Reliable Control of Decentralized Systems: An ARE-Based H-Infinity Approach
ILLINOIS UNIV AT URBANA DEPT OF ELECTRICAL ENGINEERING
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This thesis presents a new method of decentralized linear, time- invariant control systems synthesis based on the algebraic Riccati equation ARE. The basic decentralized design guarantees closed-loop stability and a predetermined level of worst-cast disturbance attenuation. Certain modifications of the basic design guarantee the stability and disturbance attenuation to be robust despite plant uncertainty or reliable despite control-component outages. Other modifications guarantee that a subset of the controllers will be open-loop stable. The derived decentralized control law consists of a full-order observer of the plant in each control channel. Each observer includes estimates of the controls generated by the other channels and of plant disturbance inputs, based on its own estimate of the state of the plant. All of the observer gains are computed from the solution of a single Riccati-like algebraic equation, while feedback gains are computed from a state-feedback design ARE. The existence of appropriate solutions to the design equations in sufficient to guarantee the various properties of the closed-loop system. A convexity property of a certain matrix Riccati function allows parameterization of families of control laws with the same desired properties. Each value of the parameter results in controller of the same order as the plant.
- Numerical Mathematics