In this paper we consider general nonlinear switching systems. Under an additional assumption, we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense.
This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity sol...This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity solution theory we show that the switching lower-value function is a viscosity solution of the appropriate systems of quasi-variational inequalities（the appropriate generalization of the Hamilton-Jacobi equation in this context） and that the minimal such switching-storage function is equal to the continuous switching lower-value for the game. With the lower value function a optimal switching control is designed for minimizing the cost of running the systems.展开更多
The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed.It is shown that if the entries of the pointwise stabilizing feedbac...The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed.It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices,then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.展开更多
基金Supported by the NSF of Commission of Education of Henan Province(200510459002)
文摘In this paper we consider general nonlinear switching systems. Under an additional assumption, we prove that there exists a state space depending switching rule which stabilizes the system in a very general sense.
基金Supported by the SRFEB of Henan Province(2003110002)
文摘This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity solution theory we show that the switching lower-value function is a viscosity solution of the appropriate systems of quasi-variational inequalities（the appropriate generalization of the Hamilton-Jacobi equation in this context） and that the minimal such switching-storage function is equal to the continuous switching lower-value for the game. With the lower value function a optimal switching control is designed for minimizing the cost of running the systems.
文摘The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed.It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices,then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.
