In this paper, a wavelet packet decomposition (WPD) based real-time transcale linearquadratic-Gaussian (LQG) tracking control algorithm is given for a class of discrete stochastic systems, which is developed with the state-space models of wavelet packet coefficients at the coarsest scale decomposition layer established by Haar WPD. The WPD-based transcale control algorithm provides a compromise...

Standard LQG control theory is generalized to a regulation problem involving specified nonzero set points for the state and control variables and nonzero-mean disturbances. For generality, the results are obtained for the problem of fixed-order (i.e., not necessarily full-order) dynamic compensation. When the state, control, and disturbance offsets are set to zero and the compensator order is s...

Consider two critical Liouville quantum gravity surfaces (i.e., $\gamma$-LQG for $\gamma=2$), each with the topology of $\mathbb{H}$ and infinite boundary length. We prove that there a.s. exists a conformal welding surfaces, when boundaries are identified according to This results in LQG surface decorated by an independent SLE$_4$. Combined proof uniqueness such welding, recently established Mc...

This article proposes a method that combines linear quadratic Gaussian (LQG) control design and structure preserving model reduction for the reduced order of infinite dimensional port Hamiltonian systems (IDPHS).For purpose weighting operators used in LQG are chosen such resulting dynamic controller is passive closed-loop system equivalent to by interconnection. The Petrov-Galerkin then approxi...

We prove that the SLE? loop measure arises naturally from conformal welding of two ?-Liouville quantum gravity (LQG) disks for ?2=??(0,4). The proof relies on our companion work LQG and uses as an essential tool concept uniform embedding surfaces. Combining result with Gwynne Miller, we get random quadrangulations decorated by a self-avoiding polygon converge in scaling limit to sphere SLE8?3 l...