Conditions For Controllability Of Linear Systems Research Articles

On the theory of constructive construction of a linear controller

The classical problem of stationary stabilization with respect to the state of a linear stationary control system is investigated. Efficient, easily algorithmic methods for constructing controllers of controlled systems are considered: the method of V. I. Zubov and the method of P. Brunovsky. The most successful modifications are indicated to facilitate the construction of a linear controller. A new modification of the construction of a linear regulator is proposed using the transformation of the matrix of the original system into a block-diagonal form. This modification contains all the advantages of both V. I. Zubov’s method and P. Brunovsky’s method, and allows one to reduce the problem with multidimensional control to the problem of stabilizing a set of independent subsystems with scalar control for each subsystem.

Согласованность дискретных линейных стационарных управляемых систем с неполной обратной связью специального вида для n=5

Согласованность дискретных линейных стационарных управляемых систем с неполной обратной связью специального вида для n=5

К свойству согласованности четырехмерных дискретных линейных стационарных управляемых систем с неполной обратной связью специального вида

К свойству согласованности четырехмерных дискретных линейных стационарных управляемых систем с неполной обратной связью специального вида

Robustness and correction of linear models

We consider problems with correction/perturbation of all parameters for the following objects and properties: systems of linear algebraic equations and feasibility properties, systems of linear algebraic inequalities and feasibility properties, a linear stationary control system and the superstability property, a function defined point by point and the linearity property, and two finite sets of points and the linear separability property.

Necessary and sufficient conditions in a spectrum control problem

For a linear stationary control system closed by a linear output feedback and for a bilinear stationary control system, we obtain new necessary and sufficient conditions for the solvability of the eigenvalue spectrum control problem in the case of a special form of the coefficients.

Structural minimization of stationary control and observation systems

The problem of determining the minimal number of control actions (inputs) such that an openloop system can be made completely controllable is solved for linear stationary control systems. The result is reduced to linear stationary observation systems, which allows us to solve the problem of determining the minimal number of outputs such that the open-loop system can be made completely observable.

Согласованность линейных стационарных управляемых систем с наблюдателем специального вида

Согласованность линейных стационарных управляемых систем с наблюдателем специального вида

Spectrum control in linear systems with incomplete feedback

For a linear stationary control system closed by a linear incomplete feedback, we obtain necessary and sufficient conditions for the solvability of the spectrum control problem in the case of coefficients of special form.

Linear stationary control systems over the Boolean semiring and their graphs of modules

We consider linear stationary dynamical systems over the Boolean semiring. We analyze the properties of complete observability, identifiability, attainability, and controllability of a system. We define the notion of the “graph of modules” of totally controllable totally attainable Boolean linear stationary systems by analogy with spaces of modules in the case of systems over fields. The above-mentioned graph is described in the simplest case of one-dimensional inputs and outputs. We prove the weak connectedness of this oriented graph.

On polynomial solutions of the linear stationary control system

It is known that the controllable system x? = Bx + Du, where the x is the n-dimensional vector, can be transferred from an arbitrary initial state x(0) = x 0 to an arbitrary finite state x(T) = x T by the control function u(t) in the form of the polynomial in degrees t. In this work, the minimum degree of the polynomial is revised: it is equal to 2p + 1, where the number (p ? 1) is a minimum number of matrices in the controllability matrix (Kalman criterion), whose rank is equal to n. A simpler and a more natural algorithm is obtained, which first brings to the discovery of coefficients of a certain polynomial from the system of algebraic equations with the Wronskian and then, with the aid of differentiation, to the construction of functions of state and control.

О стабилизации линейных стационарных управляемых систем с неполной обратной связью

О стабилизации линейных стационарных управляемых систем с неполной обратной связью

On Concepts of Controllability for Deterministic and Stochastic Systems

The new necessary and sufficient conditions, which are formulated in terms of convergence of a certain sequence of operators involving the resolvent of the negative of the controllability operator, are found for deterministic linear stationary control systems to be completely and approximately controllable, respectively. These conditions are applied to study the S-controllability (a property of attaining an arbitrarily small neighborhood of each point in the state space with a probability arbitrarily close to one) and C--controllability (the S--controllability fortified with some uniformity) of stochastic systems. It is shown that the S--controllability (the C--controllability) of a partially observable linear stationary control system with an additive Gaussian white noise disturbance on all the intervals [0,T] for T>0 is equivalent to the approximate (complete) controllability of its deterministic part on all the intervals [0,T] for T>0.

On an inverse problem in optimal control

The problem of optimizing linear-stationary control systems subject to quadratic performance indices and bounded control effort constraints is studied. This problem was first proposed by Letov [1]. His solution, however, has been found to be valid only in some special cases [3]. In this paper, necessary and sufficient conditions for the existence of the optimal control laws of the saturation type are developed. It is shown that the weighting factors in the performance index have to be chosen in a particular manner, and the plants have to satisfy certain conditions to yield an optimal saturation type control law. As the weighting on the control effort in the performance index is decreased, the optimal solution approaches a bang-bang type singular control.