Statistical MIMO controller performance monitoring. Part I: Data-driven covariance benchmark

In this paper, a data-based covariance benchmark is proposed for control performance monitoring. Within the covariance monitoring scheme, generalized eigenvalue analysis is used to extract the directions with the degraded or improved control performance against the benchmark. It is shown that the generalized eigenvalues and the covariance-based performance index are invariant to scaling of the data. A statistical inference method is further developed for the generalized eigenvalues and the corresponding confidence intervals are derived from asymptotic statistics. This procedure can be used to determine the directions or subspaces with significantly worse or better performance versus the benchmark. The covariance-based performance indices within the isolated worse and better performance subspaces are then derived to assess the performance degradation and improvement. Two simulated examples, a multiloop control and a multivariable MPC system, are provided to illustrate the utility of the proposed approach. Then an industrial wood waste burning power boiler unit is used to demonstrate the effectiveness of the method.     

Patience is a Virtue: The Effect of Slack on Competitiveness for Admission Control

We consider the on-line competitiveness for scheduling a single resource non-preemptively in order to maximize its utilization. Our work examines this model when parameterizing an instance by a new value which we term the patience. This parameter measures each job's willingness to endure a delay before starting, relative to this same job's processing time. Specifically, the slack of a job is defined as the gap between its release time and the last possible time at which it may be started while still meeting its deadline. We say that a problem instance has patience , if each job with length J has a slack of at least ·J.Without any restrictions placed on the job characteristics, previous lower bounds show that no algorithm, deterministic or randomized, can guarantee a constant bound on the competitiveness of a resulting schedule. Previous researchers have analyzed a problem instance by parameterizing based on the ratio between the longest job's processing time and the shortest job's processing time. Our main contribution is to provide a fine-grained analysis of the problem when simultaneously parameterized by patience and the range of job lengths. We are able to give tight or almost tight bounds on the deterministic competitiveness for all parameter combinations.If viewing the analysis of each parameter individually, our evidence suggests that parameterizing solely on patience provides a richer analysis than parameterizing solely on the ratio of the job lengths. For example, in the special case where all jobs have the same length, we generalize a previous bound of 2 for the deterministic competitiveness with arbitrary slacks, showing that the competitiveness for any 0 is exactly 1+1/(+1). Without any bound on the job lengths, a simple greedy algorithm is (2+(1/))-competitive for any <0. More generally we will find that for any fixed ratio of job lengths, the competitiveness of the problem tends towards 1 as the patience is increased. The converse is not true, as for any fixed <0 we find that the competitiveness is bounded away from 1, no matter what further restrictions are placed on the ratio of job lengths.