an iterative algorithm for computing mean first passage times of markov chains abstract mean first passage times are an essential ingredient in both the theory and the applications of markov chains in the literature they have been expressed in elegant closed form formulas these formulas involve explicit full matrix inversions and if computed directly may incur numerical instability in this paper we present a new iterative algorithm for computing mean first passage times in a manner that does not rely on explicit full matrix inversions results regarding the convergence behavior of this algorithm are also developed

multidimensional global extremum seeking via the direct optimisation algorithm direct is a sample based global optimisation method for lipschitz continuous functions defined over compact multidimensional domains this paper adapts the direct method with a modified termination criterion for global extremum seeking control of multivariable dynamical plants finite time semi global practical convergence is established based on a periodic sampled data control law whose sampling period is a parameter which determines the region and accuracy of convergence a crucial part of the development is dedicated to a robustness analysis of the direct method against bounded additive perturbations on the objective function extremum seeking involving multiple units is also considered within the same context as a means to increase the speed of convergence numerical examples of global extremum seeking based on direct are presented at the end

bounds for the perron root of nonnegative matrices and spectral radius of iteration matrices abstract new bounds for the perron root a of a nonnegative matrix a are proposed we prove that min 1 i n r i a b r i b a max 1 i n r i a b r i b where b is an arbitrary matrix with row sums r i b k b i k 0 i 1 n the bounds of h minc 1 and shulin liu 6 are both special cases of this result and based on this result we also get some bounds for the spectral radius of iteration matrices

inequalities for permanents involving perron complements abstract let a r n n and let and be nonempty complementary subsets of 1 n of increasing integers for a we define the generalized perron complement of a in a at as the matrix p a a a a i a 1 a for the classes of the nonnegative matrices and of the positive semidefinite matrices we study the relationship between the permanents of the whole matrices and the permanents of their perron complement our conditions which hold in many cases of interest are such that the value of the permanent increases as we pass from the whole matrix to its generalized perron complement for nonnegative and irreducible matrices we also study the relationship between the maximum circuit geometric mean of the entire matrix and the maximum circuit geometric mean of its perron complements

multi agent source seeking via discrete time extremum seeking control recent developments in extremum seeking theory have established a general framework for the methodology although the specific implementations particularly in the context of multi agent systems have not been demonstrated in this work a group of sensor enabled vehicles is used in the context of the extremum seeking problem using both local and global optimisation algorithms to locate the extremum of an unknown scalar field distribution for the former the extremum seeker exploits estimates of gradients of the field from local dithering sensor measurements collected by the mobile agents it is assumed that a distributed coordination which ensures uniform asymptotic stability with respect to a prescribed formation of the agents is employed an inherent advantage of the frameworks is that a broad range of nonlinear programming algorithms can be combined with a wide class of cooperative control laws to perform extreme source seeking semi global practical asymptotically stable convergence to local extrema is established in the presence of field sampling noise subsequently global extremum seeking with multiple agents is investigated and shown to give rise to robust practical convergence whose speed can be improved via computational parallelism nonconvex field distributions with local extrema can be accommodated within this global framework

numerical solution of functional differential integral and integro differential equations this paper describes a numerical method based on lagrange interpolation and chebyshev interpolation to treat functional integral equations of volterra type and fredholm type also the method can be extended to functional differential and integro differential equations various numerical examples are treated

uncoupling the perron eigenvector problem abstract for a nonnegative irreducible matrix a with spectral radius this paper is concerned with the determination of the unique normalized perron vector which satisfies a 62 0 j j 1 it is explained how to uncouple a large matrix a into two or more smaller matrices say p 11 p 22 p kk such that this sequence of smaller matrices has the following properties 1 each p ii is also nonnegative and irreducible so that each pii has a unique perron vector i 2 each pii has the same spectral radius as a 3 it is possible to determine the i s completely independently of each other so that one can execute the computation of the i s parallel 4 it is easy to couple the smaller perron vectors i back together in order to produce the perron vector for the original matrix a

a robust event triggered approach for fast sampled data extremization and learning this paper presents a general framework for the analysis and design of a class of model free robust and efficient sampled data based algorithms for extremization and learning in continuous time nonlinear systems that generate response maps with an optimal operational set in particular we consider plants described by differential inclusions interconnected in a sampled data setting with a robust learning algorithm characterized by a constrained difference inclusion in contrast to standard sampled data based approaches where the learning dynamics are updated after a fixed sufficiently long sampling time has passed we design a robust dynamic event based mechanism that triggers the control action as soon as the rate of change of the output of the plant is sufficiently small by using this event based update rule a significant improvement in the convergence time of the closed loop system can be achieved using the framework of set valued hybrid dynamical systems we establish for the closed loop system the existence of a uniformly asymptotically stable compact set which by an appropriate tuning of the control parameters can be made arbitrarily close to the optimal operational set our results generalize existing results for periodic sampled data extremum seeking and can be used to solve model free multivariable smooth nonsmooth constrained optimization problems as well as learning problems in game theoretical scenarios

some closer bounds of perron root basing on generalized perron complement this paper is concerned with the bounds of the perron root r a of a nonnegative irreducible matrix a two new methods utilizing the relationship between the perron root of a nonnegative irreducible matrix and its generalized perron complements are presented the former method is efficient because it gives the bounds for r a only by calculating the row sums of the generalized perron complement p t a a a or even the row sums of submatrices a a a b a a b and a b a and the latter gives the closest bounds just in this paper of r a the results obtained by these methods largely improve the classical bounds numerical examples are given to illustrate the procedure and compare it with others which shows that these methods are effective

on non local stability properties of extremum seeking control in this paper we consider several extremum seeking schemes and show under appropriate conditions that these schemes achieve extremum seeking from an arbitrarily large domain of initial conditions if the parameters in the controller are appropriately adjusted this non local stability result is proved by showing semi global practical stability of the closed loop system with respect to the design parameters we show that reducing the size of the parameters typically slows down the convergence rate of the extremum seeking controllers and enlarges the domain of the attraction our results provide guidelines on how to tune the controller parameters in order to achieve extremum seeking simulation examples illustrate our results

self triggered best response dynamics for continuous games motivated by the development of novel and practically implementable coordination algorithms for multi agent systems here we investigate the adaptation of classical best response dynamics by means of self triggered communications first we show that if the best response dynamics is defined for a continuous action space potential game convergence towards the nash equilibria set is guaranteed under continuity on utilities and component wise pseudo concavity of the potential function then we modify the best response dynamics to account for more economic self triggered communication strategies while ensuring convergence to the equilibrium set the proposed algorithm is then analyzed in the framework of hybrid systems theory

distributed convex optimization via continuous time coordination algorithms with discrete time communication this paper proposes a novel class of distributed continuous time coordination algorithms to solve network optimization problems whose cost function is a sum of local cost functions associated to the individual agents we establish the exponential convergence of the proposed algorithm under i strongly connected and weight balanced digraph topologies when the local costs are strongly convex with globally lipschitz gradients and ii connected graph topologies when the local costs are strongly convex with locally lipschitz gradients when the local cost functions are convex and the global cost function is strictly convex we establish asymptotic convergence under connected graph topologies we also characterize the algorithm s correctness under time varying interaction topologies and study its privacy preservation properties motivated by practical considerations we analyze the algorithm implementation with discrete time communication we provide an upper bound on the stepsize that guarantees exponential convergence over connected graphs for implementations with periodic communication building on this result we design a provably correct centralized event triggered communication scheme that is free of zeno behavior finally we develop a distributed asynchronous event triggered communication scheme that is also free of zeno with asymptotic convergence guarantees several simulations illustrate our results

unified frameworks for sampled data extremum seeking control global optimisation and multi unit systems two frameworks are proposed for extremum seeking of general nonlinear plants based on a sampled data control law within which a broad class of nonlinear programming methods is accommodated it is established that under some generic assumptions semi global practical convergence to a global extremum can be achieved in the case where the extremum seeking algorithm satisfies a stronger asymptotic stability property the converging sequence is also shown to be stable using a trajectory based proof as opposed to a lyapunov function type approach the former is more straightforward and insightful this allows for more general optimisation algorithms than considered in existing literature such as those which do not admit a state update realisation and or lyapunov functions lying at the heart of the analysis throughout is robustness of the optimisation algorithms to additive perturbations of the objective function multi unit extremum seeking is also investigated with the objective of accelerating the speed of convergence

inverses of perron complements of inverse m matrices the concept of the perron complement of a nonnegative and irreducible matrix was introduced by meyer in 1989 and it was used by him to construct an algorithm for computing the stationary distribution vector for markov chains here we consider properties of the perron complement of an n n matrix k which is an inverse of an irreducible m matrix we first show that the perron complements of k are inverses of m matrices and that the inverses of associated principal submatrices of k are sandwiched between the inverses of the perron complements of k and the inverses of the corresponding schur complements of k we then investigate the directed graph of the inverse of the perron complements of such matrices k

asymptotics of the partition function of a general markov random field on an infinite rectangular lattice abstract we investigate theoretically and numerically the asymptotics of the partition function of a general markov random field mrf on an infinite rectangular lattice we first propose the general local energy function lef parameterized mrf then we prove that the thermodynamic limit of the free energy of the mrf can be exactly characterized by the perron root of the fundamental transfer matrix of a particular markov additive process map this matrix possesses a special structure and many interesting properties that enable parallel computation of the perron root and may be beneficial for deriving an analytical form of the free energy we also develop another transfer matrix for numerical computation of the desired perron root specifically the former is a site to site transfer matrix on a twisted cylindrical lattice while the latter is the one associated with a row to row transition on a vertical strip numerical results show that our methods exhibit consistent finite size scaling behavior even for small values of the lattice width this study reveals that the fundamental transfer matrix is an alternative direction of research on the analysis of the partition function of general mrfs within the scope of matrix algebra

a modified algorithm for the perron root of a nonnegative matrix abstract an algorithm of diagonal transformation for the perron root of nonnegative matrices is proposed by duan and zhang f duan k zhang an algorithm of diagonal transformation for perron root of nonnegative irreducible matrices appl math comput 175 2006 762 772 this method can be used for all nonnegative irreducible matrices in this paper an improved algorithm which is based on this method is proposed the new algorithm inherits all the above mentioned advantages of the original algorithm and has higher efficiency it is testified by numerical testing that the efficiency of the new algorithm is improved greatly

localization of perron roots abstract this paper is concerned with the localization of the perron root of a nonnegative irreducible matrix a a new localization method that utilizes the relationship between the perron root of a nonnegative matrix and the estimates of the row sums of its generalized perron complement is presented the method is efficient because it gives the bounds on a only by computing the estimates of the row sums of the generalized perron complement rather than the generalized perron complement itself several numerical examples are given to illustrate the effectiveness of our method

perron complement and perron root for a nonnegative irreducible matrix a this paper is concerned with the estimation and determination of the unique perron root or spectral radius of a we present a new method that utilizes the relation between perron roots of the nonnegative matrix and its generalized perron complement several numerical examples are given to show that our method is effective at least for some classes of nonnegative matrices

an algorithm of diagonal transformation for perron root of nonnegative irreducible matrices abstract it is always to use diagonal transformation for the estimation of nonnegative matrix s perron root however it is invalid for some matrices or a long distance of bounds generated sometimes so the application of this method is limitation therefore in this paper a condition of a diagonal transformation is researched and a new method is proposed for nonnegative irreducible matrices this method can be used for all nonnegative irreducible matrices and its convergence is proved in theory it is convenient to compute by this method and it is easy to get the precision you wanted it is proved by numerical testing that this method is valid and efficient

a non gradient approach to global extremum seeking an adaptation of the shubert algorithm the main purpose of this paper is to adapt the so called shubert algorithm for extremum seeking control of general dynamic plants this algorithm is a good representative of the sampling optimization methods that achieve global extremum seeking on compact sets in the presence of local extrema the algorithm applies to lipschitz mappings the model of the system is assumed unknown but the knowledge of its lipschitz constant is assumed the controller depends on a design parameter the waiting time and tuning guidelines that relate the design parameter and the region of convergence and accuracy of the algorithm are presented the analysis shows that semi global practical convergence in the initial states to the global extremum can be achieved in presence of local extrema if compact sets of inputs are considered numerical simulations for global optimization in the presence of local extrema are provided to demonstrate the proposed approach

a framework for a class of hybrid extremum seeking controllers with dynamic inclusions abstract this paper presents a prescriptive framework for the design and analysis of a class of deterministic extremum seeking controllers escs based on hybrid dynamic inclusions this type of escs combines continuous and discrete time dynamics during the seeking process and its evolution in time is characterized by differential and difference inclusions rather than standard difference and differential equations examples of hybrid escs include but are not limited to purely continuous esc with optimizers described by set valued mappings esc with arbitrarily fast and slow switching modes esc with weakly jumping parameters as well as distributed escs for multi agent systems with time varying graphs since solutions of systems described by set valued mappings are usually not unique we do not insist on this property but rather we characterize the behavior of all possible solutions generated by the closed loop system making use of recent results in singular perturbations averaging and limit sets of sets for hybrid dynamical systems we establish a practical asymptotic stability result some examples of common classes of seeking dynamics described by hybrid systems are presented as well as some numerical simulations illustrating their application in standard maximization problems and nash seeking problems in game theoretical scenarios

adaptive neural network based event triggered control of single input single output nonlinear discrete time systems this paper presents a novel adaptive neural network nn control of single input and single output uncertain nonlinear discrete time systems under event sampled nn inputs in this control scheme the feedback signals are transmitted and the nn weights are tuned in an aperiodic manner at the event sampled instants after reviewing the nn approximation property with event sampled inputs an adaptive state estimator se consisting of linearly parameterized nns is utilized to approximate the unknown system dynamics in an event sampled context the se is viewed as a model and its approximated dynamics and the state vector during any two events are utilized for the event triggered controller design an adaptive event trigger condition is derived by using both the estimated nn weights and a dead zone operator to determine the event sampling instants this condition both facilitates the nn approximation and reduces the transmission of feedback signals the ultimate boundedness of both the nn weight estimation error and the system state vector is demonstrated through the lyapunov approach as expected during an initial online learning phase events are observed more frequently over time with the convergence of the nn weights the inter event times increase thereby lowering the number of triggered events these claims are illustrated through the simulation results

the lower and upper bounds on perron root of nonnegative irreducible matrices let a be an nxn nonnegative irreducible matrix let a a be the principal submatrix of a based on the nonempty ordered subset a of 1 2 n and define the generalized perron complement of a a by p t a a a i e p t a a a a b a b a ti a a 1a a b t r a a this paper gives the upper and lower bounds on the perron root of a an upper bound on perron root is derived from the maximum of the given parameter t 0 and the maximum of the row sums of p t 0 a a a synchronously a lower bound on perron root is expressed by the minimum of the given parameter t 0 and the minimum of the row sums of p t 0 a a a it is also shown how to choose the parameter t after a to get tighter upper and lower bounds of r a several numerical examples are presented to show that our method compared with the methods in l z lu m k ng locations of perron roots linear algebra appl 392 2004 103 117 is more effective