A novel learning-based attack detection and estimation scheme is proposed for linear networked control systems(NCS),wherein the attacks on the communication network in the feedback loop are expected to increase networ...A novel learning-based attack detection and estimation scheme is proposed for linear networked control systems(NCS),wherein the attacks on the communication network in the feedback loop are expected to increase network induced delays and packet losses,thus changing the physical system dynamics.First,the network traffic flow is modeled as a linear system with uncertain state matrix and an optimal Q-learning based control scheme over finite-horizon is utilized to stabilize the flow.Next,an adaptive observer is proposed to generate the detection residual,which is subsequently used to determine the onset of an attack when it exceeds a predefined threshold,followed by an estimation scheme for the signal injected by the attacker.A stochastic linear system after incorporating network-induced random delays and packet losses is considered as the uncertain physical system dynamics.The attack detection scheme at the physical system uses the magnitude of the state vector to detect attacks both on the sensor and the actuator.The maximum tolerable delay that the physical system can tolerate due to networked induced delays and packet losses is also derived.Simulations have been performed to demonstrate the effectiveness of the proposed schemes.展开更多
An optimal control problem governed by the Stokes equations with L^2-norra state constraints is studied. Finite element approximation is constructed. The optimality conditions of both the exact and discretized problem...An optimal control problem governed by the Stokes equations with L^2-norra state constraints is studied. Finite element approximation is constructed. The optimality conditions of both the exact and discretized problems are discussed, and the a priori error estimates of the optimal order accuracy in L^2-norm and H^1-norm are given. Some numerical experiments are presented to verify the theoretical results.展开更多
In this paper,spectral approximations for distributed optimal control problems governed by the Stokes equation are considered.And the constraint set on velocity is stated with L2-norm.Optimality conditions of the cont...In this paper,spectral approximations for distributed optimal control problems governed by the Stokes equation are considered.And the constraint set on velocity is stated with L2-norm.Optimality conditions of the continuous and discretized systems are deduced with the Karush-Kuhn-Tucker conditions and a Lagrange multiplier depending on the constraint.To solve the equivalent systems with high accuracy,Galerkin spectral approximations are employed to discretize the constrained optimal control systems.Meanwhile,we adopt a parameter l in the pressure approximation space,which also guarantees the inf-sup condition,and study a priori error estimates for the velocity and pressure.Specially,an efficient algorithm based on the Uzawa algorithm is proposed and its convergence results are investigated with rigorous analyses.Numerical experiments are performed to confirm the theoretical results.展开更多
基金supported in part by the National Science Foundation(IIP 1134721,ECCS 1406533,CMMI 1547042)
文摘A novel learning-based attack detection and estimation scheme is proposed for linear networked control systems(NCS),wherein the attacks on the communication network in the feedback loop are expected to increase network induced delays and packet losses,thus changing the physical system dynamics.First,the network traffic flow is modeled as a linear system with uncertain state matrix and an optimal Q-learning based control scheme over finite-horizon is utilized to stabilize the flow.Next,an adaptive observer is proposed to generate the detection residual,which is subsequently used to determine the onset of an attack when it exceeds a predefined threshold,followed by an estimation scheme for the signal injected by the attacker.A stochastic linear system after incorporating network-induced random delays and packet losses is considered as the uncertain physical system dynamics.The attack detection scheme at the physical system uses the magnitude of the state vector to detect attacks both on the sensor and the actuator.The maximum tolerable delay that the physical system can tolerate due to networked induced delays and packet losses is also derived.Simulations have been performed to demonstrate the effectiveness of the proposed schemes.
基金Acknowledgments. Research supported partially by National Natural Science Foundation of China, Grant 11071080 Program of Shanghai Subject Chief Scientist, No. 09XD1401600 Fundamental Research Funds for the Central Universities of China and Shanghai Leading Academic Discipline Project： B407.
文摘An optimal control problem governed by the Stokes equations with L^2-norra state constraints is studied. Finite element approximation is constructed. The optimality conditions of both the exact and discretized problems are discussed, and the a priori error estimates of the optimal order accuracy in L^2-norm and H^1-norm are given. Some numerical experiments are presented to verify the theoretical results.
基金supported by NSFC grants(Nos.11926355,and 11701253)NSF of Henan Province(No.15A110024)+1 种基金NSF of Shandong Province(Nos.ZR2019YQ05,2019KJI003,and 2017GSF216001)China Postdoctoral Science Foundation(Nos.2017T100030,and 2017M610751)。
文摘In this paper,spectral approximations for distributed optimal control problems governed by the Stokes equation are considered.And the constraint set on velocity is stated with L2-norm.Optimality conditions of the continuous and discretized systems are deduced with the Karush-Kuhn-Tucker conditions and a Lagrange multiplier depending on the constraint.To solve the equivalent systems with high accuracy,Galerkin spectral approximations are employed to discretize the constrained optimal control systems.Meanwhile,we adopt a parameter l in the pressure approximation space,which also guarantees the inf-sup condition,and study a priori error estimates for the velocity and pressure.Specially,an efficient algorithm based on the Uzawa algorithm is proposed and its convergence results are investigated with rigorous analyses.Numerical experiments are performed to confirm the theoretical results.
