The adjustment-stabilization method for constrained systems

For constrained system which has several independent first integrals, we give a new stabilization method which named adjustment-stabilization method. It can stabilize all known constants of motion for a given dynamical system very well instead of the stabilization and post-stabilization methods which only conserves one of all first integrals. Further more, new method can improve numerical accuracy too. We also point out the post-stabilization is just a simplest case of the new method.Comment: 6 pages, 5 figure

Imprecise dynamic walking with time-projection control

We present a new walking foot-placement controller based on 3LP, a 3D model of bipedal walking that is composed of three pendulums to simulate falling, swing and torso dynamics. Taking advantage of linear equations and closed-form solutions of the 3LP model, our proposed controller projects intermediate states of the biped back to the beginning of the phase for which a discrete LQR controller is designed. After the projection, a proper control policy is generated by this LQR controller and used at the intermediate time. This control paradigm reacts to disturbances immediately and includes rules to account for swing dynamics and leg-retraction. We apply it to a simulated Atlas robot in position-control, always commanded to perform in-place walking. The stance hip joint in our robot keeps the torso upright to let the robot naturally fall, and the swing hip joint tracks the desired footstep location. Combined with simple Center of Pressure (CoP) damping rules in the low-level controller, our foot-placement enables the robot to recover from strong pushes and produce periodic walking gaits when subject to persistent sources of disturbance, externally or internally. These gaits are imprecise, i.e., emergent from asymmetry sources rather than precisely imposing a desired velocity to the robot. Also in extreme conditions, restricting linearity assumptions of the 3LP model are often violated, but the system remains robust in our simulations. An extensive analysis of closed-loop eigenvalues, viable regions and sensitivity to push timings further demonstrate the strengths of our simple controller

Pole Assignment With Improved Control Performance by Means of Periodic Feedback

This technical note is concerned with the pole placement of continuous-time linear time-invariant (LTI) systems by means of LQ suboptimal periodic feedback. It is well-known that there exist infinitely many generalized sampled-data hold functions (GSHF) for any controllable LTI system to place the modes of its discrete-time equivalent model at prescribed locations. Among all such GSHFs, this technical note aims to find the one which also minimizes a given LQ performance index. To this end, the GSHF being sought is written as the sum of a particular GSHF and a homogeneous one. The particular GSHF can be readily obtained using the conventional pole-placement techniques. The homogeneous GSHF, on the other hand, is expressed as a linear combination of a finite number of functions such as polynomials, sinusoidals, etc. The problem of finding the optimal coefficients of this linear combination is then formulated as a linear matrix inequality (LMI) optimization. The procedure is illustrated by a numerical example

Automatic Stabilizers and Economic Crisis: US vs. Europe

This paper analyzes the effectiveness of the tax and transfer systems in the European Union and the US to act as an automatic stabilizer in the current economic crisis. We find that automatic stabilizers absorb 38 per cent of a proportional income shock in the EU, compared to 32 per cent in the US. In the case of an unemployment shock 48 per cent of the shock are absorbed in the EU, compared to 34 per cent in the US. This cushioning of disposable income leads to a demand stabilization of 26 to 35 per cent in the EU and 19 per cent in the US. There is large heterogeneity within the EU. Automatic stabilizers in Eastern and Southern Europe are much lower than in Central and Northern European countries. We also investigate whether countries with weak automatic stabilizers have enacted larger fiscal stimulus programs. We find no evidence supporting this view. However, we find that active fiscal policy is lower in more open economies.automatic stabilization, crisis, liquidity constraints, fiscal stimulus

Adaptive ℋ∞-control for nonlinear systems: a dissipation theoretical approach

The adaptive ℋ∞-control problem for parameter-dependent nonlinear systems with full information feedback is considered. The techniques from dissipation theory as well as the vector and parameter projection methods are used to derive the adaptive ℋ∞-control laws. Both of the projection techniques are rigorously treated. The adaptive robust stabilization for nonlinear systems with ℒ2-gain hounded uncertainties is investigated

Automatic Stabilizers and Economic Crisis: US vs. Europe

This paper analyzes the effectiveness of social protection systems in Europe and the US to provide (income) insurance against macro level shocks in terms of automatic stabilizers. We find that automatic stabilizers absorb 38% of a proportional income shock and 47% of an idiosyncratic unemployment shock in Europe, compared to 32% and 34% in the US. There is large heterogeneity within Europe with stabilization being much lower in Eastern and Southern than in Central and Northern Europe. Our results suggest that social transfers, in particular the rather generous systems of unemployment insurance in Europe, play a key role for the stabilization of disposable incomes and explain a large part of the difference in automatic stabilizers between Europe and the US.Automatic Stabilization, Crisis, Liquidity Constraints, Fiscal Stimulus

Automatic Stabilizers and Economic Crisis: US vs. Europe

This paper analyzes the effectiveness of the tax and transfer systems in the European Union and the US to act as an automatic stabilizer in the current economic crisis. We find that automatic stabilizers absorb 38 per cent of a proportional income shock in the EU, compared to 32 per cent in the US. In the case of an unemployment shock 47 percent of the shock are absorbed in the EU, compared to 34 per cent in the US. This cushioning of disposable income leads to a demand stabilization of up to 30 per cent in the EU and up to 20 per cent in the US. There is large heterogeneity within the EU. Automatic stabilizers in Eastern and Southern Europe are much lower than in Central and Northern European countries. We also investigate whether countries with weak automatic stabilizers have enacted larger fiscal stimulus programs. We find no evidence supporting this view.