T. Iwasaki’s research while affiliated with University of Virginia and other places

The central pattern generator (CPG) provides a fundamental control mechanism underlying rhythmic motions in animal locomotion. We consider a class of CPGs modeled by a group of interconnected identical neurons. Based on the idea of multivariable harmonic balance, we show how the oscillation profile is related to the connectivity matrix that specifies the architecture and strengths of the interconnections. Specifically, the frequency, amplitudes, and phases are essentially encoded in terms of a pair of eigenvalue and eigenvector. This basic principle is used to estimate the oscillation profile of a given CPG and to determine the connectivity matrix that achieves a prescribed oscillation profile

This paper considers a control synthesis problem for linear systems to meet design specifications given in terms of multiple frequency domain inequalities in (semi)finite ranges. Dynamic output feedback controllers of order equal to the plant are considered. A new multiplier expansion is proposed to convert the synthesis condition to a linear matrix inequality (LMI) condition through the linearizing change of variables by Scherer, Masubuchi, de Oliveira et al. In the single objective setting, the LMI condition may or may not be conservative, depending upon the choice of the basis for the multiplier expansion. We provide a qualification for the basis matrix to yield nonconservative LMI conditions. It turns out to be difficult to determine the basis matrix meeting such qualification in general. However, it is shown that qualified bases can be found for some cases, and that the qualification can be used to find reasonable choices of the basis for other cases. Finally, the synthesis method is applied to a multiple objective control problem for an active magnetic bearing to demonstrate its utility.

This paper proposes methods for fixed-order controller synthesis based on the generalized KYP (GKYP) lemma that provides a unified LMI characterization of frequency domain inequalities in (semi) finite frequency ranges for both continuous and discrete-time systems. We first show the GKYP lemma and how to use it for control system design including PID controller synthesis and controller order reduction with fixed poles. We then propose a recursive algorithm for fixed structure controller synthesis, where both the numerator and denominator are design parameters. We also provide a robust GKYP lemma to encompass the practical situations. The effectiveness of the proposed methods is verified by several numerical examples which include a practical application of tracking controller design for laser-driven micro-airplanes.

The generalized Kalman-Yakubovich-Popov (GKYP) lemma provides a unified LMI characterization of frequency domain inequalities in (semi)finite frequency ranges for both continuous and discrete-time systems. We developed a GKYP design toolbox which automatically generates the corresponding LMIs for controller synthesis problems with GKYP lemma just by specifying multiple design specifications without any tedious programming. This paper explains the toolbox with design examples including controller reduction and pseudo-diagonalization for MIMO plants.