Linearized analysis versus optimization-based nonlinear analysis for nonlinear systems

For autonomous nonlinear systems stability and input-output properties in small enough (infinitesimally small) neighborhoods of (linearly) asymptotically stable equilibrium points can be inferred from the properties of the linearized dynamics. On the other hand, generalizations of the S-procedure and sum-of-squares programming promise a framework potentially capable of generating certificates valid over quantifiable, finite size neighborhoods of the equilibrium points. However, this procedure involves multiple relaxations (unidirectional implications). Therefore, it is not obvious if the sum-of-squares programming based nonlinear analysis can return a feasible answer whenever linearization based analysis does. Here, we prove that, for a restricted but practically useful class of systems, conditions in sum-of-squares programming based region-of-attraction, reachability, and input-output gain analyses are feasible whenever linearization based analysis is conclusive. Besides the theoretical interest, such results may lead to computationally less demanding, potentially more conservative nonlinear (compared to direct use of sum-of-squares formulations) analysis tools

Keeping hold of Nurse

Mather draws from a lifetime devoted to studying individual octopuses in the wild and in aquaria to combine a natural history account of their actions with an argument from design adopted from second-, often third-hand sources. The \u27distributed\u27 [decentralised] nervous system said to contrast with that of vertebrates – a premise largely accepted by Mather’s commentators so far – does not reflect the original literature on motor control, nor the facts of comparative anatomy, functional morphology and morphogenesis. Ontogeny is absent. With the help of some old or little-known illustrations from my own participant-observer experimental investigations, I will try here to unpick threads of the pre-enlightenment embroidery shrouding the argument and will call into question the use of reductionist language

Help on SOS

In this issue of IEEE Control Systems Magazine, Andy Packard and friends respond to a query on determining the region of attraction using sum-of-squares methods

Uncertain Multivariable Systems from a State Space Perspective

This paper introduces some new extensions of μ analysis for LTI systems with structured uncertainty to time varying and nonlinear systems

Robust Region-of-Attraction Estimation

We propose a method to compute invariant subsets of the region-of-attraction for asymptotically stable equilibrium points of polynomial dynamical systems with bounded parametric uncertainty. Parameter-independent Lyapunov functions are used to characterize invariant subsets of the robust region-of-attraction. A branch-and-bound type refinement procedure reduces the conservatism. We demonstrate the method on an example from the literature and uncertain controlled short-period aircraft dynamics

Robust Control Structure Selection

Screening tools for control structure selection in the presence of model/plant mismatch are developed in the context of the Structured Singular Value (μ) theory. The developed screening tools are designed to aid engineers in the elimination of undesirable control structure candidates for which a robustly performing controller does not exist. Through application on a multicomponent distillation column, it is demonstrated that the developed screening tools can be effective in choosing an appropriate control structure while previously existing methods such as the Condition Number Criterion can lead to erroneous results