David Levanony

On Persistent Excitation for Linear Systems with Stochastic Coefficients

A Wiener input process is shown to be persistently exciting (PE) for linear stochastic systems with time-varying, convergent, random coefficients, provided asymptotic noise controllability holds a. s. The PE result is in the sense that the minimum eigenvalue of the integrated outer product of the state process is of O(t) (t being the upper time limit of the integral).

Linear Stochastic State Space Theory in the White Noise Space Setting

We study linear stochastic state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this commutative ring and are characterized in a number of ways. A major feature in our approach is the observation that key characteristics of a linear, time invariant, stochastic system are determined by the corresponding characteristics associated with the deterministic part of the system, namely, its average behavior.

Stochastic Lagrangian Adaptive LQG Control

This paper presents a continuous time stochastic adaptive control algorithm for completely observed linear stochastic systems with unknown parameters. The adaptive estimation algorithm is designed so that, first, it drives the estimate into a neighbourhood I δ of a set I of parameters corresponding to the true closed loop dynamics and then, second, by activating a performance monitoring feature in I δ, the estimate converges to the true system parameter and the resulting control yields optimal long run LQ closed loop performance.

Recursive nonlinear system identification by a stochastic gradient algorithm: stability, performance, and model nonlinearity considerations

A parameter estimation problem in a class of nonlinear systems is considered where the input-output relation of a nonlinear system is approximated by a polynomial model (e.g., a Volterra series). A least mean squares (LMS) type algorithm is utilized for the recursive estimation of the polynomial coefficients, and its resulting mean square error (MSE) convergence properties are investigated. Conditions for the algorithm stability (in the mean square sense) are established, steady-state MSE bounds are obtained, and the convergence rate is discussed. In addition, modeling accuracy versus steady-state performance is examined; it is found that an increase of the modeling accuracy may result in a deterioration of the asymptotic performance, that is, yielding a larger steady-state MSE. Linear system identification is studied as a special case.

On persistent excitation for linear systems with stochastic coefficients

A Wiener input process is shown to be persistently exciting (PE) for linear stochastic systems with time varying, convergent, random coefficients, provided the asymptotic noise controllability holds. The PE result is in the sense that the minimum eigenvalue of the integrated outer product of the state process is of O(t) (t being the upper time limit of the integral). Application examples are provided.

Stochastic linear-quadratic adaptive control: A conceptual scheme

A conceptual adaptive linear-quadratic (LQ) control scheme is proposed. Its derivation is based on a study of a family of asymptotic maximum likelihood (AML) estimators, and their associated limit sets. The geometric properties of such limit sets, lead to the formulation of a time-varying, constrained optimization problem, whose solution is an inherently consistent estimate of the systems unknown parameters. When incorporated within a certainty- equivalence adaptive control scheme, these estimates yield optimal long-run LQ closed-loop performance.

On persistent excitation conditions for the consistent filtering of convergent semimartingales

The filtering of a continuous, convergent semimartingale, observed via a noisy linear sensor is considered. Specifically, conditions ensuring the consistency of the Bayesian estimator are sought after. These are derived in the form of a persistence of excitation (PE) property. This PE condition is stronger than the one required in the case of the estimation of a constant random vector. It coincides with the latter, when the unobserved semimartingale has a finite quadratic variation over [0, /spl infin/]. Application examples are provided.

A white noise approach to linear stochastic systems

We present a new approach to study linear stochastic systems, where randomness is also included in the transfer function. We use the white noise setting, and the systems input-output relation is given in terms of two convolutions. The Hermite transform allows to describe the results in terms of functions analytic in a countable number of variables.