The paper deals with the control of underactuated mechanical systems between equilibrium positions across the singular positions. The considered mechanical systems are in the gravity field. The goal is to find feasible trajectory connecting the equilibrium positions that can be the basis of the system control. Such trajectory can be stabilized around both equilibrium positions and due to the gravity forces the mechanical system overcomes the singular positions. This altogether constitutes the control between the equilibrium positions. The procedure is demonstrated on the different inverse pendulum mechanisms.
In the paper, we unify and extend some basic properties for linear control systems as they appear in the continuous and discrete cases. In particular, we examine controllability, reachability, and observability for time-invariant systems and establish a duality principle.
Let G be a compact and connected semisimple Lie group and Σ an invariant control systems on G. Our aim in this work is to give a new proof of Theorem 1 proved by Jurdjevic and Sussmann in \cite{ju-su 2}. Precisely, to find a positive time sΣ such that the system turns out controllable at uniform time sΣ. Our proof is different, elementary and the main argument comes directly from the definition of semisimple Lie group. The uniform time is not arbitrary. Finally, if A=⋂t>0A(t,e) denotes the reachable set from arbitrary uniform time, we conjecture that it is possible to determine A as the intersection of the isotropy groups of orbits of G-representations which contains exp(z), where z is the Lie algebra determined by the control vectors.
In this paper, we establish the controllability conditions for a finite-dimensional dynamical control system modelled by a linear impulsive matrix Lyapunov ordinary differential equations having multiple constant time-delays in control for certain classes of admissible control functions. We characterize the controllability property of the system in terms of matrix rank conditions and are easy to verify. The obtained results are applicable for both autonomous (time-invariant) and non-autonomous (time-variant) systems. Two numerical examples are given to illustrate the theoretical results obtained in this paper.
This article considers a class of finite-dimensional linear impulsive time-varying systems for which various sufficient and necessary algebraic criteria for complete controllability, including matrix rank conditions are established. The obtained controllability results are further synthesised for the time-invariant case, and under some special conditions on the system parameters, we obtain a Popov-Belevitch-Hautus (PBH)-type rank condition which employs eigenvalues of the system matrix for the investigation of their controllability. Numerical examples are provided that demonstrate--for the linear impulsive systems, null controllability need not imply their complete controllability, unlike for the non-impulsive linear systems.
In this paper we study the approximate and complete controllability of stochastic integrodifferential system in finite dimensional spaces. Sufficient conditions are established for each of these types of controllability. The results are obtained by using the Picard iteration technique.
By max-plus algebra we mean the set of reals R equipped with the operations a⊕b=max{a,b} and a⊗b=a+b for a,b∈R. A vector x is said to be a generalized eigenvector of max-plus matrices A,B∈R(m,n) if A⊗x=λ⊗B⊗x for some λ∈R. The investigation of properties of generalized eigenvectors is important for the applications. The values of vector or matrix inputs in practice are usually not exact numbers and they can be rather considered as values in some intervals. In this paper the properties of matrices and vectors with inexact (interval) entries are studied and complete solutions of the controllable, the tolerable and the strong generalized eigenproblem in max-plus algebra are presented. As a consequence of the obtained results, efficient algorithms for checking equivalent conditions are introduced.
In this paper we use a generalized version of absolute continuity defined by J. Kurzweil, J. Jarník, Equiintegrability and controlled convergence of Perron-type integrable functions, Real Anal. Exch. 17 (1992), 110–139. By applying uniformly this generalized version of absolute continuity to the primitives of the Henstock-Kurzweil-Pettis integrable functions, we obtain controlled convergence theorems for the Henstock-Kurzweil-Pettis integral. First, we present a controlled convergence theorem for Henstock-Kurzweil-Pettis integral of functions defined on $m$-dimensional compact intervals of $\mathbb {R}^{m}$ and taking values in a Banach space. Then, we extend this theorem to complete locally convex topological vector spaces.
A closed CO2 and temperature-controlled, long-term chamber system has been developed and set up in a typical boreal forest of Scots pine (Pinus sylvestris L.) near the Mekrijärvi Research Station (62°47'N, 30°58'E, 145 m above sea level) belonging to the University of Joensuu, Finland. The main objectives of the experiment were to provide a means of assessing the medium to long-term effects of elevated atmospheric CO2 concentration (EC) and temperature (ET) on photosynthesis, respiration, growth, and biomass at the whole-tree level and to measure instantaneous whole-system CO2 exchange. The system consists of 16 chambers with individual facilities for controlling CO2 concentration, temperature, and the combination of the two. The chambers can provide a wide variety of climatic conditions that are similar to natural regimes. In this experiment the target CO2 concentration in the EC chambers was set at a fixed constant of 700 µmol mol-1 and the target air temperature in the ET chambers to track the ambient temperature but with a specified addition. Chamber performance was assessed on the base of recordings covering three consecutive years. The CO2 and temperature control in these closed chambers was in general accurate and reliable. CO2 concentration in the EC chambers was within 600-725 µmol mol-1 for 90 % of the exposure time during the "growing-season" (15 April - 15 September) and 625-725 µmol mol-1 for 88 % of the time in the "off-season" (16 September - 14 April), while temperatures in the chambers were within ±2.0 °C of the ambient or target temperature in the "growing season" and within ±3.0 °C in the "off season". There were still some significant chamber effects. Solar radiation in the chambers was reduced by 50-60 % for 82 % of the time in the "growing season" and 55-65 % for 78 % of the time in the "off season", and the relative humidity of the air was increased by 5-10 % for 72 % of the time in the "growing season" and 2-12 % for 91 % of the time in the "off season". The crown architecture and main phenophase of the trees were not modified significantly by enclosure in the chambers, but some physiological parameters changed significantly, e.g., the radiant energy-saturated photosynthesis rate, transpiration rate, maximum photochemical efficiency of photosystem 2, and chlorophyll content. and S. Kellomäki, Kai-Yun Wang, M. Lemettinen.
Starvation is the regime of elastohydrodynamic lubrication which is designated with thinner lubrication films than fully flooded regime. Paper summarizes main aspects of starvation and deals with differences in area of experimental investigation of starved lubrication phenomena in comparison with fully flooded regime. Thinner lubrication film creates obstacles in experiment process and data evaluation. Effect that can be neglected in the fully flooded regime can create obstacles. and Obsahuje seznam literatury