Full State Estimation Research Articles

Modified stochastic Luenberger observers

A modified stochastic Luenberger observer (MSLO) structure is proposed to recover the optimal performance of the coventional SLO for obtaining full-state estimates in linear discrete-time stochastic systems. The optimal MSLO (OMSLO) which gives the MMSE estimates is derived by using the general two-stage Kalman filter. A reduced-order form of the OMSLO is also proposed for systems having singular measurement noises. The connection between the OMSLO and the optimal minimal-order observer of Leondes and Novak is also shown.

Adaptive modal parameters identification for collocated position feedback vibration control

Abstract The concept of position feedback previously introduced in the vibration suppression of targe space structures is reviewed and extended. New results detailing more effective damping specifications are presented. Since effective vibration control depends on the accuracy of the modal parameters used, the problem of accurate identification of the modal frequencies, damping and mode shapes of the control modes is investigated. An adaptive estimation procedure to identify the parameters required in the position feedback control is proposed which caters for both full and partial modal state estimation. Simulation results for a multiple-degree-of-freedom vibration system are presented to illustrate the applicability of the proposed technique

Estimator design for bilinear systems with bounded inputs

Abstract Full state estimator design for both continuous‐time and discrete‐time bilinear systems is investigated. All of the system inputs are arbitrary deterministic signals with known upper bounds. We propose a sufficient condition to determine the estimator's gain matrix parameters Ho and Hi such that all the original unavailable system states are approximated asymptotically. This result is derived via the Lyapunov stability theorem and is expressed by the measurements (norm and matrix measure) of the system matrices. The main feature of this result is that in our determination of Ho and Hi, we do not need to solve any Lyapunov equations.

Adaptive Control within the Class of Stabilizing Controllers for a Time Varying Nominal Plant

In this paper, we consider enhancing the performance of a stabilizing causal controller Ko (possibly time varying) for a causal nominal plant G (possibly time varying), with controller augmentations including an adaptive stable subsystem Q. The objective is to search on-line in the class of stabilizing causal controllers for the nominal plant, characterized in terms of Q and state space descriptions of G, Ko. For the case of time-invariant plants, most of the algorithms and theory of the paper specialize to known results. One formulation of the coprime factorizations using state- space description of time-varying systems, and associated characterization of the class of all stabilizing causal controllers used in our work, specializes to known results when the stabilizing controller has a full order state estimate feedback state space description.So as to view the results in terms of familiar schemes, specialization to the well-studied self-tuning regulator and parallel model reference adaptive controller are presented. The latter provides an illustration of the application of the results to two-degree-of-freedom design.

Adaptive control within the class of stabilizing controllers for a time-varying nominal plant†

In this paper, we consider enhancing the performance of a stabilizing causal controller K0 (possibly time-varying) for a causal nominal plant G (possibly time-varying), with controller augmentations including an adaptive stable subsystem Q. The objective is to search on-line in the class of stabilizing causal controllers for the nominal plant, characterized in terms of Q and state space descriptions of G, K 0. For the case of time-invariant plants, most of the algorithms and theory of the paper specialize to known results. One formulation of the coprime factorizations using state-space description of time-varying systems, and associated characterization of the class of all stabilizing causal controllers used in our work, specializes to known results when the stabilizing controller has a full order state estimate feedback state space description. So as to view the results in terms of familiar schemes, specialization to the well-studied self-tuning regulator and parallel model reference adaptive controller ...

The properties of reduced-order minimum-variance filters for systems with partially perfect measurements

The problem of the finite-time, reduced-order, minimum variance full-state estimation of linear, continuous time-invariant systems is considered in cases where the output measurement is partially free of corrupting white-noise components. The structure of the optimal filter is obtained and a link between this structure and the structure of the system invariant zeros is established. Using expressions that are derived in closed form for the invariant zeros of the system, simple sufficient conditions are obtained for the existence of the optimal filter in the stationary case. The structure and the transmission properties of the stationary filter for general left-invertible systems are investigated. A direct relation between the optimal filter and a particular minimum-order left inverse of the system is obtained. A simple explicit expression for the filter transfer function matrix is also derived. The expression provides an insight into the mechanism of the optimal estimation. >

Sensitivity of closed-loop eigenvalues and robustness

Analytical results are obtained in a present investigation of the way in which full state feedback controller and estimator eigenvalues in a closed-loop linear control system affect these eigenvalues' sensitivity with respect to uncertain plant parameters. A controller eigenvalue lying near an estimator eigenvalue yields large eigenvalue sensitivity, which should be reduced through the separation of controller eigenvalues from estimator eigenvalues.

Use of a Virtual Control Approach in State Estimation

This work presents the development of a state estimator for dynamic systems exploring the dual function existing between state estimation and optimal control probems. An estimator algorithm similar to the Extended Kalman Filter results to be used in real-time nonlinear systems which can recursively be approximated by linear systems. The original estimation problem is transformed into an equivalent one of virtual control. This control problem is then used to generate and adaptive, locally convergent algorithm where, instead of full state estimation, one has to estimate just a control vector with smaller dimension than, or, in the worst case, the same dimension as the state vector. The control formulation allows different control structures and different convergence acceleration criteria. Two control structures and three criteria are tested in this exploratory phase. The algorithn is implemented in a digital computer to estimate the orbit of a low Earth orbit satellite under simulated conditions. Numerical results are presented for a test case considering critical initial values for the estimator and observations by three Earth stations.

Direct solution to the general reduced-order stochastic observation problem

The stochastic optimal state observation problem is considered for a general linear, continuous, time-invariant system with unmeasurable stationary inputs and measurement outputs that may be, at least in part, perfect. A general solution to the problem is obtained by processing the perfect measurements through a specific differentiation-transformation scheme in order to extract the maximum accurate information on the system states. Using this information the original system is transformed to a new reduced-order model whose measurements are corrupted by a white noise of non-singular intensity matrix. A minimum-order full-state estimator to the original system is then constructed by combining the outputs of any full-order observer to the reduced-order model and the perfect combinations of the system states that were derived by the differentiation-transformation scheme. A solution to the general singular Kalman filtering problem is then obtained by minimizing the variance of the estimation error of the obser...

Design of a state estimator for a class of time-varying multivariable systems

In this note, matrix operators are first introduced to develop a canonical transformation. Then it shows that a full order state estimator with any eigenvalues can be constructed for linear time-varying systems that are uniformly observable and lexicography-fixed. A simple algorithm is provided to design the state estimator.

Local feedback stabilization of large interconnected power systems in emergencies

On-line stabilization of the large interconnected power system poses problems which are unusual among large systems. The system can lose stability in 2–3 s or sooner—yet, even a simplified model of it consists of hundreds or thousands of state variables. Hence, a full state identification or estimation and a dynamic control utilizing the complete system dynamics is computationally out of the question. In fact, of necessity, any centralized action must be quite limited. This leaves the challenging task of using local information to achieve system-wide stabilization. Control is also limited by practical considerations to short pulses of positive or negative power of fixed magnitude. A nonlinear transformation which maps the conventional state space of the power system into a new observation decoupled state space is introduced and shown to be a homeomorphism. This state space has the property that its components can be measured piecemeal in local groups and its origin is the unique stable equilibrium point of the power system when one exists. It is then shown that a feedback control, based on such local information, is capable of assuring system-wide approach to the stable equilibrium point. The existence of a stability region for this local feedback control is also shown.