Boundary control of a laminar flow of a viscous incompressible fluid in the generalized Couette cell. The asymptotic approach

In this paper, a limiting problem for an optimal boundary control problem of a laminar flow of a viscous incompressible fluid in the generalized Couette cell, when the number of inner cylinders unrestrictedly increases, is obtained.     

Decomposition of a linear-quadratic optimal control problem with fast and slow variables

A linear-quadratic optimal control problem for a discrete different time-scale system is studied. The decomposition of the boundary value problem for the maximum principle is based on the geometric approach using the properties of invariant manifolds of slow and fast motions. This approach aids in constructing a transformation for reducing the initial problem to a boundary-value problem for slow variables and two initial-value problems for fast variables. The transformation is expressed as an asymptotic siries in powers of a small parameter.     

Robust control algorithms with compensation of bounded perturbations

A scheme of robust control of uncertain plants which does without measuring the derivatives of the controlled variable and compensates the bounded external perturbations to within δ was proposed. Consideration was given to the problems of stabilization and reference model-based control. Examples of computer-assisted simulation illustrating efficiency of the propose scheme of control were presented.     

Output control of some nonlinear system with unknown parameters and nonlinearity

The expanded remark is given that involves the possibility of the use of the control algorithm published in [1] for the provision of the semiglobal asymptotic stability of a nonlinear system without sector constraints.     

An optimal control for a Volterra distributed system

Optimal control for a Volterra distributed system on bounded and unbounded time intervals is studied, using quality criteria defined by the objective preferences of the system.     

The method of analytical design of quasi-optimal control systems with polynomial nonlinearities

A simple and effective method for solving the problem of analytical design of optimal controllers for multidimensional control objects with polynomial nonlinearities is proposed. The method of nonlinear systems synthesis is based on the solution to the two-point boundary problem in the form of a Volterra functional series.     

Synthesis of the desired law of motion control in the neighborhood of a specified set

Consideration is given to the problem of synthesis of robust regulators of a desired structure that ensure the motion of a system on bounded neighborhoods of a set. The solution to the problem is based on the representation of motion in a connected phase plane and is reduced to studying the solvability of algebraic equations.     

Causality and stability conditions for the control of a linear distributed system

For a linear distributed system controlled by nonlinear feedback, a sufficient condition for the existence, causality, and boundedness of an operator that transforms the external action and initial state of the system to the behavior of the output of a closed-loop system is formulated. A procedure is designed for determining the class of feedbacks ensuring the causality and stability of the closed-loop control system. It is applicable to a linear one-dimensional heat conduction system controlled by nonlinear temperature feedback to the boundary action.     

Sufficient optimality conditions for the control of discrete determinate systems with bounded composition of precise measurements

Sufficient optimality conditions for control of discrete determinate systems with incomplete state-vector feedback are formulated and demonstrated, and also relations for desired control determination are obtained. Application of the obtained relations is demonstrated by examples.     

Boundary control of the third boundary

In this paper, boundary control of the third boundary condition at one end of a string, assuming that the other end is fixed, is studied.     

Stability against small noises in control problems with non-Lipschitz right-hand side of the dynamic equation

Control problems in systems with non-Lipschitz right-hand side are studied for the performance functional continuously dependent on the path. Are considered two variants of the optimization problem depending on the fact whether the ally controls the realized path from the set generated by a useful control. Relaxation of original optimization problems, namely, a sequence of perturbed problems with vanishing perturbations (the right-hand side of the equation and initial conditions) is proposed. An asymptotically optimal solution to the relaxation problem is obtained by N.N. Krasovskii and A.I. Subbotin’s extreme shift method. As is shown, the value achieved at this can be considerably better than the optimal result of the original problem.     

Optimization of the boundary control by shift or elastic force at one end of string in a sufficiently long arbitrary time

The problem of the boundary control optimization by shift or elastic force at one end of the string over a sufficiently long arbitrary time interval was solved by minimizing the L _p -norm of the derivative of control by shift or the L _p -norm of control by elastic force. Solution was established in an explicit analytical form which is valid for all p ? 1.     

Optimization and control in some ecologo-economic models

An approach to the optimal control problems was described by way of example of some ecologo-economic models. A three-level system of models for prediction of the regional ecologo-economic processes was presented. The problem of optimal control was formulated for the biological resource models of the second and third levels. The results of computer experiments were cited.     

Turnpike solutions of optimal control problems

Minimizing sequences for degenerate optimal control problems are constructed from turnpike solutions. Two variational approximation schemes for the turnpike solution are described: the first is a direct improvement of the simple approximation of piecewise-continuous turnpikes by the solutions of the initial differential system and the second consists of constructing an approximate optimal control in the neighborhood of a turnpike by a parametric curve in the state space. Since a sequence of state-linear feedback controls with variable coefficients is generated in both variants, turnpikes can be easily realized in practice.     

A control problem under incomplete information

A robust control for a system of ordinary differential equations is studied under the assumption that the system, along with control, is acted upon by a noncontrollable perturbation. An algorithm, which is stable to information noises and computation errors, is designed for solving the problem of control under incomplete information on the phase trajectory (measurements of part of coordinates).     

Explicit solution for the incommensurable frequency oscillation control problem under limited resource control

An oscillation process described by the system of linear differential equations with a constant matrix is considered. The matrix is supposed to have negative linearly independent, over the field of rational numbers, eigenvalues. For this system the explicit form of the minimum resource control is found. In the cases of the system dimension 1 and 2, the controls close to optimal are presented.     

Integral minimization of the second derivative module of the boundary control of string vibrations with the fixed end

A problem of boundary control of string vibrations with the fixed end with a bounded control resource is studied. The integral of the second derivative module of the boundary control is minimized. Estimates of upper and lower bounds are found for the extremum. In the vibration suppression problem, at the time period T formulas of boundary control that is close to the optimal control with large values of the time period T are given.     

Method of passification in adaptive control, estimation, and synchronization

The main results of the method of passification which are based on applying the Yakubovich-Kalman frequency theorem to the design of the feedback systems and examples of its use in the problems of adaptive control, state estimation, and synchronization were presented. Various types of the adaptive control algorithms with implicit reference model such as the algorithms of stabilization and tracking with the prescribed dynamics, algorithms with adaptive tuning of the standard control laws, and combined signal-parametric algorithm of adaptive control were described. Brief information about the shunting method in the adaptive control problem was given. The experimental results with the adaptive control on the “Helicopter” benchmark were described. Consideration was given to the problem of adaptive control of the nonlinear plants. Examples of applying the method of passification and adaptive observers to the problems of synchronization of the nonlinear oscillators and message transmission by chaotic signals were presented.