Keynote address IV: The role of infinite dimensional direct adaptive control in autonomous systems and quantum information system

Many control systems are inherently infinite dimensional when they are described by partial differential equations. Currently, there is renewed interest in the control of these kinds of systems, especially in the quantum information field. Since the dynamics of these systems will not be perfectly known, it is especially of interest to control these systems adaptively and even autonomously via low-order finite-dimensional controllers. In our work, we have developed direct model reference adaptive control and disturbance rejection with very low-order adaptive gain laws for infinite-dimensional systems on Hilbert spaces. Quantum Information Systems are fundamentally infinite dimensional. And the basic operations that can be performed on quantum systems to manipulate information are unitary quantum gates. Because of the nature of entanglement at the quantum level, these gates suffer from decoherence and cannot operate in a fully unitary way. It is also quite difficult to perform experiments that would identify all the parametric data needed to create precise models of a particular quantum system. Instead, direct adaptive control that is suited to infinite dimensional systems could provide a reduction in the decoherence and allow the quantum gates to function in a more idealized unitary way. This talk will focus on the effect of infinite dimensionality on the adaptive control approach and the conditions required for asymptotic stability with adaptive control. Then I would like to go on and consider some of the issues in the control of quantum information systems. The topics here may sound highly technical, but I hope to give you a version of them that will be reasonably accessible and will still remain as exciting and attractive to you as they are to me.