Control system design for mechanical systems using contraction theory

Abstract

Contraction theory is a recently developed control system tool based on an exact differential analysis of convergence. After establishing new combination properties of contracting systems, this paper derives new controller and observer designs for mechanical systems such as aircraft and underwater vehicles. The classical nonlinear strap down algorithm is also shown to be marginally contracting. The relative simplicity of the approach stems from its effective exploitation of the systems' structural specificities.

On partial contraction analysis for coupled nonlinear oscillators

“…After a brief review of key results of contraction theory [40,41,39] in Section 2, we introduce the new concept of partial contraction, which extends contraction analysis to include convergence to behaviors or to specific properties (such as equality of state components, or convergence to a manifold). Partial contraction provides a very general analysis tool to investigate the stability of large-scale systems.…”

Contraction and sum of squares analysis of HCCI engines

“…The control structure consists of a nonlinear observer and controller. These two components of the control structure exploit the contractability properties (see (Lohmiller and Slotine, 1998), (Lohmiller and Slotine, 2000)) of the system and utilize a triangular structures approach (Seto et al, 1994) to synthesize the appropriate control action. For brevity, we only present the control structure here and a qualitative outline of the proof of stability.…”

“…Since only valve position is considered measurable, a nonlinear controller/observer pair is designed for EHVS control. The stability of the approach follows from contraction analysis (Lohmiller and Slotine, 1998;Lohmiller and Slotine, 2000).…”

Simple Observer Based Synchronization of Lorenz System with Parametric Uncertainty

“…Contraction theory is recently developed tool for analyzing the stability and synchronization of nonlinear control system. Some of important results of contraction theory can be found in literature [5][6][7][8][9][10] & references therein. In observer based synchronization approach, the actual system states are reconstructed by utilizing the information available at the actual system output.…”