Methods and algorithms of regular adaptive state estimation of stochastic object control

Topicality and demand of the subject of dissertation. Comprehensive measures taken by the Government of the Republic of Uzbekistan for the development of a regional and territorial control and automated creation system of a single information space, focused on the widespread introduction of information control systems based on modern information and communication technologies. In this regard, the development of efficient methods and algorithms for state estimation and control of various functional purpose and is of particular relevance, however, remains not completely solve theoretical and applied problems of wide national economic significance. The development of complex information processing systems and controls, in particular, systems of technological objects, stimulated constant increase of the performance requirements of accuracy. This task is especially difficult in real conditions of a priori uncertainty and unexpected variability of the models and the external environment. Under these conditions the introduction of the adaptation and monitoring of the system carried is expedient in relation to significant disturbance model, which can not be considered as a simple evaluation of interfering factors and which will significantly improve the quality of the system as a whole. Thus, the development and the development of effective means and methods of adaptation of the control system in conditions of high uncertainty a priori in the real-time rate will effectively handle the data of observations significantly improve the accuracy and reliability of information processing and control.
Demand dissertation is characterized by the widespread introduction of modern concepts of automation and control of complex engineering in various industries, including chemical, associated with tasks requiring close attention estimation, identification and management of objects in an uncertain environment.
This research work is focused on ensuring implementation of the Resolution of the President of the Republic of Uzbekistan the №PP-677 of 27.07.2007 y. "About the Program of modernization, technical and technological modernization of the enterprises of chemical industry", which states that one of the main objectives of the Programme is to improve the technical level and production efficiency, ensuring operational reliability and environmental safety of chemical production by introduction of modern high technology equipment and advanced process control systems.
Accordingly, the solution of these problems requires special research and development aimed at further improving the efficiency of process control systems based on modern information technology.
Thus the practical implementation of these methods of adaptation and control faced with the need to solve a variety of inverse problems of managed dynamics objects. Problems of this type are essentially ill-conditioned. They belong to the class of ill-posed problems. In this situation, the problem of synthesis methods and algorithms for adaptive state estimation control objects in the face of  uncertainty should be considered in terms of the theory of regular evaluation, defining the methodology for constructing stable algorithms for processing the current information. In this regard, the development of efficient methods and algorithms for regular adaptive state estimation process facilities control under model uncertainty and synthesis of computing circuits for their implementation acquires great importance.
Purpose of research is to develop methods and algorithms for regular adaptive state estimation process facilities control under model uncertainty and their practical application in solving problems of automation and control of specific production processes.
Scientific novelty of dissertational research consist in the following:
the algorithms of the regular evaluation of noise covariance matrix of the object developed, based on methods for solving nonlinear functional equations, taking into account the possible undecidability of the linearized system with singular or ill-conditioned matrix, allowing for the convergence of the desired solution, and thereby improve the accuracy of adaptive estimation procedures;
proposed adaptive algorithms regular state estimation control objects in a consistently correlated noise in measurements based on singular value decomposition of matrices, allowing for binding of theoretical covariance matrix of the estimation error to the actual value, and thereby eliminate the isolation process of calculating the gain matrix of Kalman filter from actual measurements;
proposed adaptive algorithms regular iterative estimation of noise covariance matrices of the object and noise measurements based innovation process and secant method that does not require calculation or approximation of partial derivatives, allowing the filter to adapt to the changing values of the covariance matrices of disturbances;
developed regular algorithms of adaptive estimation of the gain matrix of Kalman filter based on the gradient projection method and derive expressions for the error estimates right side of the matrix equation for the calculation of the gain, allowing not made directly solving the matrix equation to estimate the error of his decision;
proposed regular algorithms of adaptive estimation under auto- and crosscorrelation of noise and interference measurements of the object on the basis of approximate methods for solving ill-conditioned or singular stochastic systems of linear algebraic equations which can improve the accuracy of calculating the gain of a dynamic filter;
developed regular algorithms of adaptive estimation of the transition matrix of control objects on the basis of methods for solving variational inequalities in the framework of the principle of iterative regularization to ensure consistency and convergence of the required assessments;
proposed regular algorithms of adaptive parameter estimation of the transition matrix of managed objects and gain dynamic Kalman filter type in a complete a priori model uncertainty, allowing estimation regularize the problem under consideration on the basis of regular methods of minimizing functionals.
CONCLUSION
The thesis is based on the concepts of system analysis, the theory of adaptive control systems, and methods for dynamic filtering solution of incorrect problems developed constructive methodology regular adaptive state estimation process facilities control under model uncertainty.
As a result, the following results:
1. Algorithms for the regular assessment of noise covariance matrix of the object, based on methods for solving nonlinear functional equations, taking into account the possible undecidability of the linearized system with singular or ill-conditioned matrix, allowing for the convergence of the desired solution, and thereby improve the accuracy of adaptive estimation procedure.
2. The algorithms of adaptive regular state estimation control objects in a consistently correlated noise in measurements based on singular value decomposition of matrices, allowing for binding of the theoretical covariance matrix of the estimation error to the actual values, and thereby eliminate the isolation process of calculating the gain matrix of the Kalman filter real
measurements.
3. The algorithms of adaptive regular iterative estimation covariance matrices of noise and interference measurements of the object based on the innovation process and the secant method does not require calculation or approximation of partial derivatives, allowing for the convergence of approximations of the desired filter and adapt to the changing values of the covariance matrices of disturbances.
4. Develop a regular algorithms adaptive estimation of the gain matrix of Kalman filter based on the gradient projection method. The expressions for the error estimate the right side of the matrix equation for the calculation of the gain, allowing not made directly solving the matrix equation to estimate the error of his decision. For the resulting expression can also obtain a priori information about the order of error in the solution to obtain qualitative conclusions about the accuracy with which a reasonably continue to solve the system.
5. The proposed two-step regularized algorithms with adaptive estimation of correlated noise object to obviate the strict dependency matrix filter gain from a priori data. It is shown that the solution of this problem are very effective methods pseudoinversion regularization, l\ - minimization and moderate damage to the choice of the regularization parameter based methods quasioptimality, cross significance and A-curve.
6. A regular algorithms of adaptive estimation in terms of noise autocorrelation of the object and noise measurements on the basis of approximate methods for solving ill-conditioned or singular stochastic systems of linear algebraic equations. In forming the estimation algorithms use statistical shape discrepancy principle, achieve the best possible estimates of the regularized solutions approximate stochastic systems of equations.
7. Develop a regular adaptive estimation algorithms with mutual correlation of noise and interference measurements of the object based on decorrelation noise and interference, and regularization methods for solving operator equations with positive definite matrices and approximately given right-hand side, to improve the accuracy of calculating the gain of a dynamic filter.
8. A regular adaptive algorithms for estimating the parameters of the equation matrices dynamics control objects and covariance matrices of perturbation based on the concepts of time series, allows to synthesize the adaptive control system in a high degree of model uncertainty.
9. Develop regular algorithms adaptive estimation of the transition matrix of control objects on the basis of methods for solving variational inequalities in the framework of the principle of iterative regularization to ensure consistency and convergence of the required assessments.
10. A regular adaptive algorithms for estimating the parameters of the transition matrix of managed objects and gain dynamic Kalman filter type in a complete a priori model uncertainty, allowing estimation regularize the problem under consideration on the basis of regular methods of minimizing functionals.
11. The algorithms of synthesis of control systems dynamic objects using predictive models based on the concepts of regular adaptive estimation under varying degrees of model uncertainty that improve the accuracy of the computation of the vector of state variables and control actions.
12. On the basis of the proposed adaptive algorithms for regular state estimation control objects in a model uncertainty developed adaptive process control system granulation-drying calcium sulfate and phosphate pulp production PS-Agro and evaporation of ammonium nitrate solution. The proposed adaptive control systems allow these processes to stabilize the technological regimes of the processes and increase the efficiency of their operation.