Terminal Control of Multi-agent System

Abstract

AbstractA linear controlled dynamics is considered on a fixed time interval. Dynamics transforms control into a phase trajectory. This trajectory at discrete points of the time interval is loaded with finite-dimensional linear programming problems. These problems define intermediate, initial and boundary value solutions, which correspond to the ends of time subsegments. It is required by the choice of control to form a phase trajectory so that, starting from the initial conditions, the trajectory passes through all solutions of intermediate problems and reaches the terminal conditions at the right end of the time interval. In general, constructions that combine dynamics with mathematical programming problems will be called terminal control problems. The approach to solving these problems is based on the Lagrangian formalism and duality theory. The paper proposes an iterative saddle point computing process for solving the problem of terminal control, which belongs to the class of multi-agent systems. The study was carried out within the framework of evidence-based methodology, i.e. the convergence of computational process with respect to all components of solution is proved.KeywordsTerminal controlLagrangian formalismDualityIntermediate problemsLinear programmingSaddle point methodsEvidence-based optimizationConvergence