The authors consider the control of an underactuated mechanical system: Pendubot, which has four separated equilibrium points. A unified controller is proposed to stabilise the system at the four equilibrium points. Moreover, the proposed unified control can bring the underactuated link to ideal homoclinic orbits, which cannot be achieved by existing approaches. Simulation results verify the ef...

Linearization of nonholonomic systems at equilibrium positions has been plagued from the very beginning by mistakes and misunderstandings. Bottema [3] corrected Whittaker’s originary procedure [8]; and Naimark and Fufaev [7] developed Bottema’s idea, deriving a scheme which is the currently accepted one. Something nagging however remains about the derivation of the characteristic equation for a...

This paper considers the problem of dynamic traffic assignment under the principle that individual drivers will choose fastest paths, in the dynamic situation where path durations consist of time-dependent link travel times. Rather than constructing a unified model encompassing traffic dynamics and route choice, we decompose the model into an assignment mapping, which identifies the link travel...

blished the final version of a bold exercise in population projection: several scenarios of the future of every country in the world to 2300 [1]. According to the study, the world population will continue to grow rapidly until 2075, reaching a historic high of 9.2 billion, compared with 6.4 billion now, and then gradually stabilize at around 9 billion. But this is only the central scenario, bas...

This paper studies the relations between the local minima of a cost function f and the stable equilibria of the gradient descent flow of f . In particular, it is shown that, under the assumption that f is real analytic, local minimality is necessary and sufficient for stability. Under the weaker assumption that f is indefinitely continuously differentiable, local minimality is neither necessary...

The paper concerns the study of equilibrium points, namely the stationary solutions to the closed loop equation, of an infinite dimensional and infinite horizon boundary control problem for linear partial differential equations. Sufficient conditions for existence of equilibrium points in the general case are given and later applied to the economic problem of optimal investment with vintage cap...

In this paper, a new iterative scheme by hybrid method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of an infinite family of relatively quasi-nonexpansive mappings and set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved. Our results extend important recent ...

Preventive diagnostics and maintenance of complex dynamic systems such as chemical plants and aircraft engines benefit from knowledge of the system components. The conditions of the components are often represented by the parameters of the system, in which case the current conditions of the components can be deduced from the variations of the system parameters about their nominal values. This p...

Certain studies of the acid-base equilibrium in disease were reported from this clinic a year ago (1). The method employed was in brief the determination of the carbon dioxide dissociation (or absorption) curve, and the carbon dioxide content of the patient’s arterial and venous blood, and from these data the construction of the carbon dioxide diagram of Haggard and Henderson (2). The method wa...

Some very crude estimate on the maximal number of points of equilibrium is obtained in [GNSh] using Khovanskii’s fewnomial theory, see [Kh]. Conjecture 1 is not even settled for 3 positive point charges in which case all points of equilibrium lie in the plane spanned by these charges. (Some special cases of 3 charges are settled in the recent literature, see [Ki],[Pe],[Wa].) Observe that for ch...