Craig S. Sims

Optimal and suboptimal results in full- and reduced-order linear filtering

This short paper considers the design of linear reduced-order filters and linear full-order filters with reduced complexity. The objective of a reduced-order filter is to estimate a linear transformation of the state vector with a filter of lower dimension. This type of filter occurs frequently in applications.

An algorithm for estimating a portion of the state vector

An algorithm is developed for estimating a portion of the state of a linear dynamical system. The dimension of the filter used in the estimation procedure may be considerably smaller than the dimension of a Kalman filter used to estimate the entire state vector. Thus, an on line computational advantage is achieved. The savings may be significant if the dimension of the segment of the state vector which is of interest is much smaller than the dimension of the entire state vector.

Adaptive Deconvolution of Seismic Signals

Seismic signals are often modeled as the convolution of a wavelet with the earth reflectivity function. Deconvolution, for the purpose of obtaining the reflectivity function, can be done using state space estimation methods. Such methods are hampered, however, by lack of precise modeling information. The deconvolution problem then becomes an adaptive estimation problem. In this paper the correct model is assumed to be one of a finite set of candidate models, and adaptive deconvolution is accomplished using estimation algorithms developed for this type of model uncertainty.

Ordered sequential filtering for finite dimensional systems with distributed observations

This short paper treats the topic of suboptimal linear estimation for systems which have a finite dimensional state vector but a distributed set of observations. Such systems are of some practical interest, and are indeed considerably easier to work with than most distributed parameter systems. The method proposed here is that a filter structure of linear form, driven by a statistic which is a weighted integral of the distributed observation, be used to generate estimates of the state of the system. The filter parameters, and the weighting function for the integral are selected so that the estimate is unbiased and results in minimum mean-square error, subject to the structural constraints.

Optimal open-loop feedback control for linear systems with unknown parameters

Abstract The problem of controlling a class of linear systems with unknown parameters is considered. The optimal open-loop strategies are obtained for linear systems with unknown parameters in the system matrix with a quadratic performance index. The method of solution is based upon the use of the Hamilton-Jacobi theory.

Fixed configuration control of stochastic norm invariant systems

The control of a class of stochastic systems with a norm invariant property is considered. The average value of the terminal norm is constrained to be zero. A fixed configuration controller is used to minimize a performance measure which penalizes both excessive control energy and variance of the terminal value of the norm.

Norm estimation for systems with random damping

A method is proposed for estimating the norm of a system having a random damping term. Apart from the damping, the systems of interest would be norm invariant. Hence the estimation scheme is really a way of monitoring the damping. The estimator is a first order linear filter, and the results are suboptimal.

A method for controlling large-scale systems

A technique is suggested as an approach to developing controls for large-scale dynamical systems. The method has the advantage that it enables one to formulate a small-scale dynamic optimization problem based upon certain key indicators of behavior related to the large-scale system. The resultant control problem is algebraic.

Fixed configuration control of a linear system with random coefficients

In this paper, the optimal fixed configuration control of a linear stochastic system, having random parameters and an additive white noise input disturbance, is investigated. It is assumed that a noisy observation of the state is available. The observation is to be filtered, and the state of the filter used to control the stochastic system. The gains in the filter and control, the initial condition of the filter, and the pamameter specifying the filter dynamics, are to be selected so that optimal performance results subject to the constraint that the filter and control be a linear configuration. Optimal performance requires the minimization of the expected value of a quadratic performance criterion. A two point boundary value problem (TPBVP) is derived using the minimum principle, giving a set of necessary conditions for optimality. An important feature of the result is that when the filter and control gains are selected optimally, the selection of the filter dynamics is arbitrary. The optimization problem is singular with respect to one of the parameters of the filter which indicates a certain amount of freedom in the fixed configuration design. It should be noted that the control scheme proposed in this study must be considered suboptimal rather than optimal, since the linear configuration of the controller is specified prior to optimization. An example is included to illustrate application of the fixed configuration technique to the class of problems considered.