RNS derivation of N-point disk amplitudes from the revisited S-matrix approach

In the past year, in arXiv:1208.6066 we proposed a revisited S-matrix approach to efficiently find the bosonic terms of the open superstring low energy effective lagrangian (OSLEEL). This approach allows to compute the ${\alpha'}^N$ terms of the OSLEEL using open superstring $n$-point amplitudes in which $n$ is very much lower than $(N+2)$ (which is the order of the required amplitude to obtain those ${\alpha'}^N$ terms by means of the conventional S-matrix approach). In this work we use our revisited S-matrix approach to examine the structure of the scattering amplitudes, arriving at a closed form for them. This is a RNS derivation of the formula first found by Mafra, Schlotterer and Stieberger in arXiv:1106.2645, using the Pure Spinor formalism. We have succeeded doing this for the 5, 6 and 7-point amplitudes. In order to achieve these results we have done a careful analysis of the kinematical structure of the amplitudes, finding as a by-product a purely kinematical derivation of the BCJ relations (for N=4, 5, 6 and 7). Also, following the spirit of the revisited S-matrix approach, we have found the $\alpha'$ expansions for these amplitudes up to ${\alpha'}^6$ order in some cases, by only using the well known open superstring 4-point amplitude, cyclic symmetry and tree level unitarity: we have not needed to compute any numerical series or any integral involving polylogarithms, at any moment.Comment: 77 pages, 3 figure

Reset control systems: the zero-crossing resetting law

A novel representation of reset control systems with a zero-crossing resetting law, in the framework of hybrid inclusions, is postulated. The well-posedness and stability issues of the resulting hybrid dynamical system are investigated, with a strong focus on how non-deterministic behavior is implemented in control practice. Several stability conditions have been developed by using the eigenstructure of matrices related to the periods of the reset interval sequences and by using Lyapunov function-based conditions

A practical approach to adaptive sliding mode control

This paper is concerned with the development of a practical approach to the design of adaptive sliding mode controllers. The objective is to define an adaptive control law that presents some desired advantages such as non overestimation of the disturbance input, cancellation of the chattering phenomenon, zero overshooting response, avoid control saturation and simplicity of algorithm tuning. In this practical approach a solution is provided that uses both, adaptive sliding surfaces and adaptive control gains so the proposed controller is able to manage input disturbances with bounded derivatives.Agencia Estatal de Investigación | Ref. DPI2017-84259-C2-2-RMinisterio de Economía y Competitividad | Ref. PTQ-14-07366Ministerio de Economía y Competitividad | Ref. DPI2016-79278-C2-2-

Structural Identifiability Analysis via Extended Observability and Decomposition

7 páginasStructural identifiability analysis of nonlinear dynamic models requires symbolic manipulations, whose computational cost rises very fast with problem size. This hampers the application of these techniques to the large models which are increasingly common in systems biology. Here we present a method to assess parametric identifiability based on the framework of nonlinear observability. Essentially, our method considers model parameters as particular cases of state variables with zero dynamics, and evaluates structural identifiability by calculating the rank of a generalized observability-identifiability matrix. If a model is unidentifiable as a whole, the method determines the identifiability of its individual parameters. For models whose size or complexity prevents the direct application of this procedure, an optimization approach is used to decompose them into tractable subsystems. We demonstrate the feasibility of this approach by applying it to three well-known case studiesPeer reviewe

Reset observers alleviating the peaking and the robustness tradeoffs: A case study on force estimation in teleoperation

The peaking phenomenon is an undesirable effect appearing in observers and destroying controller performance. Several solutions have been proposed to mitigate peaking in state estimation. The literature shows that reset or impulsive observers are superior to linear (Luenberger) observers. However, the comparisons are based on particular choices of linear observers. This paper investigates this issue. First, comparative frameworks are proposed based on two traded-off performance indices: ensemble maximum-peak versus ensemble settling time for nominal conditions, and ensemble settling time versus size of the error asymptotic invariant set for quadratically bounded uncertain plants. Next, performance limitations of linear observers are represented by Pareto-optimal boundaries. In this way, not previously considered in the literature as far as known, the superiority of the chosen reset observer is more rigorously assessed. The framework is finally applied to force estimation in haptic teleoperation.Ministerio de Economía y Competitividad | Ref. DPI2016-79278-C2-2-