Mathematical Problems in Engineering

Review Article

Recent Advances on Filtering and Control for Nonlinear Stochastic Complex Systems with Incomplete Information: A Survey

Table 1

Mathematical models of incomplete information.
Types Mathematical models
Missing measurements 𝑥 𝑘 + 1 = 𝑓 ( 𝑥 𝑘 ) + 𝐸 1 𝑣 𝑘 + 𝑔 ( 𝑥 𝑘 ) 𝑤 𝑘 , 𝑦 𝑘 = 𝛾 𝑘 ℎ ( 𝑥 𝑘 ) + 𝐸 2 𝑣 𝑘 , where 𝛾 𝑘 is a stochastic variable taking value on 1 or 0.
Randomly varying sensor delays 𝑥 𝑘 + 1 = 𝑓 ( 𝑥 𝑘 ) + 𝐸 1 𝑣 𝑘 + 𝑔 ( 𝑥 𝑘 ) 𝑤 𝑘 , 𝑦 𝑘 = 𝛾 𝑘 ℎ ( 𝑥 𝑘 ) + ( 1 − 𝛾 𝑘 ) ℎ ( 𝑥 𝑘 − 1 ) + 𝐸 2 𝑣 𝑘 , where 𝛾 𝑘 is a stochastic variable taking value on 1 or 0.
Signal quantization 𝑥 𝑘 + 1 = 𝑓 ( 𝑥 𝑘 ) + 𝐸 1 𝑣 𝑘 + 𝑔 ( 𝑥 𝑘 ) 𝑤 𝑘 , 𝑦 𝑘 = 𝑞 ( ℎ ( 𝑥 𝑘 ) ) + 𝐸 2 𝑣 𝑘 , where 𝑞 ( ⋅ ) is a quantization function.
Sensor saturations 𝑥 𝑘 + 1 = 𝑓 ( 𝑥 𝑘 ) + 𝐸 1 𝑣 𝑘 + 𝑔 ( 𝑥 𝑘 ) 𝑤 𝑘 , 𝑦 𝑘 = S a t ( ℎ ( 𝑥 𝑘 ) ) + 𝐸 2 𝑣 𝑘 , where S a t ( ⋅ ) is a saturation function.
Signal sampling ̇ 𝑥 𝑡 = 𝑓 ( 𝑥 𝑡 ) + 𝐸 1 𝑣 𝑡 + 𝑔 ( 𝑥 𝑡 ) 𝑤 𝑡 , 𝑦 𝑡 = ℎ ( 𝑥 𝑡 𝑘 ) + 𝐸 2 𝑣 𝑡 𝑘 , 𝑡 𝑘 ≤ 𝑡 < 𝑡 𝑘 + 1 .