Optimal State Estimation

In this paper, the problem of sensitivity reduction by feedback is formulated as an optimization problem and separated from the problem of stabilization. Stable feedback schemes obtainable from a given plant are parameterized. Salient properties of sensitivity reducing schemes are derived, and it is shown that plant uncertainty reduces the ability of feedback to reduce sensitivity. The theory is developed for input-output systems in a general setting of Banach algebras, and then specialized to a class of multivariable, time-invariant systems characterized by n × n matrices of H? frequency response functions, either with or without zeros in the right half-plane. The approach is based on the use of a weighted seminorm on the algebra of operators to measure sensitivity, and on the concept of an approximate inverse. Approximate invertibility of the plant is shown to be a necessary and sufficient condition for sensitivity reduction. An indicator of approximate invertibility, called a measure of singularity, is introduced. The measure of singularity of a linear time-invariant plant is shown to be determined by the location of its right half-plane zeros. In the absence of plant uncertainty, the sensitivity to output disturbances can be reduced to an optimal value approaching the singularity measure. In particular, if there are no right half-plane zeros, sensitivity can be made arbitrarily small. The feedback schemes used in the optimization of sensitiviiy resemble the lead-lag networks of classical control design. Some of their properties, and methods of constructing them in special cases are presented.

Feedback and Optimal Sensitivity: Model Reference Transformations, Multiplicative Seminorms, and Approximate Inverses

In this paper, the advanced analysis of linear discrete time varying multiplicative noise system in terms of anisotropy-based theory is considered. Accurate formulae for anisotropic norm of such system with mutually independent multiplicative noises and additive input disturbances are given. There two types of anisotropy-based bounded real lemmas were derived, the first one in terms of backward-time difference Riccati equations, the another one in terms of inequalities.

Anisotropy-Based Bounded Real Lemma for Multiplicative Noise Systems: the Finite Horizon Case

In the created in the 90th the anisotropy-based control theory, the sequence of the Gaussian random vectors with zero mean and certain mean anisotropy level was accepted as input perturbations acting on a linear system. In this paper, the author considers the concept of mean anisotropy of the sequence with nonzero mean and anisotropic norm of the system with given input. The problems of anisotropy-based analysis in frequency domain and state-space representation are considered. The difference between classical formulas for computing mean anisotropy and anisotropic norm and new formulas is shown. The problem of controller design is researched.

http://ieeexplore.ieee.org/iel7/6838207/6843557/06843614.pdf

Anisotropy-based analysis and synthesis problems for input disturbances with nonzero mean

This paper extends anisotropy-based control theory methods to the class of linear discrete-time systems with multiplicative noise, which involves an informational criterion to describe the stochastic uncertainty of an external disturbance. An approximate calculation method for the anisotropic norm of such systems using decomposition into linear subsystems without multiplicative noise is suggested. The cases of perfect and imperfect state measurements are considered. The existence criterion for anisotropy-based controllers in form of special matrix inequalities is established.

Anisotropy-Based Controller Design for Linear Discrete-Time Systems with Multiplicative Noise

In this paper, the problem of computation of anisotropic norm of linear discrete time varying finite horizon stochastic system in state-space terms is solved. The relationship with the similar problem in deterministic setting is given. In contrary to this case, the obtained formulas consist of one more matrix equation because of the decomposition of random matrices of a system into two parts associated with the two first stochastic moments.

State-Space Formulas for Anisotropic Norm of Linear Discrete Time Varying Stochastic System

Suboptimal Anisotropy-based Control for Linear Discrete Time Varying Systems with Noncentered Disturbances

On the Anisotropy-Based Bounded Real Lemma Formulation for the Systems with Disturbance-Term Multiplicative Noise

The paper presents a novel concept of the anisotropy-based analysis for the stochastic sequences with nonzero mean. The formulas for the anisotropy of random vector and mean anisotropy of sequence are obtained. Basic types of shaping filter connections are presented.

Arkadiy Yu. Kustov

Papers

Anisotropy-Based Bounded Real Lemma for Multiplicative Noise Systems: the Finite Horizon Case

State-Space Formulas for Anisotropic Norm of Linear Discrete Time Varying Stochastic System

Suboptimal Anisotropy-based Control for Linear Discrete Time Varying Systems with Noncentered Disturbances

On the Anisotropy-Based Bounded Real Lemma Formulation for the Systems with Disturbance-Term Multiplicative Noise

The concept of mean anisotropy of signals with nonzero mean