Sensitivity analysis of hybrid systems with state jumps with application to trajectory tracking

This paper addresses the sensitivity analysis for hybrid systems with discontinuous (jumping) state trajectories. We consider state-triggered jumps in the state evolution, potentially accompanied by mode switching in the control vector field as well. For a given trajectory with state jumps, we show how to construct an approximation of a nearby perturbed trajectory corresponding to a small variation of the initial condition and input. A major complication in the construction of such an approximation is that, in general, the jump times corresponding to a nearby perturbed trajectory are not equal to those of the nominal one. The main contribution of this work is the development of a notion of error to clarify in which sense the approximate trajectory is, at each instant of time, a firstorder approximation of the perturbed trajectory. This notion of error naturally finds application in the (local) tracking problem of a time-varying reference trajectory of a hybrid system. To illustrate the possible use of this new error definition in the context of trajectory tracking, we outline how the standard linear trajectory tracking control for nonlinear systems -based on linear quadratic regulator (LQR) theory to compute the optimal feedback gain- could be generalized for hybrid systems

Backstepping controller synthesis and characterizations of incremental stability

Incremental stability is a property of dynamical and control systems, requiring the uniform asymptotic stability of every trajectory, rather than that of an equilibrium point or a particular time-varying trajectory. Similarly to stability, Lyapunov functions and contraction metrics play important roles in the study of incremental stability. In this paper, we provide characterizations and descriptions of incremental stability in terms of existence of coordinate-invariant notions of incremental Lyapunov functions and contraction metrics, respectively. Most design techniques providing controllers rendering control systems incrementally stable have two main drawbacks: they can only be applied to control systems in either parametric-strict-feedback or strict-feedback form, and they require these control systems to be smooth. In this paper, we propose a design technique that is applicable to larger classes of (not necessarily smooth) control systems. Moreover, we propose a recursive way of constructing contraction metrics (for smooth control systems) and incremental Lyapunov functions which have been identified as a key tool enabling the construction of finite abstractions of nonlinear control systems, the approximation of stochastic hybrid systems, source-code model checking for nonlinear dynamical systems and so on. The effectiveness of the proposed results in this paper is illustrated by synthesizing a controller rendering a non-smooth control system incrementally stable as well as constructing its finite abstraction, using the computed incremental Lyapunov function.Comment: 23 pages, 2 figure

Stability properties of equilibrium sets of non-linear mechanical systems with dry friction and impact

In this paper, we will give conditions under which the equilibrium set of multi-degree-of-freedom non-linear mechanical systems with an arbitrary number of frictional unilateral constraints is attractive. The theorems for attractivity are proved by using the framework of measure differential inclusions together with a Lyapunov-type stability analysis and a generalisation of LaSalle's invariance principle for non-smooth systems. The special structure of mechanical multi-body systems allows for a natural Lyapunov function and an elegant derivation of the proof. Moreover, an instability theorem for assessing the instability of equilibrium sets of non-linear mechanical systems with frictional bilateral constraints is formulated. These results are illustrated by means of examples with both unilateral and bilateral frictional constraint

Genetic erosion in crops: concept, research results and challenges

The loss of variation in crops clue to the modernization of agriculture has been described as genetic erosion The current paper discusses the different views that exist on the concept of genetic erosion in crops Genetic erosion of cultivated diversity is reflected in a modernization bottleneck in the diversity levels that occurred during the history of the crop Two stages in this bottleneck are recognized the initial replacement of landraces by modern cultivars, and further trends in diversity as a consequence of modern breeding practices Genetic erosion may occur at three levels of integration crop, variety and allele The different approaches in the recent literature to measure genetic erosion in crops are reviewed. Genetic erosion as reflected in a reduction of allelic evenness and richness appears to be the most useful definition, but has to be viewed in conjunction with events at variety level According to the reviewed literature, the most likely scenario of diversity trends during modernization is the following a reduction in diversity clue to the replacement of landraces by modern cultivars, but no further reduction after this replacement has been complete

Sleep and Sleep-wake Rhythm in Older Adults with Intellectual Disabilities

Everyone who has experienced poor sleep knows how it affects daytime functioning and wellbeing. A good night’s rest and a stable sleep-wake rhythm are therefore very important. The sleep-wake rhythm is regulated by several brain structures. People with an intellectual disability (ID) all have some form of brain dysfunction, and might therefore be at risk for sleep disturbances.[1-2] During the process of ageing, brain structures that are important in regulating the sleep-wake rhythm show functional deterioration,[ 3] resulting in fo

Characterisation of a collection of perennial Panicum species

A collection of 74 perennial Panicum accessions, belonging to 6 different species, maintained at the field genebank of the International Livestock Research Institute, was described using 49 agromorphological characters in a multivariate analysis. Fifty-four accessions, for which coordinates of the collection site were available, were further characterised using environmental data obtained through use of geographic information systems. Three drought-tolerant species, P. antidotale, P. turgidum and P. phragmitoides, were very different agro-morphologically from the other species. Of these drought-tolerant species, P. phragmitoides appeared to have the best agromorphological attributes for use as forage in dry areas. P. maximum, P. coloratum and P. infestum appeared more similar, and were not entirely separated using cluster analysis. The accessions of these 3 species could be divided into 5 different clusters with similar characteristics. The majority of the P. maximum accessions belonged to 2 clusters, mainly differing in the size and robustness of the plants. A strong correlation was found between characters describing the robustness of the P. maximum plant and the annual precipitation at the collection site. Promising P. maximum accessions for use in cut-and-carry systems were identified

Diterpenes from coffee beans decrease serum levels of lipoprotein(a) in humans: results from four randomized controlled trials

Objective: Unfiltered coffee raises serum LDL cholesterol in humans, owing to the presence of the diterpenes cafestol and kahweol. Norwegians with a chronic high intake of unfiltered coffee also had elevated serum levels of lipoprotein(a), an LDL-like particle which is insensitive toward dietary interventions. We now experimentally studied the influence of coffee diterpenes on lipoprotein(a) levels. Design: Four randomised controlled trials. Subjects: Healthy, normolipidemic volunteers. Interventions: Coffee, coffee oil, and pure diterpenes for 4-24 weeks. Main outcome measures: The circulating level of lipoprotein(a). Results: In 22 subjects drinking five to six strong cups of cafetiere coffee per day, the median fall in lipoprotein(a) was 1.5 mg/dL after two months (P=0.03), and 0.5 mg/dL after half a year (P>0.05), relative to 24 filter coffee drinkers. Coffee oil doses equivalent to 10-20 cups of unfiltered coffee reduced lipoprotein(a) levels by up to 5.5 mg/dL (P<0.05) in two separate trials (n=12-16 per group). A purified mixture of cafestol and kahweol, as well as cafestol alone, were also effective in reducing Lp(a) levels (n=10). Averaged over the four trials, each 10 mg/d of cafestol (plus kahweol)?the amount present in two to three cups of cafetiere coffee?decreased Lp(a) levels by 0.5 mg/dL or 4% from baseline values after four weeks (n=63). Conclusions: Coffee diterpenes are among the few dietary exceptions shown to influence serum lipoprotein(a) levels. However, the Lp(a)-reducing potency of coffee diterpenes may subside in the long run, and their adverse side effects preclude their use as lipoprotein(a)-reducing agents. Sponsorship: Supported by the Netherlands Heart Foundation through grant No. 900-562-091 of the Netherlands Organization of Scientific Research (NWO), plus supplemental funding by the Institute for Scientific Information on Coffee