Control of information horizon for cooperative differential game of pollution control
An optimal control problem is formulated for a class of nonlinear systems for which there exists a coordinate representation transforming the original system into a system with a linear main part and a nonlinear feedback. In this case the coordinate transformation significantly changes the form of original quadratic functional. The penalty matrices become dependent on the system state. The linearity of the transformed system structure and the quadratic functional make it possible to pass over from the Hamilton–Jacoby–Bellman equation (HJB) to the state dependent Riccati equation (SDRE) upon the control synthesis. Note that it is rather difficult to solve the obtained form of SDRE analytically in the general case. In this study, we construct the guaranteed control method from the point of view of the system quality based on feedback linearization of the nonlinear system; the transformation of the cost function upon linearization is examined, as well as the system behavior in the presence of disturbance and the control synthesis for this case. The presented example illustrates the application of the proposed control method for the feedback linearizable nonlinear system.
This volume is dedicated to the 80th anniversary of academician V. M. Matrosov. The book contains reviews and original articles, which address the issues of development of the method of vector Lyapunov functions, questions of stability and stabilization control in mechanical systems, stability in differential games, the study of systems with multirate time and other. Articles prepared specially for this edition.
In the present paper the game theory is applied to an important open question in economics: providing microfoundations for often-used types of production function. Simple differential games of bargaining are proposed to model a behavior of workers and capital-owners in processes of formation of a set of admissible factor prices or participants’ weights (moral-ethical assessments). These games result, correspondingly, in a factor price curve and a weight curve – structures dual to production function. Ultimately, under constant bargaining powers of the participants, the Cobb-Douglas production function is received.
Mathematical models of nonlinear systems of a certain class allow them represented as linear systems with nonlinear state feedback. In other words, let make the appropriate coordinate transformation of the original dynamic model. Such a transformation, using Lyapunov functions, a number of studies used to determine the parameters of regulators to ensure the asymptotic stability properties of the nonlinear system, ie guaranteeing bounded trajectories emanating from the initial states of the system. For linear systems, there is a powerful and convenient mathematical apparatus allows the synthesis of optimal controls, but this unit is not applicable or partially applicable for nonlinear systems. Unlike prior work in this paper for nonlinear systems linearizable feedback as in the synthesis of optimal control problems with quadratic performance applied the method based on the use of the Riccati equation with parameters depending on the state.
The task of designing the control actions for a heavy water reactor under uncertainty changes its parameters considered in the key differential game. The possibility of representing nonlinear dynamics of the object in the form of a system with parameters depending on the state (State Dependent Coefficients) and quadratic functional qualities allow you to go from having to solve a scalar partial differential equation (the Hamilton-Jacobi-Bellman) to the Riccati equation with parameters depending on the state. Feasible solution obtained by applying the min-max method. The results of mathematical modeling system in the shutdown of a nuclear reactor.