Fluctuation Bounds for the Max-Weight Policy with Applications to State Space Collapse

We consider a multihop switched network operating under a max-weight scheduling policy and show that the distance between the queue length process and a fluid solution remains bounded by a constant multiple of the deviation of the cumulative arrival process from its average. We then exploit this result to prove matching upper and lower bounds for the time scale over which additive state space collapse (SSC) takes place. This implies, as two special cases, an additive SSC result in diffusion scaling under non-Markovian arrivals and, for the case of independent and identically distributed arrivals, an additive SSC result over an exponential time scale.

Decomposition-Based Tracking Control with Particles

In this paper, a new control scheme, called\emph{additive-state-decomposition-based tracking control}, is proposed tosolve the tracking (rejection) problem for rotational position of the TORA (anonlinear nonminimum phase system). By the additive state decomposition, thetracking (rejection) task for the considered nonlinear system is decomposedinto two independent subtasks: a tracking (rejection) subtask for a lineartime invariant (LTI) system, leaving a stabilization subtask for a derivednonlinear system. By the decomposition, the proposed tracking control schemeavoids solving regulation equations and can tackle the tracking (rejection)problem in the presence of any external signal (except for the frequencies at$\pm1$) generated by a marginally stable autonomous LTI system. To demonstratethe effectiveness, numerical simulation is given.