In previous publications I have suggested that opposite thermodynamic arrows of time could coexist in our universe. This letter responds to the comments of H. D. Zeh (previous letter in this journal). In 2002 a conference took place in Bielefeld, entitled, " The direction of time: The role of reversibil-ity/irreversibility in the study of nature " [1]. In my presentation I spoke about recent wo...

Optimal control problems for possibly discontinuous entropy solutions of nonlinear multidimensional conservation laws with controls in source term and initial condition are considered. The control-to-state-mapping is analyzed by using monotone diierence schemes and existence results for optimal controls are proven. Moreover, a result on the convergence of optimal solutions of nite dimensional a...

The paper analyzes the impact of the initial condition on the problem of testing for unit roots. To this end, we derive a family of optimal tests that maximize a weighted average power criterion with respect to the initial condition. We then investigate the relationship of this optimal family to popular tests. We find that many unit root tests are closely related to specific members of the opti...

Abstract: This paper considers the problem of the stability for a control system with a state-dependent delay. Systems with state-dependent delays arise naturally in the data network congestion control schemes. Simple analytical studies of stability are provided for a particular set of initial conditions. Then, to verify these results and to extend the stability analysis, the Simulink-based sim...

In this paper we study simultaneous external and internal stabilization of linear system under input saturation and non-input additive sustained disturbances. For systems that are asymptotic null controllable with bounded control, it is shown that a nonlinear dynamic feedback controller can be designed so that the closed-loop states remain bounded for any initial condition and for two classes o...

The requirement of a uniformly bounded convergence time for all initial conditions is important for modern control theory. In particular the requirement appears in design of hybrid or switched systems. It can happen in such systems that a dynamic system repeatedly changes its configuration, and the configuration only lasts for some bounded time with its lower estimation known in advance. The na...

First order partial differential equations (PDE) are often the main tool to model problems in optimal control, differential games, image processing, physics, etc. Dependent upon the particular application, the boundary conditions are specified either at the initial time instant, leading to an initial value problem (IVP), or at the terminal time instant, leading to a terminal value problem (TVP)...

This technical report contains some additional calculations supplementing Example 6 in the paper Normcontrollability of nonlinear systems by M. A. Müller, D. Liberzon, and F. Allgöwer, IEEE Transactions on Automatic Control, 2015. References and labels in this technical report (in particular Equation labels (1)–(59) and all theorem numbers etc.) refer to those in that paper. In the following, c...

A general approach is presented for the robust stabilization of controllable systems. The proposed strategy is viable whenever one can compute a finite-time control law that steers the state from any initial condition to a point closer to the desired equilibrium. Under suitable hypotheses, such control law can be applied in an iterative fashion, obtaining exponential convergence of the state to...

Targeting control of chaos is concerned with taking advantage of sensitive dependence to initial conditions to coax a dynamical system to following a desirable trajectory. In other words, it is taking advantage of the butterfly effect so that the rich spectrum of possible trajectories embedded within a chaotic attractor can be selected with extremely small energy input. We review historical and...