IEEE Transactions on Signal Processing · 2005 · 328 citations · 22 references
EngineeringMathematicsSystems EngineeringDynamical SystemsStochastic ProcessesSystem DynamicsControl TheoryRobust ControlState EstimationStochastic ControlStochastic Differential EquationsStochastic Systems ModelingEstimation ErrorFilteringHamilton-jacobi EquationsHamilton-jacobi TheoryNonlinear FilteringNonlinear SystemsStochastic Dynamical SystemsUncertain Systems Modeling
The study considers nonlinear stochastic systems whose states and measurements are corrupted by uncertain exogenous disturbances and modeled by Ito‑type stochastic differential equations. The paper aims to develop robust H∞ filtering analysis and synthesis for nonlinear stochastic systems with disturbance‑dependent noise. The authors obtain H∞ filters by solving second‑order nonlinear Hamilton–Jacobi inequalities, and extend the design to a mixed H₂/H∞ problem by minimizing total estimation error energy under worst‑case disturbances. For a class of special nonlinear stochastic systems, the H∞ filter design reduces to solving linear matrix inequalities, and examples demonstrate the effectiveness of the proposed methods.
This paper describes the robust H/sub /spl infin// filtering analysis and synthesis of nonlinear stochastic systems with state and exogenous disturbance-dependent noise. We assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by Ito/spl circ/-type stochastic differential equations. For general nonlinear stochastic systems, the H/sub /spl infin// filter can be obtained by solving second-order nonlinear Hamilton-Jacobi inequalities. When the worst-case disturbance is considered in the design procedure, a mixed H/sub 2//H/sub /spl infin// filtering problem is also solved by minimizing the total estimation error energy. It is found that for a class of special nonlinear stochastic systems, the H/sub /spl infin// filtering design can be given via solving several linear matrix inequalities instead of Hamilton-Jacobi inequalities. A few examples show that the proposed methods are effective.
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