A New Method to Find the Forced Response of Nonlinear Systems with Dry Friction

Coulomb friction has an influence on the behavior of numerous mechanical systems. Coulomb friction systems or dry friction systems are nonlinear in nature. This nonlinear behavior requires complex and time demanding analysis tools to capture the dynamics of these systems. Recently, efforts have been made to develop efficient analysis tools able to approximate the forced response of systems with dry friction. The objective of this paper is to introduce a methodology that assists in these efforts. In this method, the piecewise-linear nonlinear response is separated into individual linear responses that are coupled together through compatibility constraint equations. The new method is demonstrated on a number of systems of varying complexity. The results obtained by the new method are validated through the comparison with results obtained by time integration. The computational savings of the new method is also discussed.

Synchronous distributed model predictive control for state-coupled systems

In this paper, we study distributed model predictive control (MPC) for the constrained system composed of a set of dynamically coupled subsystems. The proposed approach is based on the synchronous framework, so in each sub-controller, assumed state trajectories of its neighbours are involved, which are constructed by the optimal solutions at the previous sampling time. The compatibility constraint is imposed to bound the uncertain deviation between the assumed predictive trajectory and the true one. In addition, we use the constraint tightening technique in the predicted future evolutions to counteract this uncertain deviation which appears in the dynamics of each subsystem, so that physical constraints of the state and input are satisfied at each sampling time. By applying the proposed distributed MPC approach, the recursive feasibility and asymptotic stability of the overall system are guaranteed. An example is provided to verify the effectiveness and advantage of the result.

AN EVALUATION OF CONSTITUTIONAL CONSTRAINTS ON CAPITAL TAXATION

This paper investigates the desirability of constitutional constraints on capital taxation in an environment without government debt and where benevolent governments have limited commitment. In our setup, governments can choose proportional capital and labor income taxes subject to the constitutional constraint but cannot commit to an actual path of taxes. First, we explore a form of constitutional constraint: a constant cap on capital tax rates. In our quantitative exercise, we show that a three percent cap on capital taxes provides the highest welfare at the worst sustainable equilibrium. However, such a cap decreases welfare at the best sustainable equilibrium (both because it constrains feasibility and because it tightens the incentive compatibility constraint). Second, we identify a form of constitutional constraint that can improve all sustainable equilibria. That constraint features a cap on capital taxes that increases with the level of capital.

Validating Analysis on Influence of Vehicle Structure in Considering Crash Compatibility

With the finite elements analysis and topological optimization algorithm, the head structure of four-wheel independent drive pure electric vehicle is regarded as optimization objective. The vehicle’s head structure is optimized by LS-DYNA and LS-TASC on the condition that whether considering the compatibility constraint. The mass fraction curve, the mass distribution convergence curve and optimization results are used to analyze the influence of vehicle structure when considering crash compatibility, and verify that good crash compatibility means homogeneous geometric structure and homogeneous impact force in contact surface.

WEALTH INEQUALITY AND OPTIMAL MONETARY POLICY

We study the money-in-the-utility-function model in which agents are heterogeneous in their initial wealth. We show that the Friedman rule is not optimal even if the government uses nonlinear income taxation for redistribution. A positive nominal interest rate raises social welfare because it relaxes the incentive compatibility constraint for highly endowed agents. Although the setup is close to that of da Costa and Werning [Journal of Political Economy (2008) 116, 82–112], who investigate skill heterogeneity, the role of the nominal interest rate in this paper here differs from the one in their model.