We solve the linearly constrained linear-quadratic LQ and linear-quadratic-Gaussian LQG optimal control problems. Closed form expressions of the optimal controls are derived, and the Separation Theorem is generalized.

We algorithmically construct multi-output Gaussian process priors which satisfy linear differential equations. Our approach attempts to parametrize all solutions of the equations using Gröbner bases. If successful, a push forward Gaussian process along the paramerization is the desired prior. We consider several examples, among them the full inhomogeneous system of Maxwell’s equations. By bring...

Parametric approaches based on a priori models of the speech are often used in the framework of speech enhancement using a single microphone. When the speech is modeled by means of a stationary autoregressive (AR) process, a frameby-frame approach is usually considered. However, it requires the unbiased estimations of the autoregressive parameters and of the noise variances for the subsequent i...

The purpose of this paper is to present an alternate derivation of optimal linear filters. The basic technique is the use of a matrix version of the maximum principle of Pontryagin coupled with the use of gradient matrices to derive the optimal values of the ; '1 filter coefficients for minimum variance estimation under the require­ :11" ment that the estimates be unbiased. The optimal filter w...

A novel iterative quantization procedure for the design of finite wordlength linear phase FIR filters of high order and minimum frequency domain error is proposed: a one by one increased number of filter coefficients is quantized where the augmented frequency domain error is re-minimized in each case. This new approach achieves a smaller frequency domain error than rounding of the optimal non-q...

This paper presents a new recursive filter to joint input and state estimation for noisy discrete time Takagi-Sugeno (T-S) fuzzy models. For each local linear model one local filter is designed using Kalman filter theory. Steady state and unknown input solutions can be found for each of the local filters. The global filter is a linear combination of linear filters. The local filter is time inva...

With appropriate modiications, the Hooman{Ribak algorithm that constructs constrained realizations of Gaussian random elds having the correct ensemble properties can also be used to construct constrained realizations of those non-Gaussian random elds that are obtained by transformations of an underlying Gaussian eld. For example, constrained realizations of lognormal, generalized Rayleigh, and ...