Vol 79, No 6 (2018)

Foundations for the passification method were laid out by A.L. Fradkov in 1974 in the context of the adaptive stabilization problem for the output of a linear dynamic plant. Over the past decade, the passification method has been further developed, and new applications have appeared both in the field of systems theory and in practical control problems. This survey is devoted to these new results. We give a brief review of the fundamentals of the passification method, results of its applications in problems of adaptive and robust control, synchronization, control and estimation under communication constraints. We pay special attention to the method’s application for networking systems. We also present some other applications of the passification method that do not fall into these categories.

We consider the possibilities of using cyclic stochastic approximation for solving optimization problems of a nonstationary functional of the data produced by distributed observers (sensors) under constraints on the possibilities of simultaneous communication between the observers themselves. We achieve tracking the optimal value of parameters up to a certain level of quality with a multi-agent algorithm. The efficiency of the proposed approach is illustrated by an example of modeling the process of tracking the trajectories of a group of moving objects using a set of spatially distributed sensors.

This paper considers a group of systems (agents) described by linear continuous or discrete models. All systems operate in the repetitive mode with a constant pass length, with resetting to the initial state after each pass is complete. Information exchange among the systems is described by a directed graph. The problem of reaching a consensus is formulated as designing an iterative learning control law (protocol) under which the output variable of each agent converges to a reference trajectory (pass profile) as the number of passes grows infinitely. This problem is solved using an original approach based on 2D models and a 2D modification of the vector Lyapunov function method. The ultimate results are written in form of linear matrix inequalities. 2D counterparts of the Fax–Murray theorem are established. An illustrative example is given.

Consideration was given to the problem of adaptive output control of the class of MIMO (Multiple Input Multiple Output) systems that are functionally and parametrically uncertain. An approach to the design of the control law ensuring stabilization of the MIMO nonlinear Lurie system, that is, a system consisting of the linear part (strictly minimum-phase unit) and nonlinear static feedback unit, was proposed on the basis of the Fradkov theorem on feedback passification of linear systems.

The problem of synthesis of robust anisotropic suboptimal controllers is stated and solved for systems with uncertain parameters. This paper considers a general case of unstructured parametric linear-fractional uncertainty bounded in spectral norm. The initial synthesis problem for the uncertain system is embedded into the synthesis problem for some auxiliary system with certain parameters, augmented controlled output, and additional input.

Opinion dynamics in network structures of special type are considered. Each node consists of two agents interacting with each other. The properties of consensus arising in such structures are studied using the DeGroot model.

In this paper, a multiagent approach to the Multiple Depot Vehicle Routing Problem with Time Windows (MDVRPTW) is presented. A multiagent system of interacting trucks, depots and orders is considered. For limiting the intensity of negotiations, a Delaunay triangulation-based scene structure is proposed. As demonstrated below, the solutions obtained by the new algorithm vary by 10–30% from the well-known best counterparts; however, the speed of calculations is considerably higher, and hence the new algorithm can be applied in real-time systems.

This paper considers models of evolutionary non-zero-sum games on the infinite time interval. Methods of differential game theory are used for the analysis of game interactions between two groups of participants. We assume that participants in these groups are controlled by signals for the behavior change. The payoffs of coalitions are defined as average integral functionals on the infinite horizon. We pose the design problem of a dynamical Nash equilibrium for the evolutionary game under consideration. The ideas and approaches of non-zero-sum differential games are employed for the determination of the Nash equilibrium solutions. The results derived in this paper involve the dynamic constructions and methods of evolutionary games. Much attention is focused on the formation of the dynamical Nash equilibrium with players strategies that maximize the corresponding payoff functions and have the guaranteed properties according to the minimax approach. An application of the minimax approach for constructing optimal control strategies generates dynamical Nash equilibrium trajectories yielding better results in comparison to static solutions and evolutionary models with the replicator dynamics. Finally, we make a comparison of the dynamical Nash equilibrium trajectories for evolutionary games with the average integral payoff functionals and the trajectories for evolutionary games with the global terminal payoff functionals on the infinite horizon.

The article discusses the relevance of implementing scheduling system for the purposes of production and supply scheduling at refineries. For this objective, we identified the main factors that affect the complexity of the task of scheduling and reduce the accuracy of the developed schedules, and proposed a practical approach to assessing the influence of these factors in order to analyze the relevance of the implementation of scheduling system. The article also considers the issues of economic efficiency derived from the implementation of scheduling system.