Disturbance decoupled observers for systems with unknown inputs

This note deals with the design of reduced-order disturbance decoupled scalar functional observers for linear systems with unknown inputs. Based on a parametric approach, existence conditions are derived and a design procedure for finding reduced-order scalar functional observers is given. The derived existence conditions are relaxed and the procedure can find first-order disturbance decoupled scalar functional observers for some cases where the number of unknown inputs is more than the number of outputs. Also, the observer matching condition, which is the necessary requirement for the design of state observers for linear systems with unknown inputs, is not required. Numerical examples are given to illustrate the attractiveness of the proposed design method.

Time-delay systems : design of delay-free and low-order observers

This note provides a comprehensive treatment on the design of functional observers for linear systems having a time-varying delay in the state variables. The designed observers possess attractive features of being low-order and delay-free and hence they are cost effective and easy to implement. Existence conditions are derived and a design procedure for finding low-order observers is given.

Generality of functional observer structures

Functional observers estimate a linear function of the state vector directly without having to estimate all the individual states. In the past various observer structures have been employed to design such functional estimates. In this paper we discuss the generality of those various observer structures and prove the conditions under which those observer structures are unified. The paper also highlights and clarifies the need to remove the self-convergent states from the system and also from the functions to be estimated before proceeding with the design of a functional observer or else incorrect conclusions regarding the existence of functional observers can be arrived at.

Existence conditions for functional observability from an eigenspace perspective

Two theorems on conditions for nonexistence and for existence, of built functional observers, from an eigenspace perspective are presented and proved. One more theorem on Functional Observability in terms of constructed products of matrices A,C and L0 is also presented. This theorem provides an easy way to check Functional Observability before proceeding with the design of functional observers. The existence and the nonexistence theorems are used to unify previously reported theorems on Functional Observability by showing their equivalence. The connection between the concept of Functional Observability and the well known concept of State Observability is also presented.

A practical functional observer scheme for interconnected time-delay systems

This paper proposes a partially distributed functional observer scheme for a class of interconnected linear systems with very strong non-instantaneous subsystems interaction and with time delays in the local states and in the transmission of output information from the remote subsystems. A set of easily verifiable existence conditions is established and upon its satisfaction, simple distributed observers are designed using a straightforward design procedure. Simulation results of a numerical example are given to substantiate the feasibility of the approach.

New results in common functional state estimation for two linear systems with unknown inputs

This paper presents new developments in common functional observers for two systems. We improve an existing common functional observer scheme by reducing its order, and then investigate its existence conditions in terms of the original system matrices. These conditions have never been explored and they enable the users to know at the outset the class of systems for which the scheme is applicable. They also show that both observers can be designed independently of each other which significantly simplifies the design process. A numerical simulation verifies the findings.

A delay-dependent functional observer for linear time-invariant systems with input delay

A delay-dependent functional observer is designed for linear time-invariant (LTI) systems with time-varying input delay. Compared to delay-free observers, delay-dependent functional observers are less conservative and cover more systems. The designed functional observer is with minimum possible order (minimal). Necessary and sufficient conditions of the existence of the observer and asymptomatic stability of it are illustrated. The proposed observer is extended to multiple input delayed systems with time-varying delays. An algorithm is developed for designing of the minimal order observer based on the methodology of this paper. Two numerical examples and simulations are used to support our proposed methodology.

Functional observer-based fault detection of time-delay systems via an LMI approach

This paper presents a novel residual generator that uses minimum-order functional observers to trigger actuator and component faults in time-delay systems. We first present a fault detection scheme and derive existence conditions of the residual generator and functional observer. The observer and residual parameters are then systematically determined via solving some coupled generalized Sylvester matrix equations. To deal with the time-delay issue, a stabilizability condition expressed in terms of linear matrix inequality (LMI) is derived to ensure the time-delay observer error system converges to zero with a prescribed convergence rate. Our design approach has the advantage that the designed fault detection scheme has lower order than existing results in the literature. Two numerical examples are given to illustrate the effectiveness of our results.

Minimal-order functional observer-based residual generators for fault detection and isolation of dynamical systems

This paper examines the design of minimal-order residual generators for the purpose of detecting and isolating actuator and/or component faults in dynamical systems. We first derive existence conditions and design residual generators using only first-order observers to detect and identify the faults. When the first-order functional observers do not exist, then based on a parametric approach to the solution of a generalized Sylvester matrix equation, we develop systematic procedures for designing residual generators utilizing minimal-order functional observers. Our design approach gives lower-order residual generators than existing results in the literature. The advantages for having such lower-order residual generators are obvious from the economical and practical points of view as cost saving and simplicity in implementation can be achieved, particularly when dealing with high-order complex systems. Numerical examples are given to illustrate the proposed fault detection and isolation schemes. In all of the numerical examples, we design minimum-order residual generators to effectively detect and isolate actuator and/or component faults in the system.

An observer design procedure for a class of nonlinear time-delay systems

This paper considers a class of uncertain, nonlinear differential state delayed control systems and presents a reduced-order observer design procedure to asymptotically estimate any vector state functionals. The method proposed involves decomposition of the delayed portion of the system into two parts: a matched and mismatched part. Provided that the rank of the mismatched part is less than the number of the outputs, a reduced-order linear functional observer, with any prescribed stability margin, can be constructed by using a simple procedure. A numerical example is given to illustrate the new design procedure and its features.

Observer-based control of multi-agent systems under decentralized information structure

This paper addresses the problem of decentralized implementation of a global state feedback controller for multi-agent systems. The system is assumed to be under the constraint of a complete decentralized information structure. The decentralization of the control task is achieved through the construction of low-order decentralized functional observers with the purpose of generating the required corresponding control signal for each local control station. A design procedure is developed for obtaining an approximate solution to the design of the observers. Stability analysis is provided for the global system using the proposed observer-based approach. A numerical example is given to illustrate the design procedure and cases when the observers' order increases from the lowest value.

Design of minimal-order stabilisers for multi-machine unstable power systems

A reduced dynamics stabiliser for multi-machine power systems is presented in this paper. The design of the stabiliser is based on the theory of linear functional observers and the solution of a simple parameter optimisation problem. The order of the stabiliser could be as low as the number of machines in the system. The design is applied to an open-loop unstable multi-machine power system.

Observer-based decentralized approach to robotic formation control

Control of a group of mobile robots in a formation requires not only environmental sensing but also communication among vehicles. Enlarging the size of the platoon of vehicles causes difficulties due to communications bandwidth limitations. Decentralized control may be an appropriate approach in those cases when the states of all vehicles cannot be obtained in a centralized manner. This paper presents a solution to the problem of decentralized implementation of a global state-feedback controller for N mobile robots in a formation. The proposed solution is based on the design of functional observers to estimate asymptotically the global state-feedback control signals by using the corresponding local output information and some exogenous global functions. The proposed technique is tested through simulation and experiments for the control of groups of Pinoneer-based non-holonomic mobile robots.

A distributed approach to global feedback control of multi-agent systems

This paper presents a distributed approach to global state feedback control of for multi-agent systems. The proposed solution is obtained from the construction of decentralised functional observers. The required local control signal is generated asymptotically using only corresponding local output information. It is shown that a complete distribution of the control of a decentralised system having N agents can be achieved upon the satisfaction of some necessary conditions, and that the resulting controller can emulate the performance of a global state feedback controller. A step-by-step design algorithm is given. Its simplicity and correctness are illustrated through a numerical example.

A common disturbance decoupled observer for linear systems with unknown inputs

This paper presents a solution to the problem of designing a common linear functional observer that can observe a partial set of the state vector of two linear systems with unknown inputs. A new structure of a decoupled linear functional observer is proposed for systems subject unknown disturbances, using only the available output information. Existence conditions as well as a design procedure are given for constructing the proposed observer. A numerical example is given to illustrate the effectiveness of the new observer structure.