Sliding-mode neuro-controller for uncertain systems

In this paper, a method that allows for the merger of the good features of sliding-mode control and neural network (NN) design is presented. Design is performed by applying an NN to minimize the cost function that is selected to depend on the distance from the sliding-mode manifold, thus providing that the NN controller enforces sliding-mode motion in a closed-loop system. It has been proven that the selected cost function has no local minima in controller parameter space, so under certain conditions, selection of the NN weights guarantees that the global minimum is reached, and then the sliding-mode conditions are satisfied; thus, closed-loop motion is robust against parameter changes and disturbances. For controller design, the system states and the nominal value of the control input matrix are used. The design for both multiple-input-multiple-output and single-input-single-output systems is discussed. Due to the structure of the (M)ADALINE network used in control calculation, the proposed algorithm can also be interpreted as a sliding-mode-based control parameter adaptation scheme. The controller performance is verified by experimental results

Almost-Smooth Histograms and Sliding-Window Graph Algorithms

We study algorithms for the sliding-window model, an important variant of the data-stream model, in which the goal is to compute some function of a fixed-length suffix of the stream. We extend the smooth-histogram framework of Braverman and Ostrovsky (FOCS 2007) to almost-smooth functions, which includes all subadditive functions. Specifically, we show that if a subadditive function can be $(1+\epsilon)$-approximated in the insertion-only streaming model, then it can be $(2+\epsilon)$-approximated also in the sliding-window model with space complexity larger by factor $O(\epsilon^{-1}\log w)$, where $w$ is the window size. We demonstrate how our framework yields new approximation algorithms with relatively little effort for a variety of problems that do not admit the smooth-histogram technique. For example, in the frequency-vector model, a symmetric norm is subadditive and thus we obtain a sliding-window $(2+\epsilon)$-approximation algorithm for it. Another example is for streaming matrices, where we derive a new sliding-window $(\sqrt{2}+\epsilon)$-approximation algorithm for Schatten $4$-norm. We then consider graph streams and show that many graph problems are subadditive, including maximum submodular matching, minimum vertex-cover, and maximum $k$-cover, thereby deriving sliding-window $O(1)$-approximation algorithms for them almost for free (using known insertion-only algorithms). Finally, we design for every $d\in (1,2]$ an artificial function, based on the maximum-matching size, whose almost-smoothness parameter is exactly $d$

General contact mechanics theory for randomly rough surfaces with application to rubber friction

We generalize the Persson contact mechanics and rubber friction theory to the case where both surfaces have surface roughness. The solids can be rigid, elastic or viscoelastic, and can be homogeneous or layered. We calculate the contact area, the viscoelastic contribution to the friction force, and the average interfacial separation as a function of the sliding speed and the nominal contact pressure. We illustrate the theory with numerical results for a rubber block sliding on a road surface. We find that with increasing sliding speed, the influence of the roughness on the rubber block decreases, and for typical sliding speeds involved in tire dynamics it can be neglected

Microscale friction reduction by normal force modulation in MEMS.

Friction in MEMS-scale devices is troublesome because it can result in lateral stiction of two sliding surfaces. We have investigated the effect of modulation of the normal force on the friction between two sliding MEMS surfaces, using a fully MEMS-based tribometer. We have found that the friction is reduced significantly when the modulation is large enough. A simple model is presented that describes the friction reduction as a function of modulation frequency as well. Using this technique, lateral stiction-related seizure of microscopic sliding components can be mitigated

Friction of a slider on a granular layer: Non-monotonic thickness dependence and effect of boundary conditions

We investigate the effective friction encountered by a mass sliding on a granular layer as a function of bed thickness and boundary roughness conditions. The observed friction has minima for a small number of layers before it increases and saturates to a value which depends on the roughness of the sliding surface. We use an index-matched interstitial liquid to probe the internal motion of the grains with fluorescence imaging in a regime where the liquid has no significant effect on the measured friction. The shear profiles obtained as a function of depth show decrease in slip near the sliding surface as the layer thickness is increased. We propose that the friction depends on the degree of grain confinement relative to the sliding surfaces.Comment: 4 pages, 6 figure

Non-monotonicity of the frictional bimaterial effect

Sliding along frictional interfaces separating dissimilar elastic materials is qualitatively different from sliding along interfaces separating identical materials due to the existence of an elastodynamic coupling between interfacial slip and normal stress perturbations in the former case. This bimaterial coupling has important implications for the dynamics of frictional interfaces, including their stability and rupture propagation along them. We show that while this bimaterial coupling is a monotonically increasing function of the bimaterial contrast, when it is coupled to interfacial shear stress perturbations through a friction law, various physical quantities exhibit a non-monotonic dependence on the bimaterial contrast. In particular, we show that for a regularized Coulomb friction, the maximal growth rate of unstable interfacial perturbations of homogeneous sliding is a non-monotonic function of the bimaterial contrast, and provide analytic insight into the origin of this non-monotonicity. We further show that for velocity-strengthening rate-and-state friction, the maximal growth rate of unstable interfacial perturbations of homogeneous sliding is also a non-monotonic function of the bimaterial contrast. Results from simulations of dynamic rupture along a bimaterial interface with slip-weakening friction provide evidence that the theoretically predicted non-monotonicity persists in non-steady, transient frictional dynamics.Comment: 14 pages, 5 figure

Optimal sliding mode controllers for attitude tracking of spacecraft

This paper studies two optimal sliding mode control laws using integral sliding mode control (ISM) for some spacecraft attitude tracking problems. Integral sliding mode control combining the first order sliding mode and optimal control is applied to quaternion-based spacecraft attitude tracking manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state dependent Riccati equation (SDRE) and Control Lyapunov function (CLF) approaches are used to solve the infinite-time nonlinear optimal problem. The second method of Lyapunov is used to show that tracking is achieved globally. An example of multiaxial attitude tracking manoeuvres is presented and simulation results are included to verify the usefulness of these controllers

Quasi-continuous higher-order sliding mode controller designs for spacecraft attitude tracking manoeuvres

This paper studies high-order sliding mode control laws to deal with some spacecraft attitude tracking problems. Second and third order quasi-continuous sliding control are applied to quaternion-based spacecraft attitude tracking manoeuvres. A class of linear sliding manifolds is selected as a function of angular velocities and quaternion errors. The second method of Lyapunov theory is used to show that tracking is achieved globally. An example of multiaxial attitude tracking manoeuvres is presented and simulation results are included to verify and compare the usefulness of the various controllers