Observer Based Event-triggered Control for Linear Systems with Guaranteed L_∞-Gain

This paper is devoted to event-triggered control design for linear systems based on function observer. More specifically, the main purpose is to design event-triggered mechanisms that trigger transmissions when the difference between the current value of the system and its previously transmitted value which includes the plant output or the function observer output exceeds an additional threshold. For such an eventtriggered mechanism, we derive conditions in terms of matrix inequality to guarantee the stability as well as longer inter-event time. We propose two approaches to investigate the closed-loop model, namely, reformulating the event-triggered control system as a hybrid system and interpreting the event-induced error as exogenous disturbance. Furthermore, the minimum inter-event time is guaranteed to be strictly positive. An example is presented to illustrate the feasibility and efficiency of the theoretic results.

A STA Current-Constrained Control for PMSM Speed Regulation System with Function Disturbance Observer

The non-cascade permanent magnet synchronous motor control system has the advantages of simple structure and less adjustable parameters,but the non-cascade structure needs to solve the problem of over-current protection.In this paper,a current constrained control method is used to limit the starting current to a safe range.At the same time,to ensure the robustness and rapidity of the system,a super twist current constraint controller(CCSTA)is generated by combining super twist algorithm(STA)with current constraint control;Considering the diversity of internal and external disturbances,a functional disturbance observer(FDOB)is proposed to compensate the matched and unmatched disturbances,which further improves the robustness of the system.

Boundary Control Problems for 2 ×2 Cooperative Hyperbolic Systems with Infinite Order Operators

In this study, boundary control problems with Neumann conditions for 2 × 2 cooperative hyperbolic systems involving infinite order operators are considered. The existence and uniqueness of the states of these systems are proved, and the formulation of the control problem for different observation functions is discussed.

DYNAMIC OBSERVATION OF THYROID FUNCTION IN PATIENTS WITH APLASTIC ANEMIA

Accelerating cell growth is one of the functions of thyroid hormone. In the absence or lack of this hormone, hematopoietic disorder may occur. Dynamic observation of thyroid function in aplastic anemia (AA) state has not been reported yet.

Observations on the Function of Mucous Cells in the Epidermis of the Cat-fish Clarias batrachus Exposed to Sodium Dodecyl Sulfate

Response of mucous cells, in the epidermis of the catfish Clarias batrachus, to a sublethal concentration of sodium dodecyl sulfate was studied and correlated with the alteration in the status of their secretory activity after different durations of the treatment. At 4h, 8h, 24h,48h and 72h of the detergent treatment, most mucous cells attained voluminous dimensions and appeared closely approximating to or even overlapping the adjacent ones. At 12h, 36h, and 60h, in contrast, the mucous cells appeared small and slender, and seemed to be located at greater intervals. These changes in dimensions were responsible for the apparent increase or decrease in the density of mucous cells after different durations of detergent treatment. Statistically, however, no significant change was observed in the total number of the mucous cells throughout the experiment.The mucous cells appeared enlarged towards the end of the experiment signifying increased mucus production. This is considered as an adaptation, for protection, assisting the fish to adjust to the changed environment.A shift in the histochemical nature of the secretory contents at the middle and basal parts of the mucous cells, from a mixture of neutral and acid glycoproteins to neutral glycoproteins, during the early stages of the treatment suggests that acid moities could not simultaneously be synthesized as an immediate response to enhanced mucous secretion. The apical parts of the mucous cells, however, showed no histochemical change throughout the experiment.

AN APPROACH TO DESIGN OBSERVER FOR A CLASS OF DISCRETE CONTROL SYSTEMS WITH TIME-DELAY

The design of functional observer for a class of discrete systems with time-delay is concerned. The solution to Sylvester function is given. An improved method for the functional observer design is proposed by the condition of linear matrix inequality. In the end,an example is given to illustrate the feasibility of the method.

Observer Design —— A Survey

This paper surveys the results of observer design for linear time-invariant(L-T-I) deterministic irreducible open-loop systems(OLS), the most basic type of OLS. An observer estimates Kxx(t) signal where K is a constant and x(t) is the state vector of the OLS. Thus, an observer can be used as a feedback controller that implements state feedback control(SFC) or Kxx(t)-control,and observer design is therefore utterly important in all feedback control designs of state space theory. In this survey, the observer design results are divided into three categories and for three respective main purposes. The first category of observers estimate signal Kxx(t) only with a given K, and this survey has four conclusions: 1) Function observer that estimates Kxx(t) directly is more general than state observer that estimates x(t), and may be designed with order lower than that of state observer, and the additional design objective is to minimize observer order; 2) The function observer design problem has already been simplified to the solving of a single set of linear equations only while seeking the lowest possible number of rows of the solution matrix, and an apparently most effective and general algorithm of solving such a problem can guarantee unified upper and lower bounds of the observer order; 3) Because such a single set of linear equations is the simplest possible theoretical formulation of the design problem and such theoretical observer order bounds are the lowest possible, and because the general, simple, and explicit theoretical formula for the function observer order itself do not exist, the theoretical part of this design problem is solved; 4) Because the function observer order is generically near its upper bound, further improvement on the computational design algorithm so that the corresponding observer order can be further reduced,is generically not worthwhile. The second category of observers further realize the loop transfer function and robustness properties of the direct SFC, and the conclusion of this survey is also fourfold: 1) To fully realize the loop transfer function of a practically designed Kxx(t)-control, the observer must be an output feedback controller(OFC) which has zero gain to OLS input; 2) If parameter K is separately designed before the observer design, as in the separation principle which has been followed by almost all people for over half of a century, then OFC that estimates Kxx(t) does not exist for almost all OLS s; 3) As a result, a synthesized design principle that designs an OFC first and is valid for almost all OLS s, is proposed and fully developed, the corresponding K will be designed afterwards and will be constrained by the OFC order as well as the OFC parameters; 4) Although the Kxx(t)-control is constrained in this new design principle and is therefore called the "generalized SFC"(as compared to the existing SFC in which K is unconstrained), it is still strong enough for most OLS s and this new design principle overcomes many fundamental drawbacks of the existing separation principle. The third category of observers estimate Kxx(t) signal at special applications such as fault detection and identification and systems with time delay effects. Using directly the result of OFC that estimates Kxx(t) of the second category, these observers can be generally and satisfactorily designed.

Improved Flight Conflict Detection Algorithm Based on Gauss-Hermite Particle Filter

In order to improve the accuracy of free flight conflict detection and reduce the false alarm rate, an improved flight conflict detection algorithm is proposed based on Gauss-Hermite particle filter（GHPF）. The algorithm improves the traditional flight conflict detection method in two aspects：（i） New observation data are integrated into system state transition probability, and Gauss-Hermite Filter（GHF） is used for generating the importance density function.（ii） GHPF is used for flight trajectory prediction and flight conflict probability calculation. The experimental results show that the accuracy of conflict detection and tracing with GHPF is better than that with standard particle filter. The detected conflict probability is more precise with GHPF, and GHPF is suitable for early free flight conflict detection.