Engin Yaz

LINEAR UNBIASED STATE ESTIMATION UNDER RANDOMLY VARYING BOUNDED SENSOR DELAY

The motivation for the work reported in this paper accrues from the necessity of finding stabilizing control laws for systems with randomly varying bounded sensor delay. It reports the de- velopment of reduced-order linear unbiased estimators for discrete-time stochastic parameter systems and shows how to parametrize the estimator gains to achieve a certain estimation error covariance. Both finite-time and steady-state estimators are considered. The results are potentially applicable to state estimation for stabilizing output feedback control systems. (~) 1998 Elsevier Science Ltd. All rights reserved.

Linear unbiased state estimation for random models with sensor delay

The motivation for the work reported in this paper accrues from the necessity of finding stabilizing control laws for systems with randomly varying distributed delays. It reports the development of full and reduced order linear unbiased estimators for discrete-time stochastic parameter systems and shows how to parametrize the estimator gains to achieve a certain estimation error covariance. Both finite-time and steady-state estimators are considered. The results are potentially applicable to state-estimate feedback control schemes for such systems.

Stability robustness of linear discrete-time systems in the presence of uncertainty

The stability robustness problem is considered for nominally stable linear discrete-time systems. Using time-domain analysis methods and Lyapunov theory, bounds on the norms of the time-varying (non-)linear perturbations are given, to maintain the asymptotic stability of these systems in the presence of such perturbations.

Deterministic and stochastic robustness measures for discrete systems

Deterministic and stochastic Lyapunov theorems are used to demonstrate the robustness of a stable linear, time-variant, discrete-time nominal system to both unknown deterministic and stochastic perturbations. Time-domain conditions are presented on the appropriate deterministic or random characteristics of perturbations to maintain the proper stability behavior of the overall system. It is concluded that the novel robustness conditions proposed can find application in the feedback design of control systems where the closed-loop system is known to be stable with a certain degree, e.g. as in the case of linear quadratic optimal control with alpha -degree of prescribed stability. >

Variable structure observer with a boundary-layer for correlated noise/disturbance models and disturbance minimization

We present a design methodology for state estimation of nonlinear stochastic systems and measurement models with coloured noise processes. The method is based on the extension of variable structure observer schemes. The deterministic versions of these results are also included, a new approach for obtaining the required parameters in the observer design is provided, together with the design of a dynamic feedback controller to minimize the effect of known waveform-type disturbances with unknown magnitudes and arrival times. Two simulation examples illustrate the design procedures.

Sliding mode observers for nonlinear models with unbounded noise and measurement uncertainties

This work extends the applicability of variable structure observers designed for nonlinear systems in two ways. First, it is proved that these observers using a boundary-layer scheme can be applied to system models described by Ito differential equations, resulting in almost sure and mean square exponential estimation error. Second, the use of variable structure observers is extended to nonlinear measurement models containing disturbance effects. Also, a novel approach for obtaining the required parameters in the observer design is provided. Finally, two examples are given to illustrate the application and favorable convergence properties of these generalizations.

Linear state estimators for non-linear stochastic systems with noisy non-linear observations

The design of linear filters is considered for reconstructing the state of a class of discrete-time non-linear stochastic systems using noise-corrupted measurements. It is shown that for systems with mean-square stable dynamics, it is always possible to guarantee stable estimation schemes. This result is used to prove that a mean–square optimal one-step predictor has stable error dynamics and also to generate other stable predictors.

Infinite horizon quadratic optimal control of a class of nonlinear stochastic systems

The author considers a class of discrete-time nonlinear stochastic control systems whose nonlinearities are described by statistical means. By introducing the proper mean-square stabilizability and detectability properties of such systems and giving a characterization of these properties in terms of system parameters, he examines the steady-state properties of quadratically optimal controllers. A robustness property of these controllers is pointed out. >

Continuous and discrete state estimation with error covariance assignment

A novel method of state estimator design is presented for linear continuous and discrete-time systems with white noise inputs. This method provides a closed-form solution for directly assigning the steady-state estimation error covariance. The assignability conditions are interpreted using system theoretical concepts. A robustness property of such estimators is also pointed out.<<ETX>>

A control scheme for a class of discrete nonlinear stochastic systems

A control scheme is presented for effective stabilization of discrete-time, nonlinear stochastic systems where the nonlinearity involves a zero-mean, independent random sequence. The control is of a constant feedback type and makes use of finite time solutions of a Riccati-like matrix difference equation. Stability results are both in terms of mean square and almost sure stochastic stability. Moreover, a matrix inequality is given to check the existence of weighting matrices which would result in a stable regulator problem.