stable adaptive control for a class of nonlinear systems using a modified lyapunov function investigates the adaptive control design for a class of nonlinear systems using lyapunov s stability theory the proposed method is developed based on a novel lyapunov function which removes the possible controller singularity problem in some of the existing adaptive control schemes using feedback linearization techniques the resulting closed loop system is proven to be globally stable and the output tracking error converges to an adjustable neighborhood of zero

arctic boundaries of the ice model on three bundle domains in this paper we consider the six vertex model at ice point on an arbitrary three bundle domain which is a generalization of the domain wall ice model on the square or equivalently of a uniformly random alternating sign matrix we show that this model exhibits the arctic boundary phenomenon whose boundary is given by a union of explicit algebraic curves this was originally predicted by colomo and sportiello j stat phys 164 1488 1523 2016 as one of the initial applications of a general heuristic that they introduced for locating arctic boundaries called the geometric tangent method our proof uses a probabilistic analysis of non crossing directed path ensembles to provide a mathematical justification of their tangent method heuristic in this case which might be of independent interest

decentralized control design for large scale systems with strong interconnections using neural networks we propose a decentralized neural network nn controller for a class of large scale nonlinear systems with the strong interconnections the nns are used to approximate the unknown subsystems and interconnections due to the functional approximation capabilities of nns the additional precautions are not required to be made for avoiding the possible control singularity problems semiglobal asymptotic stability results are obtained and the tracking error converges to zero furthermore the issue of transient performance of the subsystems is also addressed under an analytical framework

the arctic curve of the domain wall six vertex model the problem of the form of the arctic curve of the six vertex model with domain wall boundary conditions in its disordered regime is addressed it is well known that in the scaling limit the model exhibits phase separation with regions of order and disorder sharply separated by a smooth curve called the arctic curve to find this curve we study a multiple integral representation for the emptiness formation probability a correlation function devised to detect spatial transition from order to disorder we conjecture that the arctic curve for arbitrary choice of the vertex weights can be characterized by the condition of condensation of almost all roots of the corresponding saddle point equations at the same known value in explicit calculations we restrict to the disordered regime for which we have been able to compute the scaling limit of certain generating function entering the saddle point equations the arctic curve is obtained in parametric form and appears to be a non algebraic curve in general it turns into an algebraic one in the so called root of unity cases the arctic curve is also discussed in application to the limit shape of q enumerated with 0 q 4 large alternating sign matrices in particular as q 0 the limit shape tends to a nontrivial limiting curve given by a relatively simple equation

adaptive neural pd control with semiglobal asymptotic stabilization guarantee this paper proves that adaptive neural plus proportional derivative pd control can lead to semiglobal asymptotic stabilization rather than uniform ultimate boundedness for a class of uncertain affine nonlinear systems an integral lyapunov function based ideal control law is introduced to avoid the control singularity problem a variable gain pd control term without the knowledge of plant bounds is presented to semiglobally stabilize the closed loop system based on a linearly parameterized raised cosine radial basis function neural network a key property of optimal approximation is exploited to facilitate stability analysis it is proved that the closed loop system achieves semiglobal asymptotic stability by the appropriate choice of control parameters compared with previous adaptive approximation based semiglobal or asymptotic stabilization approaches our approach not only significantly simplifies control design but also relaxes constraint conditions on the plant two illustrative examples have been provided to verify the theoretical results

binomial determinants paths and hook length formulae abstract we give a combinatorial interpretation for any minor or binomial determinant of the matrix of binomial coefficients this interpretation involves configurations of nonintersecting paths and is related to young tableaux and hook length formulae

stable adaptive control using fuzzy systems and neural networks stable direct and indirect adaptive controllers are presented which use takagi sugeno fuzzy systems conventional fuzzy systems or a class of neural networks to provide asymptotic tracking of a reference signal for a class of continuous time nonlinear plants with poorly understood dynamics the indirect adaptive scheme allows for the inclusion of a priori knowledge about the plant dynamics in terms of exact mathematical equations or linguistics while the direct adaptive scheme allows for the incorporation of such a priori knowledge in specifying the controller we prove that with or without such knowledge both adaptive schemes can learn how to control the plant provide for bounded internal signals and achieve asymptotically stable tracking of a reference input in addition for the direct adaptive scheme a technique is presented in which linguistic knowledge of the inverse dynamics of the plant may be used to accelerate adaptation the performance of the indirect and direct adaptive schemes is demonstrated through the longitudinal control of an automobile within an automated lane

dimers and amoebae we study random surfaces which arise as height functions of random perfect matchings a k a dimer configurations on a weighted bipartite doubly periodic graph g embedded in the plane we derive explicit formulas for the surface tension and local gibbs measure probabilities of these models the answers involve a certain plane algebraic curve which is the spectral curve of the kasteleyn operator of the graph for example the surface tension is the legendre dual of the ronkin function of the spectral curve the amoeba of the spectral curve represents the phase diagram of the dimer model further we prove that the spectral curve of a dimer model is always a real curve of special type namely it is a harnack curve this implies many qualitative and quantitative statement about the behavior of the dimer model such as existence of smooth phases decay rate of correlations growth rate of height function fluctuations etc

an improvement on stable adaptive control for a class of nonlinear systems in the work of zhang et al an excellent neural network controller is provided by introducing a modified lyapunov function to eliminate the singularity issue completely in this note we focus on the improvement on the work of zhang et al for a class of unknown nonlinear systems

feedback linearization using neural networks abstract for a class of single input single output continuous time nonlinear systems a multilayer neural network based controller that feedback linearizes the system is presented control action is used to achieve tracking performance for a state feedback linearizable but unknown nonlinear system the control structure consists of a feedback linearization portion provided by two neural networks plus a robustifying portion that keeps the control magniture bounded a stability proof is given in the sense of lyapunov it is shown that all the signals in the closed loop system are uniformly ultimately bounded no off line learning phase is needed initialization of the network weights is straightforward

adaptive tracking control for stochastic uncertain non linear systems satisfying short and long term cost criteria the tracking control problem for a class of stochastic and uncertain non linear systems is addressed the proposed controller uses suitable radial basis function neural network designs for the approximation of the unknown non linearities while it is arbitrarily regulated in order to effectively penalize the tracking error this regulation is implemented through a risk sensitivity parameter a stability analysis based on lyapunov functions obtained by the backstepping technique proves that all the error variables are bounded in probability simultaneously for any given risk sensitivity parameter the system performance is regulated with respect to both a desired small average tracking error and low long term average cost in accordance to a risk sensitive cost criterion moreover the larger this parameter is the mean square tracking error becomes semiglobally uniformly ultimately bounded in a smaller area while a lower level of a long term average cost is achieved the effectiveness of the design approac

arctic curves in path models from the tangent method recently colomo and sportiello introduced a powerful method known as the tangent method for computing the arctic curve in statistical models which have a non or weakly intersecting lattice path formulation we apply the tangent method to compute arctic curves in various models the domino tiling of the aztec diamond for which we recover the celebrated arctic circle a model of dyck paths equivalent to the rhombus tiling of a half hexagon for which we find an arctic half ellipse another rhombus tiling model with an arctic parabola the vertically symmetric alternating sign matrices where we find the same arctic curve as for unconstrained alternating sign matrices the latter case involves lattice paths that are non intersecting but that are allowed to have osculating contact points for which the tangent method was argued to still apply for each problem we estimate the large size asymptotics of a certain one point function using lu decomposition of the corresponding gessel viennot matrices and a reformulation of the result amenable to asymptotic analysis

arctic curves of the six vertex model on generic domains the tangent method we revisit the problem of determining the arctic curve in the six vertex model with domain wall boundary conditions we describe an alternative method by which we recover the previously conjectured analytic expression in the square domain we adapt the method to work for a large class of domains and for other models exhibiting limit shape phenomena we study in detail some examples and derive in particular the arctic curve of the six vertex model in a triangoloid domain at the ice point

gaussian networks for direct adaptive control a direct adaptive tracking control architecture is proposed and evaluated for a class of continuous time nonlinear dynamic systems for which an explicit linear parameterization of the uncertainty in the dynamics is either unknown or impossible the architecture uses a network of gaussian radial basis functions to adaptively compensate for the plant nonlinearities under mild assumptions about the degree of smoothness exhibit by the nonlinear functions the algorithm is proven to be globally stable with tracking errors converging to a neighborhood of zero a constructive procedure is detailed which directly translates the assumed smoothness properties of the nonlinearities involved into a specification of the network required to represent the plant to a chosen degree of accuracy a stable weight adjustment mechanism is determined using lyapunov theory the network construction and performance of the resulting controller are illustrated through simulations with example systems

limit shapes and the complex burgers equation in this paper we study surfaces in r 3 that arise as limit shapes in random surface models related to planar dimers these limit shapes are surface tension minimizers that is they minimize a functional of the form h dx dy among all lipschitz functions h taking given values on the boundary of the domain the surface tension has singularities and is not strictly convex which leads to formation of facets and edges in the limit shapes we find a change of variables that reduces the euler lagrange equation for the variational problem to the complex inviscid burgers equation complex hopf equation the equation can thus be solved in terms of an arbitrary holomorphic function which is somewhat similar in spirit to weierstrass parametrization of minimal surfaces we further show that for a natural dense set of boundary conditions the holomorphic function in question is in fact algebraic the tools of algebraic geometry can thus be brought in to study the minimizers and especially the formation of their singularities this is illustrated by several explicitly computed examples

preference elicitation from inconsistent judgments using multi objective optimization abstract several decision making techniques involve pairwise comparisons to elicit the preferences of a decision maker dm this paper proposes a new approach for prioritization from pairwise comparisons using the concept of indirect judgments no method exists that simultaneously minimizes deviations from both direct and indirect judgments in order to estimate preferences it is sensible to consider both the acquired judgments and the other judgments latent in the dm s mind hence a technique is developed here to minimize the deviations from both types of judgments estimated preferences are generally evaluated based on two criteria their deviation from the provided judgments and the number of judgments that have been ordinally violated here it is proposed to optimize three objectives simultaneously the deviations from both direct and indirect judgments and the number of judgments violated a prototype application has been developed to generate all non dominated solutions using a multiple objective evolutionary algorithm the new approach is shown to offer users greater flexibility than all other tested methods

the arctic curve for aztec rectangles with defects via the tangent method the tangent method of colomo and sportiello is applied to the study of the asymptotics of domino tilings of large aztec rectangles with some fixed distribution of defects along a boundary the associated non intersecting lattice path configurations are made of schroder paths whose weights involve two parameters gamma and q keeping track respectively of one particular type of step and of the area below the paths we predict the arctic curve for an arbitrary distribution of defects and illustrate our result with a number of examples involving different classes of boundary defects

a neural network based approximation method for discrete time nonlinear servomechanism problem a feedback controller that solves the discrete time nonlinear servomechanism problem relies on the solution of a set of nonlinear functional equations known as the discrete regulator equations the exact solution of the discrete regulator equations is usually unavailable due to the nonlinearity of the system the paper proposes to approximately solve the discrete regulator equations using a feedforward neural network this approach leads to an effective way to practically solve the discrete nonlinear servomechanism problem the approach has been illustrated using the well known inverted pendulum on a cart system the simulation shows that the control law designed by the proposed approach performs much better than the conventional linear control law

planar dimers and harnack curves in this article we study the connection between dimers and harnack curves discovered in 15 we prove that every harnack curve arises as a spectral curve of some dimer model we also prove that the space of harnack curves of given degree is homeomorphic to a closed octant and that the areas of the amoeba holes and the distances between the amoeba tentacles give these global coordinates we characterize harnack curves of genus zero as spectral curves of isoradial dimers and also as minimizers of the volume under their ronkin function with given boundary conditions

a tangent method derivation of the arctic curve for q weighted paths with arbitrary starting points we use a tangent method approach to obtain the arctic curve in a model of non intersecting lattice paths within the first quadrant including a q dependent weight associated with the area delimited by the paths our model is characterized by an arbitrary sequence of starting points along the positive horizontal axis whose distribution involves an arbitrary piecewise differentiable function we give an explicit expression for the arctic curve in terms of this arbitrary function and of the parameter q a particular emphasis is put on the deformation of the arctic curve upon varying q and on its limiting shapes when q tends to 0 or infinity our analytic results are illustrated by a number of detailed examples

projection based adaptive neurocontrol with switching logic deadzone tuning in this brief an adaptive neural network nn controller is proposed for multiple input multiple output mimo nonlinear systems with triangular control structure and unknown control directions deadzones are employed in the projection based nn weight learning laws and the nussbaum parameter update laws with levels tuned by an innovative switching logic tuning mechanism detailed analysis using a family of lyapunov like integral functions and the function approximation capability of nns proves that all the tracking errors are semiglobal uniform ultimate bounded in small neighborhoods of the origin while the closed loop system variables state vector nn weights nussbaum parameters and the control law remain bounded a simulation study confirms the theoretical results and verifies the effectiveness of the proposed design