Reduced-order State Estimation Research Articles

Input-Output Selection for LSTM-Based Reduced-Order State Estimator Design

In this work, we propose a sensitivity-based approach to construct reduced-order state estimators based on recurrent neural networks (RNN). It is assumed that a mechanistic model is available but is too computationally complex for estimator design and that only some target outputs are of interest and should be estimated. A reduced-order estimator that can estimate the target outputs is sufficient to address such a problem. We introduce an approach based on sensitivity analysis to determine how to select the appropriate inputs and outputs for data collection and data-driven model development to estimate the desired outputs accurately. Specifically, we consider the long short-term memory (LSTM) neural network, a type of RNN, as the tool to train the data-driven model. Based on it, an extended Kalman filter, a state estimator, is designed to estimate the target outputs. Simulations are carried out to illustrate the effectiveness and applicability of the proposed approach.

Input-output selection for LSTM-based reduced-order state estimator design

In this paper, we present a sensitivity-based approach to construct reduced-order state estimators based on recurrent neural networks (RNNs). Our approach assumes that a mechanistic model is available but too computationally complex for estimator design and that only a subset of the states needs to be estimated. To address this problem, a reduced-order estimator that can estimate the target outputs is sufficient. We propose an approach based on sensitivity analysis to determine the appropriate inputs and outputs for data collection and data-driven model training so that the target outputs can be estimated accurately. In particular, we consider RNN networks as the tool to train the data-driven model and extended Kalman filter (EKF) as the estimator. Simulations are carried out to illustrate the effectiveness of the proposed approach.

Reduced-Order State Estimation for a Class of Nonlinear Fractional-Order Systems

Reduced-Order State Estimation for a Class of Nonlinear Fractional-Order Systems

Reduced-order state estimation of complex-valued neural networks with generally uncertain transition rates Markovian jump

In this work, a reduced-order state estimator is used to estimate the state of the complex-valued neutral networks (CVNNs) while do not divide it into a real component and an imaginary component. On the one hand, new state feedback controllers are designed to stabilize the error system we obtained; On the other hand, a example is given to prove the validity and correctness of our theorem.

Reduced-order state estimation of delayed recurrent neural networks

Different from the widely-studied full-order state estimator design, this paper focuses on dealing with the reduced-order state estimation problem for delayed recurrent neural networks. By employing an integral inequality, a delay-dependent design approach is proposed, and global asymptotical stability of the resulting error system is guaranteed. It is shown that the gain matrix of the reduced-order state estimator is determined by the solution of a linear matrix inequality. Numerical examples are provided to illustrate the effectiveness of the developed result.

Spatial discretization error in Kalman filtering for discrete-time infinite dimensional systems

We derive a reduced-order state estimator for discrete-time infinite dimensional linear systems with finite dimensional Gaussian input and output noise. This state estimator is the optimal one-step estimate that takes values in a fixed finite dimensional subspace of the system's state space --- consider, for example, a Finite Element space. We then derive a Riccati difference equation for the error covariance and use sensitivity analysis to obtain a bound for the error of the state estimate due to the state space discretization.

Real-time implementation of neural optimal control and state estimation for a linear induction motor

A reduced order state estimator based on recurrent high-order neural networks (RHONN) trained using an extended Kalman filter (EKF) is designed for the magnetic fluxes of a linear induction motor (LIM). The proposed state estimator does not need the mathematical model of the plant. This state estimator is employed to obtain the unmeasurable state variables of the LIM in order to use a state feedback nonlinear controller. A neural inverse optimal control is implemented to achieve trajectory tracking for a position reference. Real-time implementation results on a LIM prototype illustrate the applicability of the proposed scheme.

Observer Design for a Class of Exothermal Plug-Flow Tubular Reactors

A semi-linear reduced-order state estimator is presented to reconstruct approximately the state variable initially unknown of a class of nonlinear tubular reactors models, namely the exothermal plug-flow tubular reactor involving sequential reactions for which the kinetics depends on both the temperature and the reactant concentration. Our conception is based on bounded observations and the analysis of the nonlinear set of partial differential equations. It is shown that the given observer design admits a global unique solution and ensures asymptotic state estimator with exponentially decay error, when only the temperature is available for measurement at the reactor outlet. Simulation results are also presented showing the effectiveness of the proposed observer design.

Observers-Based Synchronization and Input Recovery for a Class of Nonlinear Chaotic Models

In this paper, we propose a simple and efficient crypto-system based on a chaotic time delay model. It consists of two steps: the first one assures the transmitter/receiver synchronization while the second step focuses on the encryption/decryption procedure. The synchronization is performed through a non linear state observer design, driven by the transmitted signal. Both full order and reduced order state estimation techniques are established. One of the main results is that sufficient conditions for asymptotic convergence, to assure the synchronization, are derived in terms of linear matrix inequalities (i.e., convex problem) easily and numerically tractable. Efficiency of the proposed approach is shown through the transmission of two encrypted messages: a sound wave and a digital picture. Finally, some security issues are discussed at the end of this paper

Commutation of permanent-magnet synchronous AC motors for military and traction applications

A commutation method for the permanent-magnet AC motor is presented, which combines a Hall-effect encoder with a quadratic extrapolation scheme, and reduced-order state estimation in order to satisfy the design constraints prescribed by certain military and traction applications.

Discrete-time reduced-order estimator design for bilinear stochastic systems with error covariance assignment

This paper is concerned with the design of reduced-order state estimators for bilinear stochastic discrete-time systems subjected to estimation error covariance assignment. The purpose of the problem addressed is to design the reduced-order state estimators for the bilinear stochastic discrete-time systems such that the steady-state estimation error covariances achieve the prespecified values. A simple, effective matrix inequality approach is developed to solve this problem. Specifically, (1) the parameterisation of estimation error covariances that certain bilinear error dynamic processes may possess is presented, (2) the characterisation of all reduced-order state estimators that assign such error covariances is explicitly derived, and (3) the solvability of the assignability conditions is discussed. Furthermore, an illustrative example is used to demonstrate the effectiveness of the proposed design procedure.

Compensator control for chemical vapor deposition film growth using reduced-order design models

We present a summary of investigations on the use of proper orthogonal decomposition techniques as a reduced basis method for computation of feedback controls and compensators in a high-pressure chemical vapor deposition (HPCVD) reactor. These investigations incorporate multiple species and controls, gas phase reactions, and time dependent tracking signals that are consistent with pulsed vapor reactant inputs. Numerical implementation of the model-based feedback control uses a reduced-order state estimator, based on partial state observations of the fluxes of reactants at the substrate center, which can be achieved with current sensing technology. We demonstrate that the reduced-order state estimator or compensator system is capable of substantial control authority when applied to the full system.

Reduced order model compensator control of species transport in a CVD reactor

We propose the use of proper orthogonal decomposition (POD) techniques as a reduced basis method for computation of feedback controls and compensators in a high-pressure chemical vapour deposition (HPCVD) reactor. In this paper, we present a proof-of-concept computational implementation of this method with a simplified growth example for III–V layers in which we implement Dirichlet boundary control of a dilute Group III reactant transported by convection and diffusion to an absorbing substrate with no reactions. We implement the model-based feedback control using a reduced order state estimator based on observations of the flux of reactant at the substrate centre. This is precisely the type of measurements available with current sensing technology. We demonstrate that the reduced order state estimator or compensator system is capable of substantial control authority when applied to a high-order system. In principle, these ideas can be extended to more general HPCVD control situations by including multiple species with gas-phase reactions and surface reactions. Copyright © 2000 John Wiley & Sons, Ltd.

Reduced order model compensator control of species transport in a CVD reactor

We propose the use of proper orthogonal decomposition (POD) techniques as a reduced basis method for computation of feedback controls and compensators in a high-pressure chemical vapour deposition (HPCVD) reactor. In this paper, we present a proof-of-concept computational implementation of this method with a simplified growth example for III–V layers in which we implement Dirichlet boundary control of a dilute Group III reactant transported by convection and diffusion to an absorbing substrate with no reactions. We implement the model-based feedback control using a reduced order state estimator based on observations of the flux of reactant at the substrate centre. This is precisely the type of measurements available with current sensing technology. We demonstrate that the reduced order state estimator or compensator system is capable of substantial control authority when applied to a high-order system. In principle, these ideas can be extended to more general HPCVD control situations by including multiple species with gas-phase reactions and surface reactions. Copyright © 2000 John Wiley & Sons, Ltd.

Reduced‐order observer for systems with piecewise constant inputs

The problem of reduced-order state estimators for systems with deterministic, i.e. known input is considered. Since below a certain order exact tracking of the state with reduced-order estimator is, in general, impossible, the approximation should take into account the class of expected inputs. In this paper a reduced-order estimator is designed for systems subjected to inputs consisting of set functions with varying amplitudes. The estimation error is required to be zero at steady state and its transient is minimized in the L2 sense. The optimal estimator is given explicitly and its structure is determined by three projection matrices. Copyright © 1999 John Wiley & Sons, Ltd.

Reduced-order observer for systems with piecewise constant inputs

The problem of reduced-order state estimators for systems with deterministic, i.e. known input is considered. Since below a certain order exact tracking of the state with reduced-order estimator is, in general, impossible, the approximation should take into account the class of expected inputs. In this paper a reduced-order estimator is designed for systems subjected to inputs consisting of set functions with varying amplitudes. The estimation error is required to be zero at steady state and its transient is minimized in the L2 sense. The optimal estimator is given explicitly and its structure is determined by three projection matrices. Copyright © 1999 John Wiley & Sons, Ltd.

Robust discrete time observer with application to fault diagnosis

An approach for designing reduced order state estimators for discrete time systems driven by completely unknown exogenous disturbances is provided here. Necessary, as well as necessary and sufficient, conditions for existence of the discrete estimator are given, along with an easy to follow and implement approach for construction of the estimator. Such estimators have been proved useful in a variety of robust control applications, as well as in designing control systems with monitoring and fault detection capabilities. Here, the application of the estimator for actuator fault detection in robotic applications is explored. Also, although the estimator design is carried out in a deterministic setting, the presence of measurement noise is explored and it is shown that the estimator and fault detection strategy can still be very successful even in the presence of random noise.

Discrete-time observers with random noises in dynamic block

The minimum variance state estimation of linear stochastic discrete-time systems by an observer of reduced-order is investigated. There is an additional random noise with known intensity in the dynamic block of the observer. The local optimal reduced-order state estimator is found which takes into account the presence of such noise. The equations of an optimal stationary observer are derived for linear stochastic time-invariant system.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

State-Optimization Method for Order Reduction of Linear Models and of State Estimators

Solution of the problem of optimal model reduction and that of optimal reduced-order state estimation are obtained by adopting a proposed state-optimization method. The method is based on the concept of nonsimilarity transformation on states. Factorization of the transformation in terms of a partial isometry enables the controllability and observability conditions of the optimal reduced versions to be expressed in optimal projection equations. The effect of the factorization is interpreted to be that of an additional constrained-condition to the reduction problems. The method is found applicable to systems of any nature with the possibility of preserving the physical significances of original modelled-states in the reduced ones

Optimal reduced-order state estimation for unstable plants

The problem of optimal reduced-order steady-state state estimation is considered for the case in which the plant has unstable poles. In contrast to the standard full-order estimation problem involving a single algebraic Riccati equation, the solution to the reduced-order problem involves one modified Riccati equation and one Lyapunov equation coupled by a projection matrix. This projection is completely distinct from the projection obtained by Bernstein and Hyland (1985) for stable plants.