\(H_\infty\) norm constraint and variance control for stochastic uncertain large-scale systems via the sliding mode concept. (English) Zbl 0962.93027
One considers a linear time-invariant uncertain large-scale system consisting of \(n\) uncertain interconneted stochastic subsystems. The dynamical equation of the \(i\)-th subsystem involves the usual linear term \(A_{i}x_{i}(t) + B_{i}u_{i}(t)\) plus a linear coupling term plus an additive noisy term in the form \( D_{i}w_{i}(t)\) where \(w\) is a white noise. By using the sliding mode control scheme and with the aid of upper bound covariance control, a new controlling method is developed for the problems of local-state upper bound covariance control in stochastic uncertain large-scale systems. The key is to guess a good switching function and a good Lyapunov function, and this is done in the present paper.
Reviewer: Guy Jumarie (Montréal)
MSC:
93B36 | \(H^\infty\)-control |
93A15 | Large-scale systems |
93B12 | Variable structure systems |
93E20 | Optimal stochastic control |