Adaptive Control of a Family of Plants

Consider a linear time-invariant (LTI) plant which is not completely specified, but instead belongs to a finite set of known plants, say {P i : i ∈ p}. Our objective is to design a controller which provides “good” tracking and disturbance rejection, in a sufficiently well-defined sense, for this partially known plant. We first design a high-performance LTI controller K i for each possible P i if the pair (P i , K j ) is stable iff i = j and has no eigenvalues on the imaginary axis for any i, j ∈ p and if an upper bound on the magnitude of the unmeasurable disturbance signal is available, then it is shown that a switching mechanism can be used to find the correct LTI controller; furthermore, each LTI controller need only be tried once. This kind of problem often arises in an industrial setting, and is often approached using heuristic “gain-scheduling” techniques.