We formulate two general classes of M-player deterministic and stochastic nonzero-sum games where the players can be placed into two groups such that there are strong interactions within each group and a weak interact...
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ISBN:
(纸本)3540537872
We formulate two general classes of M-player deterministic and stochastic nonzero-sum games where the players can be placed into two groups such that there are strong interactions within each group and a weak interaction between the two groups. This weak interaction is characterized in terms of a small parameter ε which, when set equal to zero, leads to two independent nonzero-sum games. Under the Nash equilibrium solution concept both within and in between the groups, we study the merits of an iterative method for the construction of the equilibrium by solving simpler problems at each stage of the iteration. In this iterative scheme, the zero'th order solution is the Nash equilibrium of the two independent games obtained by setting ε = 0, whereas the higher-order solutions are Nash equilibria of quadratic games, even though the original problem may have non-quadratic cost functions.
A new type of H∞ control problem, which considers a mixed attenuation of disturbances and initial-uncertainties for time-varying systems, is formulated and solved;the approach is based only on completing the square.
ISBN:
(纸本)3540537872
A new type of H∞control problem, which considers a mixed attenuation of disturbances and initial-uncertainties for time-varying systems, is formulated and solved;the approach is based only on completing the square.
A robust stabilization problem is discussed for time delay systems. By introducing an indefinite Riccati type operator equation for time delay systems, we propose a design method of robust stabilizing control law agai...
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ISBN:
(纸本)3540537872
A robust stabilization problem is discussed for time delay systems. By introducing an indefinite Riccati type operator equation for time delay systems, we propose a design method of robust stabilizing control law against the parametric uncertainties, which occur in lumped parameter element and in all types of delay element. In the derivation of the control law, the key point is that we take a twofold approach;one is an internal approach based on Lyapunov type operator equation and another is an external approach based on small-gain theorem. This twofold approach first enable us to deal the uncertainties of time delay systems in a unified way.
In this paper we consider the classical problem of pursuit and evasion for continuous-time and discrete-time systems. We prove the convergence, as the time step goes to 0, of the upper and lower value functions of the...
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ISBN:
(纸本)3540537872
In this paper we consider the classical problem of pursuit and evasion for continuous-time and discrete-time systems. We prove the convergence, as the time step goes to 0, of the upper and lower value functions of the discrete-time game to the upper and lower values of the differential game. This is done assuming a capturability condition either on the differential game, or on the discrete-time game uniformly for small values of the time step. An application is the existence of the value in the sense of Fleming under rather general conditions.
We propose a differential game as a model for the optimal control of systems affected by an unpredictable disturbance, when the controller follows a policy of total risk aversion. We study the problem of small disturb...
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ISBN:
(纸本)3540537872
We propose a differential game as a model for the optimal control of systems affected by an unpredictable disturbance, when the controller follows a policy of total risk aversion. We study the problem of small disturbances of a given deterministic system, and estimate the difference between the value functions of the unperturbed and of the perturbed problem.
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