Showing papers by "Petar V. Kokotovic published in 1985"

Time scale modeling of sparse dynamic networks

Abstract: This paper develops a time-scale approach to the decomposition and aggregation of dynamic networks with dense and sparse connections. Two parameters are used to characterize time-scale and weak coupling properties. Bounds in terms of these parameters determine when there are two time-scales in sparse networks. Simplified models of the slow and fast subsystems are proposed and physical interpretations are provided. The results are illustrated with a 2000-node power network.

A Slow Manifold Approach to Feedback Control of Nonlinear Flexible Systems

Abstract: In this paper we consider the control problem for a class of coupled, second-order singularly perturbed nonlinear dynamical systems. The problem has important application to flexible mechanical systems including robot manipulators with flexible joinra, where the singular perturbation parameter ? is the inverse of the joint stiffness. For this class of systems it is known that the reduced order model corresponding to the mechanical system under the assumption of perfect rigidity is globally linearizable via nonlinear state feedback, but that the full order flexible system is not, in general, linearizable. We utilize the concept of integral manifold to represent the dynamics of the slow subsystem, which reduces to the rigid model as the perturbation parameter tends to zero. We show that linearizability of the rigid model implies linearizability of the flexible system restricted to the integral manifold. Based on a power series expansion of the integral manifold around ? = 0 we show how to approximate the feedback linearizing control to any order in ?. The result is a nonlinear feedback control scheme to "stiffen" the nonlinear flexible system. That is, the behavior of the closed loop flexible system is nearly that of the controlled rigid system.

Stability analysis of an adaptive system with unmodelled dynamics

Abstract: Stability bounds for fast and slow adaptation are derived for a simple adaptive system with one unmodelled (‘parasitic’) pole which is approximated by a right half-plane zero. In fast adaptation the product of the adaptive gain and power of the reference input must be smaller than the parasitic pole. In slow adaptation most of the input signal energy must be in the frequency range lower than the square root of the parasitic pole. It is shown that a plant bypass ensures a global stability property by making the linear time-invariant part of the adaptive loop strictly positive real (SPR). The price paid is an increase of the tracking error at very low frequencies and with slow adaptation when the equilibrium of the system without bypass is exponentially stable.

Integral manifold approach to slow adaptation

Abstract: The notion of an integral manifold M is used to obtain an exact separation of the parameter update equation from the state equations in continuous adaptive schemes. The update equation on M is then analyzed by averaging and the results used to interpret and justify several previous approaches.

A corrective feedback design for nonlinear systems with fast actuators

Abstract: Recent two-time scale results can be derived from a geometric framework which allows further extensions and computational improvements. In this paper the two-time scale behavior of singularly perturbed systems is exploited to design slow and fast controls and to combine them into a composite control. As an illustration we present a corrective design to compensate for fast actuator dynamics modeled as singular perturbations.