State Space

We develop and apply several novel methods quantifying dynamic multi-agent team interactions. These interactions are detected information-theoretically and captured in two ways: via (i) directed networks (interaction diagrams) representing significant coupled dynamics between pairs of agents, and (ii) state-space plots (coherence diagrams) showing coherent structures in Shannon information dynamics. This model-free analysis relates, on the one hand, the information transfer to responsiveness of the agents and the team, and, on the other hand, the information storage within the team to the teamʼs rigidity and lack of tactical flexibility. The resultant interaction and coherence diagrams reveal implicit interactions, across teams, that may be spatially long-range. The analysis was verified with a statistically significant number of experiments (using simulated football games, produced during RoboCup 2D Simulation League matches), identifying the zones of the most intense competition, the extent and types of interactions, and the correlation between the strength of specific interactions and the results of the matches.

This brief shows how a min–max MPC with bounded additive uncertainties and a quadratic cost function results in a piecewise affine and continuous control law. Proofs based on properties of the cost function and the optimization problem are given. The boundaries of the regions in which the state space can be partitioned are also treated. The results are illustrated by an example.

We present a continuous extension of the recent Monte Carlo entropic method for sampling a density of states restricted in dimensionless macroscopic parameters. The method performs a random walk through a two-dimensional macrostate space and provides complete ...

We propose a theory of deterministic chaos for discrete systems, based on their representations in binary state spaces $ \Omega $, homeomorphic to the space of symbolic dynamics. This formalism is applied to neural networks and cellular automata; it is found that such systems cannot be viewed as chaotic when one uses the Hamming distance as the metric for the

In this study, the estimation power of Extended Kalman Filter is tested within a simple Keynesian macroeconomic model. After the model is written in a non-linear state space form, Extended Kalman Filter emerges as the appropriate methodology to estimate both state variables and the parameters. The simulation results suggest that such a methodology can also be employed in explaining more complex macroeconomic dynamics.

Robust calibration of option valuation models to quoted option prices is non-trivial but crucial for good performance. A framework based on the state-space formulation of the option valuation model is introduced. Non-linear (Kalman) filters are needed to do inference since the models have latent variables (e.g. volatility). The statistical framework is made adaptive by introducing stochastic dynamics for the parameters. This allows the parameters to change over time, while treating the measurement noise in a statistically consistent way and using all data efficiently. The performance and computational efficiency of standard and iterated extended Kalman filters (EKF and IEKF) are investigated. These methods are compared to common calibration such as weighted least squares (WLS) and penalized weighted least squares (PWLS). A simulation study, using the Bates model, shows that the adaptive framework is capable of tracking time varying parameters and latent processes such as stochastic ...

An investigation is carried out into the control techniques implemented on a tandem linear direct current machine. The purpose is to control the both motions of the conducting bar such that it moves extremely quickly at the reference velocity of 3.7m/s from the beginning of the rail track to the end of the rail track while bringing itself to a halt at a specific displacement. Standard state variable feedback with pole placement was implemented for controller design to obtain the desired performance specifications and compared with basic linear quadratic control. Simulations conducted revealed that the system dynamics that were set were successfully achieved however there is room for improvement and suggestions for future work is provided. The report concludes that standard pole placement feedback produced better results than linear quadratic control due to the nature of the system.

Nonlinear systems, which are differentially flat, have several properties that can be useful on designing effective controllers. In this paper we show that the n-trailer system equipped with a sliding kingpin mechanism is a differentially flat system, like its non-sliding kingpin counter part. The sliding kingpin technique is used to eliminate the undesired deviation of the path of each intermediate vehicle from that of the leading one (off-tracking phenomenon). The linearizing outputs of the flat system are the Cartesian coordinates of the middle of the last semi-trailer's axle. The state space and the kinematic equations of the new modified system are derived and the conditions for flatness are examined. The flatness conservation is also checked relatively to several kinds of dynamic sliding feedback control.

A semi-analytical analysis for the transient elastodynamic response of an arbitrarily thick simply supported beam due to the action of an arbitrary moving transverse load is presented, based on the linear theory of elasticity. The solution of the problem is derived by means of the powerful state space technique in conjunction with the Laplace transformation with respect to the time coordinate. The inversion of Laplace transform has been carried out numerically using Durbin’s approach based on Fourier series expansion. Special convergence enhancement techniques are invoked to completely eradicate spurious oscillations and obtain uniformly convergent solutions. Detailed numerical results for the transient vibratory responses of concrete beams of selected thickness parameters are obtained and compared for three types of harmonic moving concentrated loads: accelerated, decelerated and uniform. The effects of the load velocity, pulsation frequency and beam aspect ratio on the dynamic response are examined. Also, comparisons are made against solutions based on Euler–Bernoulli and Timoshenko beam models. Limiting cases are considered, and the validity of the model is established by comparison with the solutions available in the existing literature as well as with the aid of a commercial finite element package.