Two-Person Zero-Sum Differential Game Problems For Some Uncertain Systems

Differential game theory is an important branch of game theory,which is also a significant extension of optimal control theory.It investigates a game process in which the involved players optimize their objectives by exerting controls on the dynamical system.Two-person zero-sum differential game theory is one of the important research fields,which has profound theoretical value and broad application value.In addition,there exist various noises affecting the system in real life.When the noise is a kind of subjective indeterminacy,or we have no enough data to model this noise,it is not appropriate to use probability and statistics tools to describe it.Thus,we use uncertainty theory to deal with this kind of system noise.Assume that the dynamical system is described by an uncertain differential equation,on the basis of previous research about differential game and uncertain optimal control,this thesis studies the two-person zero-sum differential game problems for some uncertain systemsThe main research contents of this thesis areIt proposes an optimistic value-based two-person zero-sum differential game model for a continuous uncertain system.Assuming that the value functions are twice differentiable,an equation of equilibrium is derived.And it studies a one-dimensional linear quadratic uncertain two-person zero-sum differential game whose solution is equivalent to the solution of a Riccati differential equationIt studies the differential game problem for a linear continuous uncertain system.The saddle point equilibrium solution of the game is proved to have a bang-bang property.It studies the expected value and optimistic value-based optimal control models for a multifactor uncertain system.Furthermore,it constructs a two-person zero-sum differential game model for the multifactor uncertain system and derives the equilibrium equation.It introduces a non-anticipating strategy into the uncertain two-person zero-sum differential game and proves the continuity of the Elliott-Kalton value function.And it constructs the relation between the equilibrium equation and the Elliott-Kalton value function using the viscosity solution methodIt obtains the recurrence equation of the uncertain two-person zero-sum dynamic game for a multi-stage uncertain dynamical system by the dynamic programming approach.In addition,it designs a hybrid intelligent algorithm integrated with uncertain simulation,artificial neural network and imperialist competitive algorithm to solve the game.It applies the uncertain two-person zero-sum differential game to some practical problems such as counter terror model,game of attrition,game of duopoly and portfolio game.