Spherical robots (SRs) have the characteristics of nonholonomic constraints, underactuation, nonchain, and strong coupling, which increase the difficulty of modeling and motion control compared with traditional robots. In this study, we develop an adaptive motion control scheme for a nonholonomic SR, in which an omnidirectional dynamic model is carried out by using the Euler–Lagrange method to describe the omnidirectional motion of the SR more accurately. Furthermore, to facilitate the design of the motion controller, the dynamic model is simplified to obtain the state space expression of the SR. Aiming at the problem of poor control effect caused by the change of system model parameters which are influenced by dynamic model reduction, an adaptive motion control law of SR is designed based on MRAC. And the coefficient adjustment of the controller is obtained by the Lyapunov method, with the guaranteed stability of the closed-loop system. Finally, the controller designed in this thesis is compared with four controllers including linear quadratic regulator, Fuzzy PID, PSO-ADRC, and hierarchical SMC. The experimental comparison proves that the control scheme proposed in this study still has good control ability when the motion parameters are disturbed.

Hunter–gatherer occupations of small islands are rare in world prehistory and it is widely accepted that island settlement is facilitated by agriculture. The Ryukyu Islands contradict that understanding on two counts: not only did they have a long history of hunter–gatherer settlement, but they also have a very late date for the onset of agriculture, which only reached the archipelago between the eighth and thirteenth centuries AD. Here, we combine archaeology and linguistics to propose a tripartite model for the spread of agriculture and Ryukyuan languages to the Ryukyu Islands. Employing demographic growth, trade/piracy and the political influence of neighbouring states, this model provides a synthetic yet flexible understanding of farming/language dispersals in the Ryukyus within the complex historical background of medieval East Asia.

State spaces are, in the most general sense, sets of entities that contain information. Examples include states of dynamical systems, processes of observations, or possible worlds. We use domain theory to describe the structure of positive and negative information in state spaces. We present examples ranging from the space of trajectories of a dynamical system, over Dunn’s aboutness interpretation of fde, to the space of open sets of a spectral space. We show that these information structures induce so-called hype models which were recently developed by Leitgeb (2019). Conversely, we prove a representation theorem: roughly, hype models can be represented as induced by an information structure. Thus, the well-behaved logic hype is a sound and complete logic for reasoning about information in state spaces.

As application of this framework, we investigate information fusion. We motivate two kinds of fusion. We define a groundedness and a separation property that allow a hype model to be closed under the two kinds of fusion. This involves a Dedekind–MacNeille completion and a fiber-space like construction. The proof-techniques come from pointless topology and universal algebra.

This paper presents a new testing method for the scapegoat model of exchange rates. A number of steps are implemented to determine whether macro-fundamentals are scapegoats for the evolution of exchange rates. Estimation is conducted using a Bayesian Gibbs sampling approach applied to eight countries (five developed and three emerging) versus the USA over the period 2002Q1–2014Q4. The macro-fundamentals that we consider are real GDP growth, the inflation rate, the long-run nominal interest rate, and the current account to GDP ratio. We calculate the posterior probabilities that these macro-fundamentals are scapegoats. For the inflation rate, these probabilities are considerably higher than the imposed prior probabilities of ½ in five out of eight countries (in particular, the Anglo-Saxon economies).

We present an exact analysis of axisymmetric bending of circular plates according to elasticity theory. On the basis of Hamiltonian state space approach, a rigorous solution of the problem is determined by means of separation of variables and symplectic eigenfunction expansion in a systematic way. The thickness effect on bending of circular plates and the applicability of the classical plate solutions for the problem are evaluated accordingly.

We present a general solution approach for analysis of transversely isotropic cylindrical tubes and circular plates. On the basis of Hamiltonian state space formalism in a systematic way, rigorous solutions of the twisting problems are determined by means of separation of variables and symplectic eigenfunction expansion.

We present an exact analysis of the displacement and stress fields in an elastic 2-D cantilever subjected to axial force, shear force and moment, in which the end conditions are exactly satisfied. The problem is formulated on the basis of the state space formalism for 2-D deformation of an orthotropic body. Upon delineating the Hamiltonian characteristics of the formulation and by using eigenfunction expansion, a rigorous solution which satisfies the end conditions is determined. The results show that the end condition alters the stress significantly only near the end, and elementary solutions in the form of polynomials can give sufficiently accurate results except near the ends. Such a system would give rise to localized stresses and displacements in the immediate neighborhood of the ends, and the effect may be expected to diminish with distance on account of geometrical divergence.

Analysis of deformation and stress field in a circular elastic cylinder under the extension is presented, with emphasis on the end effect. The problem is formulated on the basis of the state space formalism for axisymmetric deformation of transversely isotropic materials. A rigorous solution that satisfies the prescribed end conditions is determined by using symplectic eigenfunction expansion, thereby, the applicability of the Saint-Venant solution is examined. The results show that the end effect is significant but confined to a local region near the base of the cylinder where the end plane is perfectly bonded or subjected to a concentrated load. As the axial stiffness increases, the end effect on the stress state increases at the loaded end but decreases at the bonded end. The displacement and stress distributions across the section are uniform throughout the length of the cylinder except near the ends.

This paper compares the different dynamics of the simple-sum monetary aggregates and the Divisia monetary aggregate indices over time, over the business cycle, and across high and low inflation and interest-rate phases. Although traditional comparisons of the series sometimes suggest that simple-sum and Divisia monetary aggregates share similar dynamics, there are important differences around turning points that cannot be evaluated by their average behavior. We use a factor model with a regime-switching model that separates the common movements underlying the monetary aggregate indices from idiosyncratic variations in each series. We find that the major differences between the simple-sum aggregates and Divisia indices occur around the beginnings and ends of recessions and during some high-interest-rate phases. We note the inferences' policy relevance, which is particularly dramatic at the broadest (M3) level of aggregation. Indeed, as Belongia [Journal of Political Economy, 104 (5) (1996), 1065–1083] has observed in this regard, “measurement matters.”

Design space exploration is a long-standing focus in computational design research. Its three main threads are accounts of designer action, development of strategies for amplification of designer action in exploration, and discovery of computational structures to support exploration. Chief among such structures is the design space, which is the network structure of related designs that are visited in an exploration process. There is relatively little research on design spaces to date. This paper sketches a partial account of the structure of both design spaces and research to develop them. It focuses largely on the implications of designers acting as explorers.

A state space approach to heat conduction in a cylindrically anisotropic circular tube of functionally graded materials (FGM) is presented. A power-law type of the radial inhomogeneity for the FGM is considered. By means of eigenfunction expansion and matrix algebra, analytic solutions for transient and steady-state heat conduction in the FGM tube under general thermal boundary conditions are derived.

Regression analysis with stationary errors is extended to the case when observations are not equally spaced. The errors are modelled as either a discrete-time ARMA process with missing observations, or as a continuous-time autoregression with observational error observed at arbitrary times. Using a state-space representation, a Kalman filter is used to calculate the exact likelihood. The linear regression coefficients are separated out of the likelihood so non-linear optimization is required only with respect to the parameters modelling the error structure.