Robert B. Asher

Bibliography on adaptive control systems

This bibliography contains the references to the major papers and reports on adaptive systems. The refmences listed are divided into two main sections, one for books and the other for journal, papers, reports, dissertations, patents, and conference papers. In the second section, papers, reports, etc., are indexed into categories e.g., applications, model reference systems, self-oscillating systems, etc.

Paper: Bias, variance, and estimation error in reduced order filters

It is shown that a reduced order filter is in general biased. The equations necessary to evaluate the bias, variance, and mean square estimation error for a reduced order filter are presented. From these equations it can be observed that separation between control and estimation does not occur. The equations can be used for hardware tradeoff analysis, reduced order filter sensitivity analysis, and reduced order filter synthesis.

An algebraic representation of parameter sensitivity in linear time-invariant systems

Abstract This paper presents a new algebraic representation of trajectory parameter sensitivities for linear time-invariant ordinary differential equation systems. By working from first principles, the parameter sensitivities are obtained from the partial derivatives of the system matrices and state transition matrix. The resulting matrix-operator form allows one to compute the complete set of parameter sensitivities with at most 2nr quadrature integrals where n is the state dimension and r is the control dimension. Additionally, this form provides considerable geometric-insight into the sensitivity system and, in particular, some of the properties related to controllability are discussed. Finally, the results concerning the partial derivatives of the state transition matrix are interesting in their own right, and they allow us to extend some previously reported ( 15 , 16 ) structural properties of the sensitivity system to a more general case.

Performance Evaluation of Suboptimal Filters

The use of a Kalman filter in an applications problem requires a detailed model of both the system dynamics and the measurement dynamics. The model for many problems may be extremely large in dimensionality. However, in many instances one has a limited computer capability and, thus, must purposely introduce modeling errors into the filter in order to gain a computational advantage. However, as is well known, this may lead to the phenomenon of filter divergence. This paper considers the development of equations which allow one to evaluate a filter of reduced state. The equations are based upon using covariance analysis techniques in order to determine the true root-mean-square estimation error. These equations are computationally more advantageous than others appearing in the literature.

Linear discrete stochastic control with a reduced-order dynamic compensator

In continuous-time linear stochastic control with a fixed structure, reduced-order, dynamic compensator one obtains a quasisingular problem whereby part of the structure is arbitrary. The dual of this problem in discrete time is considered with a more general formulation. Using a quadratic performance index, the Hamiltonian for obtaining the necessary conditions is obtained which may be used to define the optimal linear reduced-order dynamic compensator and the controller gain. It is shown that the discrete problem does not have the quasisingular property of the continuous-time case as is seen by consideration of the Hamiltonian.

Filtering for precision pointing and tracking with application for aircraft to satellite tracking

Abstract : Many aerospace problems include the requirement for precision pointing and tracking from one accelerating vehicle to another. This paper considers the use of Kalman filtering for a general class of high precision pointing and tracking applications and the application of the general framework to a specific problem. A general framework which contains all known error sources is developed for a particular Kalman filter. With a covariance sensitivity analysis, this framework can be used to determine the performance of a reduced order filter and conduct a hardware requirements analysis and trade off. In particular, the paper addresses the application of the general framework for an aircraft to satellite precision tracking problem.

Adaptive estimation of doubly stochastic poisson processes

Abstract The optimal adaptive estimator structures for a class of doubly stochastic Poisson processes (DSPP) are presented. The structure is used along with a moment assumption to obtain implementable estimators. The class of DSPP considered is that of a linear Markov diffusion process modulating a linear intensity rate. The uncertainty for which the adaptation process is developed includes both structures uncertainty in the Markov diffusion process and parameter uncertainty in the Markov diffusion process and the intensity rate process. Results are given on the problem of adaptation of which of a finite number of Markov realizations is modulating the intensity process. The nonlinear adaptive estimator structures are obtained by use of a particular theorem that yields an optimal structure for the adaptive estimator. The structure is used to obtain a quasi-optimal adaptive estimator for the problem by use of a zero third central moment assumption. The estimator structure consists of a nonlinear, nonadaptive part, and a nonlinear, adaptive part which contains the parameter structure adaptations. The necessary covariance equations for performance evaluation are obtained. The theory is applied to the problem of wavefront estimation in adaptive optics for use in high-energy lasers and in imaging through atomospheric turbulence. Other examples are given.

Adaptive estimation of doubly stochastic Poisson processes with application to adaptive optics

The optimal adaptive estimator structure for a class of doubly stochastic Poisson processes (DSPP) is presented. Moment assumptions are used to obtain a quasi-optimal structure. Examples are given including applications to adaptive optics.

Estimation and control in multidither adaptive optics

This paper develops optimal statistical estimation formulation for multidither adaptive optics control loops which potentially can enhance stable beam control performance in the presence of spurious signal-like noise. A multidither autofocus example is chosen to compare estimated assisted and conventional adaptive optical performance in the presence of speckle-generated noise.

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.