Incentive equilibrium in bioresource sharing problem

A dynamic game model of bioresource management problem is considered. The center (referee) which shares a reservoir, and the players (countries) which harvest the fish stock on their territory are the participants of this game. In this paper we investigate the new type of equilibrium—cooperative incentive equilibrium. The equilibria are constructed in the case, when the players punish each other for a deviation from the cooperative equilibrium, and in the case, when the center punishes them for a deviation. Some results of the numerical modelling are given.     

Uncertainty of asymptotic dynamics in bioresource management simulation

Specific features of simulating a system that experiences structural changes in the course of its development are studied by the example of a controlled biological population. The problem of whether nonattracting chaotic sets can arise in dynamic systems with more than one attractor is considered in this context. The formalism of hybrid automata as applied to simulation problems of biological processes is described. Specific features of the phase portrait of the developed dynamic model are characterized by locally disconnected boundaries of basins of attraction of two attractors. The conclusion on limited predictability of the dynamics of some controlled natural systems is made, which is a consequence of uncertainty with respect to the motion of the system towards one of possible stable states.     

具有通信时延的离散时间二阶多个体网络的一致性问题

针对具有通信时延的离散时间二阶多个体系统的一致性问题,采用了具有静态领导者的一致性算法.根据广义Nyquist判据和Gerschgorin圆盘定理,得到了系统渐近收敛到领导者状态的充分条件.在个体与领导者构成的连接拓扑满足一定连通性的前提下,该充分条件是分散形式的,与控制参数、邻居个体之间的连接权值相关,而与通信时延大小无关.仿真结果证明了结论的正确性.     

Regulator problem for uncertain linear discrete-time systems with constrained control

A necessary and sufficient condition to test the robustness of a regulator of uncertain linear systems with constrained control is given. The candidate regulator for this test is that stabilizing nominal systems. An illustrative example is also given.     

Regulator problem for linear discrete-time systems with non-symmetrical constrained control

The regulator problem is studied for linear discrete-time systems with non-symmetrical constrained control, i.e. systems described by the state equation x _k+1 = Ax _k + Bu _k, where u _k ? Ω, and u _k = Fx _k. Necessary and sufficient conditions allowing us to obtain the largest non-symmetrical polyhedral domain of positive invariance and contractivity with respect to motions of the system in the closed loop are established. The case of symmetrically constrained control is obtained as a particular case.     

Pole-placement problem for discrete-time linear periodic systems

The pole-placement problem for the monodromy matrix of a discrete-time linear periodic system is considered. Given a partition of the complex plane into a ‘good’ part ? and a ‘bad’ part ?_b, the result obtained by Wonham (1979) is extended to the periodic case. This extension is based on the decomposition of a completely controllable periodic system into two subsystems, such that the first subsystem is completely reachable and the eigenvalues of the monodromy matrix of the second one are equal to zero.     

Pole-assignment problem for discrete-time linear periodic systems

This paper considers the pole-assignment problem for discrete-time linear periodic systems through the use of linear periodic state-variable feedback control. It is shown that if the N-periodic system with m inputs and n states is completely reachable then the problem can be reduced to the pole-assignment problem for a discrete-time linear invariant system with Nm inputs and n states.     

Separability-assignment problem for q-dimensional linear discrete-time systems

Separability-assignment problem for q-dimensional system is formulated. Sufficient conditions for the existence of a solution to the problem are presented. An algorithm for finding the feedback-gain matrix is given and illustrated by an example of a 4-D system.     

The discrete-time tracking problem with a time delay in the control

The linear-quadratic tracking problem is solved for a discrete-time system with a control delay ofTtime periods. Two closed-loop solutions are seen to result, one of which applies to the firstTtime periods, and the second of which holds for the remaining time.     

The discrete-time H∞ control problem with measurement feedback

This paper is concerned with the discrete-time H_∞ control problem with measurement feedback. We extend previous results by having weaker assumptions on the system parameters. We also show explicitly the structure of H_∞ controllers. Finally, we show that it is in certain cases possible, without loss of performance, to reduce the dynamical order of the controllers.     

Linear quadratic regulation problem for discrete-time systems with multi-channel multiplicative noise

This paper investigates the linear quadratic regulation (LQR) problem for discrete-time systems with multiplicative noise. Multiplicative noise is usually assumed to be a scalar in existing literature works. Motivated by recent applications of networked control systems and MIMO communication technology, we consider multi-channel multiplicative noise represented by a diagonal matrix. We first show that the finite horizon LQR problem can be solved using a generalized Riccati equation. We then prove the convergence of the generalized Riccati equation under the conditions of stabilization and exact observability, and obtain the solution to the infinite horizon LQR problem. Finally, we provide a numerical example to demonstrate the proposed approach.     

A formula for the optimal cost in the general discrete-time LEQG problem

This paper is aimed at deriving an explicit formula for the optimal cost for discrete-time linear exponential-of-quadratic Gaussian (LEQG) control problems. We make direct calculations for the general case with cross terms in the cost and noise covariance matrices using an information-state approach.     

The problem of the moody chess players

We analyze a sorting problem where for every element there is a hard upper bound on the overall number of lost comparisons: Given are n elements and n non-negative integers a₁,…,an. The goal is to sort these n elements by pairwise comparisons, subject to the condition that the kth element must not be the loser (= smaller element) in more than ak of its comparisons against the other elements.We completely characterize the sequences a₁,…,an for which this sorting problem can be solved.     

The model matching problem for periodic discrete-time systems

In this paper, the model matching problem via state feedback is studied for discrete-time periodic systems. It is shown that, under some zero-matching conditions, it is possible to assign a target input-output periodic system by means of a periodic state-feedback control law. Furthermore, this entails that a periodic system can be converted into a closed-loop time-invariant system via state feedback     

A new genetic algorithm for the asymmetric traveling salesman problem

The asymmetric traveling salesman problem (ATSP) is one of the most important combinatorial optimization problems. It allows us to solve, either directly or through a transformation, many real-world problems. We present in this paper a new competitive genetic algorithm to solve this problem. This algorithm has been checked on a set of 153 benchmark instances with known optimal solution and it outperforms the results obtained with previous ATSP heuristic methods.     

A comparative analysis of several asymmetric traveling salesman problem formulations

In this survey, a classification of 24 asymmetric traveling salesman problem (ATSP) formulations is presented. The strength of their LP relaxations is discussed and known relationships from the literature are reviewed. Some new relationships are also introduced, and computational results are reported.     

Manipulation in the division problem for two players

In the division problem for two players it is assumed that one of them is honest and informs his true preferences. The second player knows in advance the preferences of the first player and he tends to use this information in the maximum beneficial way for himself. In essence, this article is the recommendation for the second player. Here, it turns out that the optimal strategy does not practically depend on the division procedure (if the latter is sufficiently reasonable, i.e., if at the given preference of the partners there exist fair divisions, the procedure suggests one of them).     

Minimum time output regulation problem of linear discrete-time systems

This paper deals with the minimum time output regulation problem of finite-dimensional linear time-invariant discrete-time systems with an incomplete state observation. First, the necessary and sufficient condition is obtained for the existence of controllers which regulate the system for any arbitrary initial state to a certain given subspace in finite steps. Then, the minimum time is obtained in which the system satisfying the above conditions can be regulated, and a minimum time regulating controller is designed. These are obtained by the geometric approach which is a powerful tool for the investigation of the structural property of linear systems.