Optimal control in unobservable integral Volterra systems. (English) Zbl 1011.93111
The authors consider the solution of the optimal linear-quadratic controller problem for unobservable integral Volterra systems with continuous/discontinuous states under deterministic uncertainties, over continuous/discontinuous observations.
As a result, the system of the optimal controller equations are obtained, including the linear equation for the optimally controlled minimax estimate and two Riccati equations for its ellipsoid matrix and the optimal regulator gain matrix. Then, in the discontinuous problems, the equation for the optimal controller and the equations for the optimal filter and regulator gain matrices are obtained using the filtering procedure for deriving the filtering equations over discontinuous observations proceeding from the known filtering equations over continuous ones and the dual results in the optimal control problem for integral systems. A technical example illustrating an application of the obtained results is given.
As a result, the system of the optimal controller equations are obtained, including the linear equation for the optimally controlled minimax estimate and two Riccati equations for its ellipsoid matrix and the optimal regulator gain matrix. Then, in the discontinuous problems, the equation for the optimal controller and the equations for the optimal filter and regulator gain matrices are obtained using the filtering procedure for deriving the filtering equations over discontinuous observations proceeding from the known filtering equations over continuous ones and the dual results in the optimal control problem for integral systems. A technical example illustrating an application of the obtained results is given.
Reviewer: Jong Yeoul Park (Pusan)
MSC:
| 93E20 | Optimal stochastic control |
| 45D05 | Volterra integral equations |
| 49N10 | Linear-quadratic optimal control problems |
| 93E11 | Filtering in stochastic control theory |
Keywords:
linear-quadratic controller; unobservable integral Volterra systems; continuous/discontinuous states; continuous/discontinuous observations; minimax estimate; Riccati equations; optimal filterReferences:
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