Showing papers by "Petar V. Kokotovic published in 1983"

Weak connections, time scales, and aggregation of nonlinear systems

Abstract: If nonlinear subsystems with continuous equilibria are weakly connected, their local behavior is fast compared with the system-wide behavior caused by the connections. The slow behavior is described by an aggregate model which appears as a slow subsystem in the singular perturbation form of the model. In this way earlier linear aggregation results by Simon et al. in economics and slow coherency results in power systems are extended to nonlinear systems and related to singular perturbations.

Sparsity and Time Scales

Abstract: This paper develops an asymptotic approach to the analysis of dynamic networks with dense and sparse connections. A measure of the sparsity is shown to have a meaning similar to the weak connection parameter in the slow coherency method. The asymptotic sparsity analysis reveals the effect of the system dimension on the slow aggregate model and provides an interpretation for the inclusion of a higher order term neglected in the weak connection analysis. Two network sequences with different types of sparsity are used to demonstrate how the sparsity properties influence the dynamic behavior and lead to a separation of time scales.

Decentralized Adaptive Control in the Presence of Multiparameter Singular Perturbations and Bounded Disturbances

Abstract: The adaptive control of interconnected systems whose subsystems possess slow and fast modes is investigated in the presence of external disturbances. Local filters are introduced to filter the local outputs and an approach is developed for stabilization and tracking using decentralized adaptive controllers. The effects of disturbances, unmodeled interconnections and fast parasitics are examined. In the absence of parasitics all signals converge to a residual set which contains the equilibrium for exact regulation and tracking. The size of this set depends on design parameters, the magnitude of disturbances, the size of interconnections and the characteristics of the reference input signal. In the presence of parasitics global stability properties are no longer guaranteed, but a region of attraction exists from which all signals converge to a residual set.

Disturbance instabilities in an adaptive system

Abstract: Two types of disturbance instability of simple adaptive schemes are analyzed. A drift equation shows how stable equilibria are forced to infinity by infrequent but persistent switches of a constant disturbance. The ?-modification proposed by P. Ioannou counteracts these instabilities.

Weak connections, time scales, and aggregation of nonlinear systems

Abstract: If nonlinear subsystems with continuous equilibria are weakly connected, their local behavior is fast compared with the system-wide behavior caused by the connections. The slow behavior is described by an aggregate model which appears as a slow subsystem in the singular perturbation form of the model. In this way earlier linear aggregation results by Simon et al in economics and slow coherency results in power systems are extended to nonlinear systems and related to singular perturbations.

Aggregate modeling of dynamic networks with sparse connections

Abstract: This paper develops a time scale approach to the aggregation and decomposition of dynamic networks with dense and sparse connections. Two density 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.

Weak connections, time scales, and aggregation of nonlinear systems

Abstract: If nonlinear subsystems with continuous equilibria are weakly connected, their local behavior is fast compared with the systemwide behavior caused by the connections. The slow behavior is described by an aggregate model which appears as a slow subsystem in the singular perturbation form of the model. In this way earlier linear aggregation results by Simon et al. in economics and slow coherency results in power systems are extended to nonlinear systems and related to singular perturbations.