Ph.D Student | Kristalny Maxim |
---|---|

Subject | Exploiting Previewed Information in Estimation and Control |

Department | Department of Mechanical Engineering |

Supervisor | Professor Leonid Mirkin |

Full Thesis text |

Information preview can be encountered in numerous control (e.g., robotics and automotive control) and signal processing applications. We appreciate this frequently when slowing down after seeing a speed bump ahead while driving. Although the availability of preview can improve control/estimation the performance, the question of how to exploit this potential is by no means trivial. In the current work this question is addressed in the general setting of model matching optimization, which can be considered as a unified framework for estimation and control problems.

The first part of the thesis is dedicated to the input-output stabilization problem, which can be associated with asymptotic behavior constraints and considered as a preliminary step to the optimization. The existing stabilization methods are either constrained to a simpler one-sided version of the problem or lead to complicated parametrizations of all stabilizing solutions. In this work mild and intuitively clear assumptions are found, facilitating derivation of a convenient parametrization, given in terms of a single stable but otherwise arbitrary parameter. The derivation is based on a solution of rational bilateral Diophantine equation, which is a standalone mathematical result.

The second part of the thesis
deals with the H ^{2} optimization with preview and asymptotic
behavior constraints. Although the one-sided case of this problem is currently
well studied, its general two-sided version has not been addressed in the
literature. In this work an explicit and numerically efficient solution of the
two-sided problem is derived. Advantages of the proposed solution are
demonstrated by two laboratory experiments and simulations of an active
suspension problem.

The last part of this thesis is
dedicated to the one-sided H ^{
∞} model matching problem
with multiple preview. Although in the H ^{
2} setting this
problem can be solved channel wise, this is not true in the
H ^{∞}
case. In this work the H ^{
∞} problem is solved using the
J-spectral
factorization approach. The resulting formulae reveal the structure of the
optimal solution and suggest a way to analyze the effects of the preview in
different channels on the achievable performance.