L-2 and L-infinity multiobjective control for linear systems

Guoming Zhu, Purdue University

Abstract

In this research the Block diagonal Output Covariance Constraint (BOCC) problem is addressed for both continuous and discrete periodic systems. The stochastic BOCC problem is defined for white noise inputs, and the deterministic BOCC for ${\cal L}\sb2$ inputs. The ${\cal L}\sb2$ to ${\cal L}\sb\infty$ gains of continuous and discrete periodic systems pave the way to equate stochastic and deterministic BOCC problems. The BOCC algorithm developed in this research has been applied to design controllers for the JPL's Control Technology Experiment Facility. The covariance control theory has been extended to the discrete periodic case. New and less conservative bounds are derived for six different robustness problems of continuous and discrete periodic systems: ${\cal L}\sb2$ to ${\cal L}\sb\infty$ gains, time-varying structured and unstructured parameter variations. This is the first treatment for the discrete periodic case. All of the new bounds are shown to be directly related to the properties of the closed loop covariance of a related system driven by white noise. The BOCC controllers minimize the control power subject to output covariance inequality constraints on each output group. The theoretical contribution of this research is an iterative controller design algorithm to solve the BOCC problem with the proof of feasibility. Due to the equivalence of the stochastic and deterministic BOCC problems, the algorithm can also be applied to satisfy ${\cal L}\sb\infty$ constraints on multiple outputs. The BOCC problem is addressed for both continuous and discrete periodic systems. The BOCC algorithm can be also applied to design multirate controllers guaranteeing the output covariance or $l\sb\infty$ bounds, because a multirate sampling system can be put into a discrete periodic model. Psuedo-decentralized multirate controllers can be designed by the algorithm to reduce the amount of real time computation. A design strategy is proposed which integrates both model reduction and BOCC controller synthesis. The corresponding software has been well developed for this strategy, which has been applied to the JPL LSCL Experiment Facility, a large flexible structure. The covariance control theory characterizes the set of all positive definite covariance functions that a linear discrete periodic system with a fixed order controller may process. The controller assigning such covariance function to any linear discrete periodic system is explicitly in the closed form.

Degree

Ph.D.

Advisors

Skelton, Purdue University.

Subject Area

Aerospace materials|Mechanical engineering

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