Simulated Annealing: Rigorous finite-time guarantees for optimization on continuous domains

Simulated annealing is a popular method for approaching the solution of a global optimization problem. Existing results on its performance apply to discrete combinatorial optimization where the optimization variables can assume only a finite set of possible values. We introduce a new general formulation of simulated annealing which allows one to guarantee finite-time performance in the optimization of functions of continuous variables. The results hold universally for any optimization problem on a bounded domain and establish a connection between simulated annealing and up-to-date theory of convergence of Markov chain Monte Carlo methods on continuous domains. This work is inspired by the concept of finite-time learning with known accuracy and confidence developed in statistical learning theory.

Robust finite-time consensus tracking algorithm for multirobot systems

This paper studies the finite-time consensus tracking control for multirobot systems. We prove that finite-time consensus tracking of multiagent systems can be achieved on the terminal sliding-mode surface. Also, we show that the proposed error function can be modified to achieve relative state deviation between agents. These results are then applied to the finite-time consensus tracking control of multirobot systems with input disturbances. Simulation results are presented to validate the analysis.

Observer-based robust finite-time cooperative consensus control for multi-agent networks

This paper studies the finite-time consensus tracking control for multi-agent networks. The time-varying control input and the velocity of the leader is unknown to any follower. Only the position of the leader is known to its neighbors. We first propose a new finite-time multiple-surface sliding mode observer to estimate the leader's velocity. It is seen that the estimation error of the observer can converge to zero in a finite time. Then, we prove that finite-time consensus tracking of multi-agent networks can be achieved on a new terminal sliding mode surface. Simulation results are presented to validate the analysis.

Robust finite-time tracking control of nonholonomic mobile robots without velocity measurements

The problem of robust finite-time trajectory tracking of nonholonomic mobile robots with unmeasurable velocities is studied. The contributions of the paper are that: first, in the case that the angular velocity of the mobile robot is unmeasurable, a composite controller including the observer-based partial state feedback control and the disturbance feed-forward compensation is designed, which guarantees that the tracking errors converge to zero in finite time. Second, if the linear velocity as well as the angular velocity of mobile robot is unmeasurable, with a stronger constraint, the finite-time trajectory tracking control of nonholonomic mobile robot is also addressed. Finally, the effectiveness of the proposed control laws is demonstrated by simulation.

Collateral, default penalties and almost finite-time solvency

We argue that it is possible to adapt the approach of imposing restrictions on available plans through finitely effective debt constraints, introduced by Levine and Zame (1996), to encompass models with default and collateral. Along this line, we introduce in the setting of Araujo, Páscoa and Torres-Martínez (2002) and Páscoa and Seghir (2008) the concept of almost finite-time solvency. We show that the conditions imposed in these two papers to rule out Ponzi schemes implicitly restrict actions to be almost finite-time solvent. We define the notion of equilibrium with almost finite-time solvency and look on sufficient conditions for its existence. Assuming a mild assumption on default penalties, namely that agents are myopic with respect to default penalties, we prove that existence is guaranteed (and Ponzi schemes are ruled out) when actions are restricted to be almost finite-time solvent. The proof is very simple and intuitive. In particular, the main existence results in Araujo et al. (2002) and Páscoa and Seghir (2008) are simple corollaries of our existence result.

UNIFORMLY ACCELERATED FINITE-TIME DETECTORS

The behavior of uniformly accelerated detectors in the Minkowski and Rindler vacua is analyzed when the detector is coupled to a scalar field during a finite amount of time T. We point out that the logarithmic ultraviolet divergences reported in the literature are due to the instantaneous switching of the detector. We explicitly show this by considering a detector switched on and off continuously. The usual Planckian spectrum for the excitation probability is recovered in the limit T --> infinity.

Local dimension and finite time prediction in spatiotemporal chaotic systems

Predictability is related to the uncertainty in the outcome of future events during the evolution of the state of a system. The cluster weighted modeling (CWM) is interpreted as a tool to detect such an uncertainty and used it in spatially distributed systems. As such, the simple prediction algorithm in conjunction with the CWM forms a powerful set of methods to relate predictability and dimension.

Local dimension and finite time prediction in coupled map lattices

Forecasting, for obvious reasons, often become the most important goal to be achieved. For spatially extended systems (e.g. atmospheric system) where the local nonlinearities lead to the most unpredictable chaotic evolution, it is highly desirable to have a simple diagnostic tool to identify regions of predictable behaviour. In this paper, we discuss the use of the bred vector (BV) dimension, a recently introduced statistics, to identify the regimes where a finite time forecast is feasible. Using the tools from dynamical systems theory and Bayesian modelling, we show the finite time predictability in two-dimensional coupled map lattices in the regions of low BV dimension. © Indian Academy of Sciences.

Finite time blow-up and breaking of solitary wind waves

The evolution of surface water waves in finite depth under wind forcing is reduced to an antidissipative Korteweg-de Vries-Burgers equation. We exhibit its solitary wave solution. Antidissipation accelerates and increases the amplitude of the solitary wave and leads to blow-up and breaking. Blow-up occurs in finite time for infinitely large asymptotic space so it is a nonlinear, dispersive, and antidissipative equivalent of the linear instability which occurs for infinite time. Due to antidissipation two given arbitrary and adjacent planes of constant phases of the solitary wave acquire different velocities and accelerations inducing breaking. Soliton breaking occurs in finite space in a time prior to the blow-up. We show that the theoretical growth in amplitude and the time of breaking are both testable in an existing experimental facility.