This volume has extended major ideas and results of linear control theory to systems with nonlinear actuators and sensors. Namely, the linear frequency domain methods (based on the frequency of harmonic inputs) are extended to the quasilinear frequency domain (based on the bandwidth of random inputs). The linear time domain methods are extended to quasilinear ones by introducing tracking quality indicators (instead of overshoot and settling time) and by modifying the root locus technique (e.g., the saturated root locus). The LQR/LQG methodology has been extended to SLQR/SLQG (where the “S” stands for “saturated”). Although not included in this volume, the H∞ and LMI techniques have also been extended to systems with nonlinearities in sensors and actuators.

In addition, new problems, specific for LPNI systems, have been formulated and solved. These include Instrumented LQR/LQG, where the optimal controller and instrumentation are synthesized simultaneously, and the problem of performance recovery, where the performance losses due nonlinear instrumentation are either contained to a desired level or eliminated altogether.

What made these results possible?

1. The method of stochastic linearization provided a tool for reducing the nonlinear systems addressed in this volume to quasilinear ones.

2. The methods of linear control theory could be applied, with some modifications, to the quasilinear systems mentioned above.

3. The resulting relationships and techniques, as it turns out, are quite similar to those of linear control theory.