Eugene P. Ryan

A universal adaptive stabilizer for a class of nonlinear systems

Abstract An adaptive stabilizer is described, which is universal for a class of single-input nonlinear systems modelled as a controlled differential inclusion on R n . The stabilizer has a discontinous feedback structure and incorporates a gain of Nussbaum type. The analysis draws on an extension, to differential inclusions, of LaSalles principle for ordinary differential equations.

Universal l-tracking for nonlinearly-perturbed systems in the presence of noise

Abstract For a class l of multivariable, nonlinearly-perturbed, linear, minimum-phase systems of relative degree one, with output measurement noise of Sobolev class W 1,∞ (absolutely continuous on compact intervals, and bounded with essentially bounded derivative), the following servomechanism problem is solved. Determine a l-universal adaptive strategy to control the output to track any reference signal in W 1,∞ , with tracking error asymptotic to a ball of arbitrary prescribed radius λ >0. The control strategy is simple and does not invoke an internal model principle.

On asymptotically stabilizing feedback control of bilinear systems

Asymptotically stabilizing feedback controls for a class of bilinear systems are discussed; a simple modification which strengthens a result of Slemrod [1] is noted and illustrated by example.

Tracking with Prescribed Transient Behavior for Nonlinear Systems of Known Relative Degree

Tracking of a reference signal (assumed bounded with essentially bounded derivative) is considered in the context of a class

Feedback control of uncertain systems: robustness with respect to neglected actuator and sensor dynamics†

\Sigma_{\rho}

A variable structure approach to feedback regulation of uncertain dynamical systems

of multi-input, multi-output dynamical systems, modelled by functional differential equations, affine in the control and satisfying the following structural assumptions: (i) arbitrary—but known—relative degree

Tracking control: performance funnels and prescribed transient behaviour

\rho \ge 1; (ii) the “high-frequency gain” is sign definite—but possibly of unknown sign. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains (as a prototype subclass) all finite-dimensional, linear,

Singular optimal controls for second-order saturating systems

m

PID control of second-order systems with hysteresis

-input,

Universal stabilization of a class of nonlinear systems with homogeneous vector fields

m