On general systems with randomly occurring incomplete information

In the system and control community, the incomplete information is generally regarded as the results of (1) our limited knowledge in modelling real-world systems; and (2) the physical constraints on the devices for collecting, transmitting, storing and processing information. In terms of system modelling, the incomplete information typically includes the parameter uncertainties and norm-bounded non-linearities that occur with certain bounds. As for the physical constraints, two well-known examples are the actuator/sensor saturation caused by the limited power/altitude of the devices as well as the signal quantization caused by limited bandwidth for signal propagation

Development of Ellipsoidal Analysis and Filtering Methods for Nonlinear Control Stochastic Systems

The methods of the control stochastic systems (CStS) research based on the parametrization of the distributions permit to design practically simple software tools. These methods give the rapid increase of the number of equations for the moments, the semiinvariants, coefficients of the truncated orthogonal expansions of the state vector Y, and the maximal order of the moments involved. For structural parametrization of the probability (normalized and nonnormalized) densities, we shall apply the ellipsoidal densities. A normal distribution has an ellipsoidal structure. The distinctive characteristics of such distributions consist in the fact that their densities are the functions of positively determined quadratic form of the centered state vector. Ellipsoidal approximation method (EAM) cardinally reduces the number of parameters. For ellipsoidal linearization method (ELM), the number of equations coincides with normal approximation method (NAM). The development of EAM (ELM) for CStS analysis and CStS filtering are considered. Based on nonnormalized densities, new types of filters are designed. The theory of ellipsoidal Pugachev conditionally optimal control is presented. Basic applications are considered

A Survey of the Probability Density Function Control for Stochastic Dynamic Systems

Probability density function (PDF) control strategy investigates the controller design approaches in order to to realise a desirable distributions shape control of the random variables for the stochastic processes. Different from the existing stochastic optimisation and control methods, the most important problem of PDF control is to establish the evolution of the PDF expressions of the system variables. Once the relationship between the control input and the output PDF is formulated, the control objective can be described as obtaining the control input signals which would adjust the system output PDFs to follow the pre-specified target PDFs. This paper summarises the recent research results of the PDF control while the controller design approaches can be categorised into three groups: 1) system model-based direct evolution PDF control; 2) model-based distribution-transformation PDF control methods and 3) databased PDF control. In addition, minimum entropy control, PDF-based filter design, fault diagnosis and probabilistic decoupling design are also introduced briefly as extended applications in theory sense

Computable infinite dimensional filters with applications to discretized diffusion processes

Let us consider a pair signal-observation ((xn,yn),n 0) where the unobserved signal (xn) is a Markov chain and the observed component is such that, given the whole sequence (xn), the random variables (yn) are independent and the conditional distribution of yn only depends on the corresponding state variable xn. The main problems raised by these observations are the prediction and filtering of (xn). We introduce sufficient conditions allowing to obtain computable filters using mixtures of distributions. The filter system may be finite or infinite dimensional. The method is applied to the case where the signal xn = Xn is a discrete sampling of a one dimensional diffusion process: Concrete models are proved to fit in our conditions. Moreover, for these models, exact likelihood inference based on the observation (y0,...,yn) is feasable