Dr. Andrey Barabanov
St. Petersburg State University
A survey of recent achievements in L1-control theory and in the polynomial approach of the H-infinity control theory is presented.
The standard L1 control problem of peak-to peak minimization was generalized to processes with dependent values. This minimax analogue of the stochastic stationary processes was called renewing processes. Theory of these processes and the optimal control technique belongs to the infinite-dimensional convex analysis in the l-infinity space.
A new spectral approach to the H-infinity control and estimation problems is proposed. It contains direct operations with the initial open loop transfer functions of the plant without any preliminary parameterization and right or left factorization. The method has a graphical interpretation as some geometrical manipulations with the Bode plots of the open loop transfer functions.