Preface: Developments in the simple adaptive control (SAC) methodology and its various applications
Control systems design meets the permanent challenge of continuously improving performance (such as speed and accuracy), while maintaining the guarantee of safe operation. In spite of the impressive developments in various domains of applications, performance of classical designs is inherently limited because of the uncertainty of the actual parameters of real-world systems, which may differ from the nominal values used for design and also because parameter may vary under various operational conditions. Therefore, use of adaptive control methodologies which should continuously fit the right control parameters values to the right situation seems very attractive.
However, after first requiring that the plant to be controlled be strictly passive (or strictly positive real in LTI systems), property that is not met in real-world systems, classical model reference adaptive control (MRAC) moved to assuming full-state availability that facilitated ending with proofs of stability without requiring the plant itself to be strictly passive. Either it assumes full-state availability or full-state observers, the basic idea of classical MRAC is that a plant of order $n$ contains a 'good' part and $n$ unwanted parameter that must be identified and eliminated. For a SISO plant of order $n$, this requires the use of $n$ adaptive control gains (and, of course, more in MIMO sytems).