Robust adaptive control. (Disk included).

*(English)*Zbl 0839.93002
Upper Saddle River, NJ: Prentice Hall PTR. xvii, 825 p. (1996).

The class of systems under consideration consists mainly of finite-dimensional continuous-time, time-invariant, linear, single-input, single-output systems. Sometimes, the author goes further to study multivariable and/or nonlinear and/or time-varying systems.

The author presents, as a self-contained textbook, the “state of the art” in the field of adaptive control which is based on estimation, identification or reference models. Known results are unified, simplified and presented in a tutorial manner so that the communities of practical engineers and mathematicians both do benefit. In particular, each theoretically investigated adaptive controller is summarized in a table listing: plant, observer, adaptive law, control law, design variables, assumptions etc. This might be very useful for implementations.

The text of 820 pages is organized as follows: In the introduction, several different adaptation mechanisms are explained and a brief history is given. Chapter 2 contains different models of the plant to be controlled. Chapter 3 gives a nice collection of existing relevant stability results; proofs are not given but for most of the results, the reader is referred to the original literature. Adaptation mechanisms by ‘on line parameter estimation’, ‘parameter identifiers and adaptive observers’, ‘model reference adaptive control’, and ‘adaptive pole placement control’ are given in Chapter 4 to 7, respectively.

Each chapter starts with simple examples to give an intuition before it goes on to more complicated algorithms but it remains still very structured and easy to follow.

All previously described algorithms may go unstable in the presence of small disturbances or unmodelled dynamics. Hence, in the last two chapters (i.e. ‘robust adaptive laws’ and ‘robust adaptive control schemes’) input and output corruption by noise, unmodeled dynamics as well as disturbances are taken into account. Previous adaptation schemes are redesigned to establish robustness properties and to ensure the relevance of the adaptation mechanisms to many practical applications.

The author presents, as a self-contained textbook, the “state of the art” in the field of adaptive control which is based on estimation, identification or reference models. Known results are unified, simplified and presented in a tutorial manner so that the communities of practical engineers and mathematicians both do benefit. In particular, each theoretically investigated adaptive controller is summarized in a table listing: plant, observer, adaptive law, control law, design variables, assumptions etc. This might be very useful for implementations.

The text of 820 pages is organized as follows: In the introduction, several different adaptation mechanisms are explained and a brief history is given. Chapter 2 contains different models of the plant to be controlled. Chapter 3 gives a nice collection of existing relevant stability results; proofs are not given but for most of the results, the reader is referred to the original literature. Adaptation mechanisms by ‘on line parameter estimation’, ‘parameter identifiers and adaptive observers’, ‘model reference adaptive control’, and ‘adaptive pole placement control’ are given in Chapter 4 to 7, respectively.

Each chapter starts with simple examples to give an intuition before it goes on to more complicated algorithms but it remains still very structured and easy to follow.

All previously described algorithms may go unstable in the presence of small disturbances or unmodelled dynamics. Hence, in the last two chapters (i.e. ‘robust adaptive laws’ and ‘robust adaptive control schemes’) input and output corruption by noise, unmodeled dynamics as well as disturbances are taken into account. Previous adaptation schemes are redesigned to establish robustness properties and to ensure the relevance of the adaptation mechanisms to many practical applications.

Reviewer: A.Ilchmann (Lübeck)