Об одной задаче управляемости и преследования в линейных дискретных системах

In this paper, it is considered linear discrete control and pursuit game problems. Control vectors are subjected to total constraints those are a discrete analogue of the integral constraints. Necessary and sufficient conditions of solvability of the 0-controllability problem are obtained. The connection between 0-controllability and solvability of the pursuit problem is studied. В статье рассмотрена линейные дискретные игровые задачи управления и преследования. На векторы управления накладываются полные ограничения, которые являются дискретным аналогом интегральных ограничений. Получены необходимые и достаточные условия разрешимости проблемы 0-управляемости. Изучается связь между 0-управляемостью и разрешимостью задачи преследования.

Linear evasion differential game of one evader and several pursuers with integral constraints

An evasion differential game of one evader and many pursuers is studied. The dynamics of state variables $$x_1,\ldots , x_m$$ x 1 , … , x m are described by linear differential equations. The control functions of players are subjected to integral constraints. If $$x_i(t) \ne 0$$ x i ( t ) ≠ 0 for all $$i \in \{1,\ldots ,m\}$$ i ∈ { 1 , … , m } and $$t \ge 0$$ t ≥ 0 , then we say that evasion is possible. It is assumed that the total energy of pursuers doesn’t exceed the energy of evader. We construct an evasion strategy and prove that for any positive integer m evasion is possible.

Transient Response of Linear Systems Under Integral Constraints

The requirement of satisfying an integral constraint imposed on a linear system's transient step-response is considered in this paper. The problem is first analyzed to determine the specific structure of a system's transfer function that helps satisfy such constraints. Analytical results are derived for a class of second-order systems with an additional zero. The results are extended to higher order transfer functions. Subsequently, a standard compensation consisting of a combination of feedforward and feedback actions is proposed to transform a given transfer function to the desired structure. Necessary and sufficient conditions to guarantee stability of the resulting closed-loop system are derived. Next, the problem of satisfying integral constraints in the presence of parametric uncertainty is addressed by augmenting adaptive estimation strategies to the feedforward and feedback compensation structure. Simulation results are provided for validation. The theory presented here is an abstraction from power management algorithms for hybrid power systems, such as a fuel cell hybridized with an ultracapacitor. Further work is ongoing to extend the theory to nonlinear systems.

Optimization of Short-term Modes of Hydrothermal Power System

Optimal planning of short-term modes of power systems is a complex nonlinear programming problem with many simple, functional and integral constraints in the form of equalities and inequalities. Especially, the presence of integral constraints causes significant difficulties in solving of such problem. Since, under such constraints, the modes of power system in separate time intervals of the considered planning period become dependent on the values of the parameters in other intervals. Accordingly, it becomes impossible to obtain the optimal mode plan as the results of separate optimization for individual time intervals of the period under consideration. And the simultaneous solution of the problem for all time intervals of the planning period in the conditions of large power systems is associated with additional difficulties in ensuring the reliability of convergence of the iterative computational process. In this regard, the issues of improving the methods and algorithms for optimization of short-term modes of power systems containing thermal and large hydroelectric power plants with reservoirs, in which water consumption is regulated in the short-term planning period, remains as an important task. In this paper, we propose the effective algorithm for solving the problem under consideration, which makes it possible to quickly and reliably determine the optimal operating modes of the power system for the planned period. The results of research of effectiveness of this algorithm are presented on the example of optimal planning of daily mode of the power system, which contains two thermal and three hydraulic power plants..