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A computational method for simultaneous LQ optimal control design via piecewise constant output feedback.

Y Y Cho¹, J Lam

¹Dept. of Electr. & Comput. Eng., Virginia Univ., Charlottesville, VA.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society

|February 5, 2008

Summary

This study presents a method for simultaneous linear-quadratic (LQ) optimal control design for multiple LTI systems using piecewise constant output feedback. The approach simplifies complex control problems into solvable matrix inequalities, enabling efficient feedback gain computation.

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Area of Science:

Control Theory
Systems Engineering
Applied Mathematics

Background:

Designing controllers for multiple Linear Time-Invariant (LTI) systems simultaneously presents significant challenges.
Existing methods often lack efficiency or applicability to piecewise constant output feedback scenarios.

Purpose of the Study:

To develop a unified framework for simultaneous linear-quadratic (LQ) optimal control design for a set of LTI systems.
To address the design using piecewise constant output feedback for both discrete-time and continuous-time systems.

Main Methods:

Reducing the discrete-time simultaneous LQ optimal control problem to solving coupled matrix inequalities.
Employing an iterative Linear Matrix Inequality (LMI) algorithm for feedback gain computation.
Transforming the continuous-time problem into an equivalent discrete-time problem using periodic piecewise constant feedback.

Main Results:

An iterative LMI algorithm effectively computes the feedback gain for discrete-time systems.
The continuous-time simultaneous LQ optimal control design is successfully reduced to a discrete-time equivalent.
Explicit formulas for deriving equivalent discrete-time systems and performance indexes were derived.

Conclusions:

The proposed method provides an effective approach for simultaneous LQ optimal control design using piecewise constant output feedback.
The reduction of continuous-time problems to discrete-time equivalents simplifies the design process.
Demonstrated effectiveness through illustrative examples.