adaptive predefined performance control for mimo systems with unknown direction via generalized fuzzy hyperbolic model an adaptive predefined performance control problem is investigated for a class of multiple input multiple output systems with unknown control direction and unknown backlash like hysteresis nonlinearities by using generalized fuzzy hyperbolic model gfhm compared with the existing methods the main features are as follows the prediction error is introduced to construct the adaptive laws which means that the approximate accuracy of the gfhm is solved the nussbaum type gain is utilized to deal with the unknown control direction which avoids the requirement of direction a priori and by transforming the tracking errors into new error variables the prescribed steady state and transient performance can be ensured it is shown that the proposed control approach can guarantee that all the signals of the resulting closed loop systems are bounded and the output tracks a desired trajectory while the tracking errors are confined all times within the prescribed bounds finally two simulation results and some comparisons are provided to verify the effectiveness of the proposed approach since the proposed control strategy is only implemented in a healthy case how to extend the strategy to a faulty case will be a further topic

robust mean field linear quadratic gaussian games with unknown l 2 disturbance this paper considers a class of mean field linear quadratic gaussian games with model uncertainty the drift term in the dynamics of the agents contains a common unknown function we take a robust

optimal control of mean field jump diffusion systems with delay this paper is concerned with an optimal control problem under mean field jump diffusion systems with delay firstly some existence and uniqueness results are proved for a jump diffusion mean field stochastic delay differential equation and a jump diffusion mean field advanced backward stochastic differential equation then necessary and sufficient maximum principles for control systems of mean field type and with delay are established under certain conditions a mean field delayed linear quadratic control problem is finally discussed using the obtained maximum principles

approximations of two dimensional mean field games with nonsymmetric controls abstract the numerical methods are presented for solving economic problems formulated in the mean field game mfg form the mean field equilibrium is a solution of the coupled system of two parabolic partial differential equations the fokker planck kolmogorov equation and the hamilton jacobi bellman one the description focuses on the discrete approximation of these equations and on the application of the mfg theory directly at discrete level this approach results in an efficient algorithm for finding the corresponding grid control functions contrary to other difference schemes here the semi lagrangian approximation is applied which improves properties of a discrete problem of this type this implies the fast convergence of an iterative algorithm for the minimization of the cost functional the constructed algorithms are implemented to the problem of carbon dioxide pollution

brief paper stochastic maximum principle in the mean field controls in buckdahn djehiche li and peng 2009 the authors obtained mean field backward stochastic differential equations bsdes in a natural way as a limit of some highly dimensional system of forward and backward sdes corresponding to a great number of particles or agents the objective of the present paper is to deepen the investigation of such mean field bsdes by studying their stochastic maximum principle this paper studies the stochastic maximum principle smp for mean field controls which is different from the classical ones this paper deduces an smp in integral form and it also gets under additional assumptions necessary conditions as well as sufficient conditions for the optimality of a control as an application this paper studies a linear quadratic stochastic control problem of mean field type

nash social and centralized solutions to consensus problems via mean field control theory the purpose of this paper is to synthesize initial mean consensus behavior of a set of agents from the fundamental optimization principles of i stochastic dynamic games and ii optimal control in the stochastic dynamic game model each agent seeks to minimize its individual quadratic discounted cost function involving the mean of the states of all other agents in this formulation we derive the limiting infinite population mean field equation system and explicitly compute its unique solution the resulting mean field mf control strategies drive each agent to track the overall population s initial state distribution mean and by applying these decentralized strategies any finite population system reaches mean consensus asymptotically as time goes to infinity furthermore these control laws possess an en nash equilibrium property where en goes to zero as the population size n goes to infinity finally the analysis is extended to the case of random mean field couplings in the social cooperative formulation the basic objective is to minimize a social cost as the sum of the individual cost functions containing mean field coupling in this formulation we show that for any individual agent the decentralized mean field social mf social control strategy is the same as the mean field nash mf nash equilibrium strategy hence mf nash controls unashn mf social controls usocn on the other hand the solution to the centralized lqr optimal control formulation yields the standard consensus sc algorithm whenever the graph representing the corresponding topology of the network is completely connected cc hence cent lqr controls ucentn sc cc controls uscn moreover a system with centralized control laws reaches consensus on the initial state distribution mean as time and population size n go to infinity hence asymptotically in time mf nash controls unashn mf social controls usocn cent lqr controls ucent sc cc controls usc finally the analysis is extended to the long time average lta cost functions case

a general approach for obtaining joint representations in signal analysis i characteristic function operator method a general approach for obtaining joint representations for arbitrary physical quantities is presented the characteristic function operator method of moyal 1949 and ville 1960 and generalized by cohen 1966 1976 and scully and cohen 1987 for the time frequency case is developed for arbitrary variables

brief paper maximum principle for the stochastic optimal control problem with delay and application in this paper we consider an optimal control problem for the stochastic system described by stochastic differential equations with delay we obtain the maximum principle for the optimal control of this problem by virtue of the duality method and the anticipated backward stochastic differential equations our results can be applied to a production and consumption choice problem the explicit optimal consumption rate is obtained

adaptive control for uncertain continuous time systems using implicit inversion of prandtl ishlinskii hysteresis representation in this note an implicit inversion approach is introduced to avoid difficulties associated with stability analysis in the direct application of inversion for operator based hysteresis models based on this implicit inversion an adaptive control algorithm is formulated for continuous time linear dynamical systems preceded with hysteresis nonlinearities described by the prandtl ishlinskii model a stability analysis of the controlled system is performed to show that zero output tracking error can be achieved simulation results show the effectiveness of the proposed algorithm

globally stable adaptive backstepping fuzzy control for output feedback systems with unknown high frequency gain sign this paper addresses the problem of globally stable adaptive backstepping output feedback tracking control for a class of nonlinear systems with unknown high frequency gain sign the fuzzy systems are used as feedforward compensators to model some system functions depending on the reference signal thus the global stability of closed loop system can be guaranteed under the assumption that the unknown system functions are bounded by partly known nonlinear functions the other advantage of the proposed control scheme is that the designer can determine the approximation domain a priori via the bound of the reference signal which is very important for the choice of the centers and widths of membership functions moreover the nussbaum type function is employed to deal with the unknown high frequency gain sign two simulation examples are provided to illustrate the feasibility of control scheme presented in this paper

wellposedness of mean field games with common noise under a weak monotonicity condition in this paper we consider mean field games in the presence of common noise relaxing the usual independence assumption of individual random noise we assume a simple linear model with terminal cost satisfying a convexity and a weak monotonicity property our main result is showing existence and uniqueness of a mean field game solution using the stochastic maximum principle the uniqueness is a result of a monotonicity property similar to that of lasry and lions we use the banach fixed point theorem to establish an existence over a small time duration and show that it can be extended over an arbitrary finite time duration

on the linear quadratic gaussian nash game with one step delay observation sharing pattern this paper studies a two player nash dynamic discrete time linear quadratic game under the so called one step delay observation sharing pattern it is shown that under very weak assumptions the solution exists and is unique and linear in the information

maximum principle for mean field jump diffusion stochastic delay differential equations and its application to finance abstract this paper investigates a stochastic optimal control problem with delay and of mean field type where the controlled state process is governed by a mean field jump diffusion stochastic delay differential equation two sufficient maximum principles and one necessary maximum principle are established for the underlying system as an application a bicriteria mean variance portfolio selection problem with delay is studied to demonstrate the effectiveness and potential of the proposed techniques under certain conditions explicit expressions are provided for the efficient portfolio and the efficient frontier which are as elegant as those in the classical mean variance problem without delays

mean field lqg control in leader follower stochastic multi agent systems likelihood ratio based adaptation we study large population leader follower stochastic multi agent systems where the agents have linear stochastic dynamics and are coupled via their quadratic cost functions the cost of each leader is based on a trade off between moving toward a certain reference trajectory which is unknown to the followers and staying near their own centroid on the other hand followers react by tracking a convex combination of their own centroid and the centroid of the leaders we approach this large population dynamic game problem by use of so called mean field mf linear quadratic gaussian lqg stochastic control theory in this model followers are adaptive in the sense that they use a likelihood ratio estimator on a sample population of the leaders trajectories to identify the member of a given finite class of models which is generating the reference trajectory of the leaders under appropriate conditions it is shown that the true reference trajectory model is identified by each follower in finite time with probability one as the leaders population goes to infinity furthermore we show that the resulting sets of mean field control laws for both leaders and adaptive followers possess an almost sure en nash equilibrium property for a system with population n where en goes to zero as n goes to infinity numerical experiments are presented illustrating the results

linear quadratic n person and mean field games with ergodic cost we consider stochastic differential games with n players linear gaussian dynamics in arbitrary state space dimension and long time average cost with quadratic running cost admissible controls

linear quadratic mean field games with a major player the multi scale approach this paper considers linear quadratic lq mean field games with a major player and analyzes an asymptotic solvability problem it starts with a large scale system of coupled dynamic programming equations and applies a re scaling technique introduced in huang and zhou 2018 and huang and zhou 2020 to derive a set of riccati equations in lower dimensions the solvability of which determines the necessary and sufficient condition for asymptotic solvability we next derive the mean field limit of the strategies and the value functions finally we show that the two decentralized strategies can be interpreted as the best responses of a major player and a representative minor player embedded in an infinite population which have the property of consistent mean field approximations

a high resolution time frequency representation for musical instrument signals analyzing musical signals to obtain the time varying magnitudes and frequencies of instruments partial frequency components is important for resynthesis transcription and instrument physics windowing techniques including fourier series extensions short time fourier transforms and constant q transforms generate bias in time and frequency dictated by the uncertainty principle this is significant to analysis requirements of such properties as attack which involve changes over millisecond time ranges and require frequency accuracy on the order of cents alternatives such as the wigner distribution avoid the uncertainty principle restriction and associated bias but nonlinear cross products of magnitude and frequency computations are not smoothed as with windowing methods increasing those sources of bias all these techniques belong to cohen s class a framework where this paper develops the modal distribution exhibiting decreased total bias computation of the modal distribution and a constant q v

large population lqg games involving a major player the nash certainty equivalence principle we consider linear quadratic gaussian lqg games with a major player and a large number of minor players the major player has a significant influence on others the minor players individually have negligible impact but they collectively contribute mean field coupling terms in the individual dynamics and costs to overcome the dimensionality difficulty and obtain decentralized strategies the so called nash certainty equivalence methodology is applied the control synthesis is preceded by a state space augmentation via a set of aggregate quantities giving the mean field approximation subsequently within the population limit the lqg game is decomposed into a family of limiting two player games as each is locally seen by a representative minor player next when solving these limiting two player games we impose certain interaction consistency conditions such that the aggregate quantities initially assumed coincide with the ones replicated by the closed loop of a large number of minor players this procedure leads to a set of decentralized strategies for the original lqg game which is an varepsilon nash equilibrium

a class of interference induced games we consider a multi agent system with linear stochastic individual dynamics and individual linear quadratic ergodic cost functions the agents partially observe their own states their cost functions and initial statistics are a priori independent but they are coupled through an interference term the mean of all agent states entering each of their individual measurement equations while in general for a finite number of agents the resulting optimal control law may be a non linear function of the available observations we establish that for certain classes of cost and dynamic parameters optimal separated control laws obtained by ignoring the interference coupling are asymptotically optimal when the number of agents goes to infinity thus forming for finite n an nash equilibrium more generally though optimal separated control laws may not be asymptotically optimal and can in fact result in unstable overall behavior thus we consider a class of parameterized decentralized control laws whereby the separated kalman gain is treated as the arbitrary gain of a luenberger like observer system stability regions are characterized and the nature of optimal cooperative control policies within the considered class is explored numerical results and an application example for wireless communications are reported

mean field linear quadratic gaussian lqg games for stochastic integral systems in this technical note we formulate and investigate a class of mean field linear quadratic gaussian lqg games for stochastic integral systems unlike other literature on mean field games where the individual states follow the controlled stochastic differential equations sdes the individual states in our large population system are characterized by a class of stochastic volterra type integral equations we obtain the nash certainty equivalence nce equation and hence derive the set of associated decentralized strategies the epsilon nash equilibrium properties are also verified due to the intrinsic integral structure the techniques and estimates applied here are significantly different from those existing results in mean field lqg games for stochastic differential systems for example some fredholm equation in the mean field setup is introduced for the first time as for applications two types of stochastic delayed systems are formulated as the special cases of our stochastic integral system and relevant mean field lqg games are discussed

decentralized tracking type games for multi agent systems with coupled arx models asymptotic nash equilibria a class of decentralized tracking type games is considered for large population multi agent systems mas the agents are described by stochastic discrete time auto regressive models with exogenous inputs arx models and coupled together through their individual dynamics and performance indexes by terms of the unknown population state average psa the performance index of each agent to minimize is a stochastic long term averaged group tracking type functional in which there is a nonlinear term of the unknown psa the control law is decentralized and implemented via the nash certainty equivalence principle by probability limit theory under mild conditions it is shown that a the estimate of the psa is strongly consistent b the closed loop system is stable almost surely and the stability is independent of the number n of agents c the decentralized control law is an asymptotic nash equilibrium almost surely or in probability according to the property of the nonlinear coupling function in the performance indexes

mean field stochastic h 2 h control with delay the finite horizon h 2 h control problem of mean field type for delayed stochastic systems is considered in this paper firstly we derive a sufficient mean field generalised stochastic bounded

the uncertainty principle global local or both we address the issue of the relation between local quantities and the uncertainty principle we approach the problem by defining local quantities as conditional standard deviations and we relate these to the uncertainty product appearing in the standard uncertainty principle we show that the uncertainty product for the average local standard deviations is always less than or equal to the standard uncertainty product and that it can be arbitrarily small we apply these results to the short time fourier transform spectrogram to explore the commonly held notion that the uncertainty principle somehow limits local quantities we show that indeed for the spectrogram there is a lower bound on the local uncertainty product of the spectrogram due to the windowing operation of this method this limitation is an inherent property of the spectrogram and is not a property of the signal or a fundamental limit we also examine the local uncertainty product for a large class of time frequency distributions that satisfy the usual uncertainty principle including the wigner distribution the choi williams distribution and many other commonly used distributions we obtain an expression for the local uncertainty product in terms of the signal and show that for these distributions the local uncertainty product is less than that of the spectrogram and can be arbitrarily small extension of our approach to an entropy formulation of the uncertainty principle is also considered

adaptive variable structure control of a class of nonlinear systems with unknown prandtl ishlinskii hysteresis control of nonlinear systems preceded by unknown hysteresis nonlinearities is a challenging task and has received increasing attention in recent years due to growing industrial demands involving varied applications in the literature many mathematical models have been proposed to describe the hysteresis nonlinearities the challenge addressed here is how to fuse those hysteresis models with available robust control techniques to have the basic requirement of stability of the system the purpose of the note is to show such a possibility by using the prandtl ishlinskii pi hysteresis model an adaptive variable structure control approach serving as an illustration is fused with the pi model without necessarily constructing a hysteresis inverse the global stability of the system and tracking a desired trajectory to a certain precision are achieved simulation results attained for a nonlinear system are presented to illustrate and further validate the effectiveness of the proposed approach

discrete time mean field stochastic linear quadratic optimal control problems this paper firstly presents necessary and sufficient conditions for the solvability of discrete time mean field stochastic linear quadratic optimal control problems secondly the optimal control within a class of linear feedback controls is investigated using a matrix dynamical optimization method thirdly by introducing several sequences of bounded linear operators the problem is formulated as an operator stochastic linear quadratic optimal control problem by the kernel range decomposition representation of the expectation operator and its pseudo inverse the optimal control is derived using solutions to two algebraic riccati difference equations finally by completing the square the two riccati equations and the optimal control are also obtained

kernel design for reduced interference distributions the authors present a class of time frequency signal representations tfrs called the reduced interference distribution rid an overview of commonly used tfrs is given and desirable distribution properties are introduced particular attention is paid to the interpretation of cohen s class of time frequency distributions of tfrs in the ambiguity temporal correlation spectral correlation and time frequency domains based on the desirable kernel requirements the rid is discussed and further defined a systematic procedure to create rid kernels or equivalently compute rids is proposed some aspects and properties of the rid are discussed the authors estimate design considerations for rids and compare various selections of the primitive window some experimental results demonstrating the performance of the rid are presented

mean field stochastic linear quadratic optimal control with markov jump parameters abstract this paper considers a class of mean field stochastic linear quadratic optimal control problems with markov jump parameters the new feature of these problems is that means of state and control are incorporated into the systems and the cost functional based on the modes of markov chain the corresponding decomposition technique of augmented state and control is introduced it is shown that under some appropriate conditions there exists a unique optimal control which can be explicitly given via solutions of two generalized difference riccati equations a numerical example sheds light on the theoretical results established

asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity and unknown gain signs two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented we consider two possible input nonlinearities that is backlash like hysteresis and symmetric dead zone which can be simultaneously dealt with by using the proposed compensation controllers the knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required only the boundedness of the reference signal is assumed the nussbaum gain approach is employed to remove the assumption on the control gain sign the first scheme is based on the backstepping technique the final step of the recursive design is crucial for the closed loop stability in the second scheme a direct adaptive control law is designed the controller has a simple structure and only one adaptation parameter is updated in both controllers it is shown that asymptotic tracking is ensured two numerical examples are provided to show the effectiveness of the theor

mean field equations for stochastic firing rate neural fields with delays derivation and noise induced transitions abstract in this manuscript we analyze the collective behavior of mean field limits of large scale spatially extended stochastic neuronal networks with delays rigorously the asymptotic regime of such systems is characterized by a very intricate stochastic delayed integro differential mckean vlasov equation that remain impenetrable leaving the stochastic collective dynamics of such networks poorly understood in order to study these macroscopic dynamics we analyze networks of firing rate neurons i e with linear intrinsic dynamics and sigmoidal interactions in that case we prove that the solution of the mean field equation is gaussian hence characterized by its two first moments and that these two quantities satisfy a set of coupled delayed integro differential equations these equations are similar to usual neural field equations and incorporate noise levels as a parameter allowing analysis of noise induced transitions we identify through bifurcation analysis several qualitative transitions due to noise in the mean field limit in particular stabilization of spatially homogeneous solutions synchronized oscillations bumps chaotic dynamics wave or bump splitting are exhibited and arise from static or dynamic turing hopf bifurcations these surprising phenomena allow further exploring the role of noise in the nervous system

electric load model synthesis by diffusion approximation of a high order hybrid state stochastic system a statistical approach is used to model the dynamics of the electric demand of large aggregates of electric space heaters or air conditioners the importance of such loads is twofold first they account for a significant portion of power system dynamics following a power outage second because they are associated with energy storage they are often selected for load shedding within a load management program the derivation of the aggregate electrical dynamics is considered first for a homogeneous group of devices subsequently a perturbation analysis yields the dynamics for a nonhomogeneous group the homogeneons group aggregrate load model is a system of coupled ordinary and partial differential equations fokker planck equations it is obtained by writing evolution equations for the probability density of a hybrid state markov system used to model the switching dynamics of individual devices this result is new and could give a clue to the analysis of a broad class of hybrid state stochastic systems in turn this could provide a new impetus not only in the area of electric load modeling but other areas such as power system reliability and the design of relay control systems where stochastic hybrid state models occur frequently simulation results which illustrate the dynamical properties of the model are presented

stability analysis of systems with impulse effects the authors establish conditions for the uniform stability and the uniform asymptotic stability of equilibria of systems with impulse effects described by systems of nonlinear time varying ordinary differential equations under mild additional assumptions these sufficient conditions turn out to be necessary as well for the case of time invariant systems with impulse effects described by nonlinear ordinary differential equations the above results are used to establish conditions under which the uniform asymptotic stability of equilibria can be deduced from the linearizations of such systems

hierarchically accelerated dynamic programming for finite state machines a procedure called hierarchically accelerated dynamic programming hadp is presented which at the cost of a degree of suboptimality can significantly accelerate dynamic programming algorithms for discrete event systems modeled by finite state machines fsms the methodology is based upon the possibly iterated dynamical abstraction of a given fsm by state aggregation in order to generate a so called partition machine hierarchy necessary and sufficient conditions for the hadp procedure to generate globally optimal solutions are given as well as bounds on the degree of suboptimality of the method a group of examples called the broken manhattan grid problems is used to illustrate an implementation of hadp with two and three level hierarchies a set of open problems is described concerning the construction and selection of the partition machine abstractions and the improvement of the estimation of hadp suboptimality

linear quadratic mean field stochastic zero sum differential games abstract in this paper we consider the two player linear quadratic mean field stochastic differential game lq mf szsdg where the expected values of state and players control variables are included in the corresponding mean field stochastic system and the objective functional we characterize the explicit condition under which the feedback saddle point equilibrium for the lq mf szsdg exists the results are obtained by using the completion of squares method and the ordered interchangeability property of multiple saddle points we show that the corresponding saddle point equilibrium is linear in state which is characterized by the two coupled riccati differential equations crdes we also discuss the solvability conditions of the crdes numerical results are presented to verify the theoretical results of the paper

asymptotically optimal decentralized control for large population stochastic multiagent systems the interaction of interest coupled decision makers and the uncertainty of individual behavior are prominent characteristics of multiagent systems mas how to break through the framework of conventional control theory which aims at single decision maker and single decision objective and to extend the methodology and tools in the stochastic adaptive control theory to analyze mas are of great significance in this paper a preliminary exploration is made in this direction and the decentralized control problem is considered for large population stochastic mas with coupled cost functions different from the deterministic discounted costs in the existing differential game models a time averaged stochastic cost function is adopted for each agent the decentralized control law is constructed based on the state aggregation method and tracking like quadratic optimal control by using probability limit theory the stability and optimality of the closed loop system are analyzed the main contributions of this paper include the following points 1 the concepts of asymptotic nash equilibrium in probability and almost surely respectively are introduced and the relationship between these concepts is illuminated which provide necessary tools for analyzing the optimality of the decentralized control laws 2 the closed loop system is shown to be almost surely uniformly stable and bounded independently of the number of agents n 3 the population state average psa is shown to converge to the infinite population mean ipm trajectory in the sense of both l2 norm and time average almost surely as n increases to infinity 4 the decentralized control law is designed and shown to be almost surely asymptotically optimal the cost of each agent based on local measurements converges to that based on global measurements almost surely as n increases to infinity

large deviation properties of weakly interacting processes via weak convergence methods we study large deviation properties of systems of weakly interacting particles modeled by ito stochastic differential equations sdes it is known under certain conditions that the corresponding sequence of empirical measures converges as the number of particles tends to infinity to the weak solution of an associated mckean vlasov equation we derive a large deviation principle via the weak convergence approach the proof which avoids discretization arguments is based on a representation theorem weak convergence and ideas from stochastic optimal control the method works under rather mild assumptions and also for models described by sdes not of diffusion type to illustrate this we treat the case of sdes with delay

convex analysis for lqg systems with applications to major minor lqg mean field game systems abstract we develop a convex analysis approach for solving lqg optimal control problems and apply it to major minor mm lqg mean field game mfg systems the approach retrieves the best response strategies for the major agent and all minor agents that attain an nash equilibrium an important and distinctive advantage to this approach is that unlike the classical approach in the literature we are able to avoid imposing assumptions on the evolution of the mean field in particular this provides a tool for dealing with complex and non standard systems

decentralized adaptive stabilization in the presence of unknown backlash like hysteresis due to the difficulty of handling both hysteresis and interactions between subsystems there is still no result available on decentralized stabilization of unknown interconnected systems with hysteresis even though the problem is practical and important in this paper we provide solutions to this challenging problem by proposing two new schemes to design decentralized output feedback adaptive controllers using backstepping approach for each subsystem a general transfer function with arbitrary relative degree is considered the interactions between subsystems are allowed to satisfy a nonlinear bound with certain structural conditions in the first scheme no knowledge is assumed on the bounds of unknown system parameters in case that the uncertain parameters are inside known compact sets we propose an alternative scheme where a projection operation is employed in the adaptive laws in both schemes the effects of the hysteresis and the effects due to interactions are taken into consideration in devising local control laws it is shown that the designed local adaptive controllers can ensure all the signals in the closed loop system bounded a root mean square type of bound is obtained for the system states as a function of design parameters this implies that the transient system performance can be adjusted by choosing suitable design parameters with scheme ii the proposed control laws allow arbitrarily strong interactions provided their upper bounds are available in the absence of hysteresis perfect stabilization is ensured and the l 2 norm of the system states is also shown to be bounded by a function of design parameters when the second scheme is applied

the use of cone shaped kernels for generalized time frequency representations of nonstationary signals generalized time frequency representations gtfrs which use cone shaped kernels for nonstationary signal analysis are presented the cone shaped kernels are formulated for the gtfrs to produce good resolution simultaneously in time and frequency specifically for a gtfr with a cone shaped kernel finite time support is maintained in the time dimension along with an enhanced spectrum in the frequency dimension and the cross terms are smoothed out experimental results on simulated data and real speech show the advantages of the gtfrs with the cone shaped kernels through comparisons to the spectrogram and the pseudo wigner distribution

social optima in mean field lqg control centralized and decentralized strategies we study a class of linear quadratic gaussian lqg control problems with n decision makers where the basic objective is to minimize a social cost as the sum of n individual costs containing mean field coupling the exact socially optimal solution determining a particular pareto optimum requires centralized information for each agent and has high implementational complexity as an alternative we subsequently exploit a mean field structure in the centralized optimal control problem to develop decentralized cooperative optimization so that each agent only uses its own state and a function which may be computed offline the resulting set of strategies asymptotically achieves the social optimum as n a key feature in this scheme is to let each agent optimize a new cost as the sum of its own cost and another component capturing its social impact on all other agents we also discuss the relationship between the decentralized cooperative solution and the so called nash certainty equivalence based solution presented in previous work on mean field lqg games

mean field backward stochastic differential equations a limit approach mathematical mean field approaches play an important role in different fields of physics and chemistry but have found in recent works also their application in economics finance and game theory the objective of our paper is to investigate a special mean field problem in a purely stochastic approach for the solution y z of a mean field backward stochastic differential equation driven by a forward stochastic differential of mckean vlasov type with solution x we study a special approximation by the solution x n y n z n of some decoupled forward backward equation which coefficients are governed by n independent copies of x n y n z n we show that the convergence speed of this approximation is of order 1 root n moreover our special choice of the approximation allows to characterize the limit behavior of root n x n x y n y z n z we prove that this triplet converges in law to the solution of some forward backward stochastic differential equation of mean field type which is not only governed by a brownian motion but also by an independent gaussian field

response of dynamical systems to nonstationary inputs we obtain the time frequency response of the output of a dynamical system when the input belongs to a class of common nonstationary signals namely an impulse a linear chirp a causal sinusoid and a short duration sinusoid the obtained results clarify how the system processes the time varying frequencies of the input signal to generate the time frequency spectrum of the output all analytic results are exact the solution is obtained by developing a method which can be used to evaluate the output of a dynamical system for complex combinations of nonstationary inputs we show numerical examples which prove that the response of a system to a nonstationary input is made by a series of events occurring in the joint time frequency domain

robust adaptive control of a class of nonlinear systems with unknown backlash like hysteresis deals with adaptive control of a class of nonlinear dynamic systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is modeled by a differential equation by exploiting solution properties of the differential equation and combining those properties with adaptive control techniques a robust adaptive control algorithm is developed without constructing a hysteresis inverse the new control law ensures global stability of the adaptive system and achieves both stabilization and tracking to within a desired precision simulations performed on a nonlinear system illustrate and clarify the approach

improved time frequency representation of multicomponent signals using exponential kernels the authors introduce a time frequency distribution of l cohen s 1966 class and examines its properties this distribution is called exponential distribution ed after its exponential kernel function first the authors interpret the ed from the spectral density estimation point of view they then show how the exponential kernel controls the cross terms as represented in the generalized ambiguity function domain and they analyze the ed for two specific types of multicomponent signals sinusoidal signals and chirp signals next they define the ed for discrete time signals and the running windowed exponential distribution rwed which is computationally efficient finally the authors present numerical examples of the rwed using the synthetically generated signals it is found that the ed is very effective in diminishing the effects of cross terms while retaining most of the properties which are useful for a time frequency distribution

adaptive dynamic surface control for mimo nonlinear time varying systems with prescribed tracking performance in this paper an adaptive dynamic surface control scheme is proposed for a class of multi input multi output mimo nonlinear time varying systems by fusing a bound estimation approach a smooth function and a time varying matrix factorisation the obstacle caused by unknown time varying parameters is circumvented the proposed scheme is free of the problem of explosion of complexity and needs only one updated parameter at each design step moreover all tracking errors can converge to predefined arbitrarily small residual sets with a prescribed convergence rate and maximum overshoot such features result in a simple adaptive controller which can be easily implemented in applications with less computational burden and satisfactory tracking performance simulation results are presented to illustrate the effectiveness of the proposed scheme

two aspects of the donoho stark uncertainty principle abstract we present some forms of uncertainty principle which involve in a new way localization operators the concept of e concentration and the standard deviation of l 2 functions we show how our results improve the classical donoho stark estimate in two different aspects a better general lower bound and a lower bound in dependence on the signal itself

short time solution to the master equation of a first order mean field game abstract the goal of this paper is to show existence of short time classical solutions to the so called master equation of first order mean field games which can be thought of as the limit of the corresponding master equation of a stochastic mean field game as the individual noises approach zero despite being the equation of an idealistic model its study is justified as a way of understanding mean field games in which the individual players randomness is negligible in this sense it can be compared to the study of ideal fluids we restrict ourselves to mean field games with smooth coefficients but do not impose any monotonicity conditions on the running and initial costs and we do not require convexity of the hamiltonian thus extending the result of gangbo and swiech to a considerably broader class of hamiltonians

synchronization of coupled oscillators is a game the purpose of this paper is to understand phase transition in noncooperative dynamic games with a large number of agents applications are found in neuroscience biology and economics as well as traditional engineering applications the focus of analysis is a variation of the large population linear quadratic gaussian lqg model of huang et al 2007 comprised here of a controlled n dimensional stochastic differential equation model coupled only through a cost function the states are interpreted as phase angles for a collection of heterogeneous oscillators and in this way the model may be regarded as an extension of the classical coupled oscillator model of kuramoto a deterministic pde model is proposed which is shown to approximate the stochastic system as the population size approaches infinity key to the analysis of the pde model is the existence of a particular nash equilibrium in which the agents opt out of the game setting their controls to zero resulting in the incoherence equilibrium methods from dynamical systems theory are used in a bifurcation analysis based on a linearization of the partial differential equation pde model about the incoherence equilibrium a critical value of the control cost parameter is identified above this value the oscillators are incoherent and below this value when control is sufficiently cheap the oscillators synchronize these conclusions are illustrated with results from numerical experiments

stable adaptive fuzzy control of nonlinear systems preceded by unknown backlash like hysteresis this paper deals with adaptive control of nonlinear dynamic systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is described by a dynamic equation by utilizing this dynamic model and by combining a fuzzy universal function approximator with adaptive control techniques a stable adaptive fuzzy control algorithm is developed without constructing a hysteresis inverse the stability of the closed loop system is shown using lyapunov arguments the effectiveness of the proposed method is demonstrated through simulations

uplink power adjustment in wireless communication systems a stochastic control analysis this paper considers mobile to base station power control for lognormal fading channels in wireless communication systems within a centralized information stochastic optimal control framework under a bounded power rate of change constraint the stochastic control problem and its associated hamilton jacobi bellman hjb equation are analyzed by the viscosity solution method then the degenerate hjb equation is perturbed to admit a classical solution and a suboptimal control law is designed based on the perturbed hjb equation when a quadratic type cost is used without a bound constraint on the control the value function is a classical solution to the degenerate hjb equation and the feedback control is affine in the system power in addition in this case we develop approximate but highly scalable solutions to the hjb equation in terms of a local polynomial expansion of the exact solution when the channel parameters are not known a priori one can obtain on line estimates of the parameters and get adaptive versions of the control laws in numerical experiments with both of the above cost functions the following phenomenon is observed whenever the users have different initial conditions there is an initial convergence of the power levels to a common level and then subsequent approximately equal behavior which converges toward a stochastically varying optimum

anticipated backward stochastic differential equations in this paper we discuss new types of differential equations which we call anticipated backward stochastic differential equations anticipated bsdes in these equations the generator includes not only the values of solutions of the present but also the future we show that these anticipated bsdes have unique solutions a comparison theorem for their solutions and a duality between them and stochastic differential delay equations

asymptotic solutions to weakly coupled stochastic teams with nonclassical information the authors develop a new iterative approach toward the solution of a class of two agent dynamic stochastic teams with nonclassical information when the coupling between the agents is weak either through the state dynamics or through the information channel in each case the weak coupling is characterized in terms of a small perturbation parameter when this parameter value say in is set equal to zero the original fairly complex dynamic team with a nonclassical information pattern is decomposed into or converted to relatively simple stochastic control or team problems the solution of which makes up the zeroth order approximation in a function space to the team optical solution of the original problem the fact that the zeroth order solution approximates the optimal cost up to at least o in is shown it is also shown that approximations of all orders can be obtained by solving a sequence of stochastic control and or simpler team problems

an open loop stackelberg strategy for the linear quadratic mean field stochastic differential game this paper is concerned with the open loop linear quadratic lq stackelberg game of the mean field stochastic systems in finite horizon by means of two generalized differential riccati equations the follower first solves a mean field stochastic lq optimal control problem then the leader turns to solve an optimization problem for a linear mean field forward backward stochastic differential equation by introducing new state and costate variables we present a sufficient condition for the existence and uniqueness of the stackelberg strategy in terms of the solvability of some riccati equations and a convexity condition furthermore it is shown that the open loop stackelberg equilibrium admits a feedback representation involving the new state and its mean finally two examples are given to show the effectiveness of the proposed results

continuum and finite player noncooperative models of competition the anonymous interaction of large numbers of economic agents is a kind of noncooperative situation which is markedly different from small numbers strategic conflict the mathematical model of a nonatomic game or a game with a continuum of players has been introduced as a model for these many agent situations on the basis that its equilibria should closely approximate those of games with large finite numbers of players this paper contains a precise definition of what it means for a nonatomic game to be the limit of a sequence of finite player games and a theorem which states when the limit of equilibria of finite player games will be an equilibrium of the nonatomic limit game this is analogous to theorems prompted by edgeworth s conjecture in core theory it is derived from a general set of sufficient conditions for the graph of a noncooperative equilibrium correspondence to be closed

risk sensitive mean field games in this paper we study a class of risk sensitive mean field stochastic differential games we show that under appropriate regularity conditions the mean field value of the stochastic differential game with exponentiated integral cost functional coincides with the value function satisfying a hamilton jacobi bellman hjb equation with an additional quadratic term we provide an explicit solution of the mean field best response when the instantaneous cost functions are log quadratic and the state dynamics are affine in the control an equivalent mean field risk neutral problem is formulated and the corresponding mean field equilibria are characterized in terms of backward forward macroscopic mckean vlasov equations fokker planck kolmogorov equations and hjb equations we provide numerical examples on the mean field behavior to illustrate both linear and mckean vlasov dynamics

a stochastic maximum principle for delayed mean field stochastic differential equations and its applications in this technical note we discuss the stochastic optimal control problems of mean field stochastic differential delayed equations mfsddes which arise naturally from various backgrounds including economics finance engineering and physics etc to this end some new estimates are used to handle the complex structure of our controlled system due to the presence of both delay and mean field characters as the main result a stochastic maximum principle for the mean field stochastic optimal control with delay mfsocd is derived in terms of necessary and sufficient conditions in particular applying the convex variation and duality relation we obtain the necessary condition for optimality see theorem 1 in addition the sufficient condition of the optimality is also obtained under some convex condition see theorem 2 based on our maximum principle the related mean field linear quadratic delayed mflqd optimal control problems are also investigated the optimal control is derived and its existence is also verified refer theorem 3 as illustration an example is also proposed and its explicit optimal control is derived

linear quadratic gaussian mixed games with continuum parametrized minor players we consider a mean field linear quadratic gaussian game with a major player and a large number of minor players parametrized by a continuum set the mean field generated by the minor players is approximated by a random process depending only on the initial state and the brownian motion of the major player and this leads to two limiting optimal control problems with random coefficients which are solved subject to a consistency requirement on the mean field approximation the set of decentralized strategies constructed from the limiting control problems has an varepsilon nash equilibrium property when applied to the large but finite population model

mean field games convergence of a finite difference method mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to infty have been recently introduced by lasry and lions numerical methods for the approximation of the stationary and evolutive versions of such models have been proposed by the authors in previous works here convergence theorems for these methods are proved under various assumptions on the coupling operator

the nce mean field principle with locality dependent cost interactions we study large population stochastic dynamic games where each agent assigns individually determined coupling strengths with possible spatial interpretation to the states of other agents in its performance function the mean field methodology yields a set of decentralized controls which generates an nash equilibrium for the population of size a key feature of the mean field approximation here with localized interactions is that the resulting th individual agent s control law depends on that agent s state and the precomputable weighted average trajectory of the collection of all agents each applying a decentralized control law

the self duality of discrete short time fourier transform and its applications the self duality of short time fourier transform stft is an elegant property and is useful in shedding light on the construction of stft and its resolution capability in this paper the discrete version of self duality is studied and the property is interpreted in the context of resolution capabilities of time frequency distributions in addition two applications are provided as showcases of these insights obtained from the interpretation in the first application the problem of stft synthesis is considered and self duality serves as an important indication of whether the synthesis problem at hands is properly formulated in the second application a new kind of high resolution time frequency distribution is constructed based on the understandings obtained by contrasting two of the most popular time frequency analysis tools namely the stft and the wigner distribution

brief paper adaptive tracking of nonlinear systems with non symmetric dead zone input quite successfully adaptive control strategies have been applied to uncertain dynamical systems subject to dead zone nonlinearities however adaptive tracking of systems with non symmetric dead zone characteristics has not been fully discussed with minimal knowledge of the dead zone parameters it is shown that the controlled system preceded by a non symmetric dead zone input can be represented as an uncertain nonlinear system subject to a linear input with time varying input coefficient to cope with this problem a new adaptive compensation algorithm is employed without constructing the dead zone inverse the proposed adaptive scheme requires only the information of bounds of the dead zone slopes and treats the time varying input coefficient as a system uncertainty the new control scheme ensures bounded error trajectory tracking and assures the boundedness of all the signals in the adaptive closed loop by appropriate selections of the controller parameters we show that the smoothness of the controller does not affect the accuracy of trajectory tracking control a numerical example is included to show the effectiveness of the theoretical results

adaptive backstepping control of a class of uncertain nonlinear systems with unknown backlash like hysteresis in this note we consider the same class of systems as in a previous paper i e a class of uncertain dynamic nonlinear systems preceded by unknown backlash like hysteresis nonlinearities where the hysteresis is modeled by a differential equation in the presence of bounded external disturbances by using backstepping technique robust adaptive backstepping control algorithms are developed unlike some existing control schemes for systems with hysteresis the developed backstepping controllers do not require the uncertain parameters within known intervals also no knowledge is assumed on the bound of the disturbance like term a combination of the external disturbances and a term separated from the hysteresis model it is shown that the proposed controllers not only can guarantee global stability but also transient performance

a singular perturbation approach to modeling and control of markov chains finite state continuous time markov processes with weak interactions are modeled as singularly perturbed systems aggregate states are obtained using a grouping algorithm two time scale expansions simplify cost equations and lead to decentralized optimization algorithms

global and local consistencies in distributed fault diagnosis for discrete event systems in this paper we present a unified framework for distributed diagnosis we first introduce the concepts of global and local consistency in terms of supremal global and local supports then present two distributed diagnosis problems based on them after that we provide algorithms to achieve supremal global and local supports respectively and discuss in detail the advantages and disadvantages of each finally we present an industrial example to demonstrate our distributed diagnosis approach

optimal control of mean field jump diffusion systems with noisy memory abstractthis paper is concerned with an optimal control problem under mean field jump diffusion systems with delay and noisy memory first we derive necessary and sufficient maximum principles using malliavin calculus technique meanwhile we introduce a new mean field backward stochastic differential equation as the adjoint equation which involves not only partial derivatives of the hamiltonian function but also their malliavin derivatives then applying a reduction of the noisy memory dynamics to a two dimensional discrete delay optimal control problem we establish the second set of necessary and sufficient maximum principles under partial information moreover a natural link between the above two approaches is established via the adjoint equations finally we apply our theoretical results to study a mean field linear quadratic optimal control problem

robust adaptive control of a class of nonlinear systems with unknown dead zone this paper deals with the adaptive control of a class of continuous time nonlinear dynamic systems preceded by an unknown dead zone by using a new description of a dead zone and by exploring the properties of this dead zone model intuitively and mathematically a robust adaptive control scheme is developed without constructing the dead zone inverse the new control scheme ensures global stability of the adaptive system and achieves desired tracking precision simulations performed on a typical nonlinear system illustrate and clarify the validity of this approach

open loop nash equilibrium in polynomial differential games via state dependent riccati equation this paper studies finite as well as infinite time horizon nonzero sum polynomial differential games in both cases we explore the so called state dependent riccati equations to find a set of strategies that guarantee an open loop nash equilibrium for this particular class of nonlinear games such a method presents advantages in simplicity of the design of equilibrium strategies and yields computationally effective solution algorithms we demonstrate that this solution leads the game to an e or quasi equilibrium and provide an upper bound for this e quantity the proposed solution is given as a set of n coupled polynomial riccati like state dependent differential equations where each equation includes a p linear form tensor representation for its polynomial part we provide an algorithm for finding the solution of the state dependent algebraic equation in the infinite time case based on a hamiltonian approach and give conditions on the existence of such stabilizing solutions for a third order polynomial a numerical example is presented to illustrate effectiveness of the approach

pitt s inequality and the uncertainty principle associated with the quaternion fourier transform abstract the quaternion fourier transform a generalized form of the classical fourier transform has been shown to be a powerful analyzing tool in image and signal processing this paper investigates pitt s inequality and uncertainty principle associated with the two sided quaternion fourier transform it is shown that by applying the symmetric form f f 1 i f 2 f 3 j i f 4 j of quaternion from hitzer and the novel module or l p norm of the quaternion fourier transform f then any nonzero quaternion signal and its quaternion fourier transform cannot both be highly concentrated two part results are provided one part is heisenberg weyl s uncertainty principle associated with the quaternion fourier transform it is formulated by using logarithmic estimates which may be obtained from a sharp of pitt s inequality the other part is the uncertainty principle of donoho and stark associated with the quaternion fourier transform

large population cost coupled lqg problems with nonuniform agents individual mass behavior and decentralized varepsilon nash equilibria we consider linear quadratic gaussian lqg games in large population systems where the agents evolve according to nonuniform dynamics and are coupled via their individual costs a state aggregation technique is developed to obtain a set of decentralized control laws for the individuals which possesses an epsiv nash equilibrium property a stability property of the mass behavior is established and the effect of inaccurate population statistics on an isolated agent is also analyzed by variational techniques

linear exponential quadratic control for mean field stochastic systems in this technical note we consider linear exponential quadratic leq control for mean field stochastic differential equations mfsdes the mfsde includes the expectation value of state and control and the objective functional is exponential of a quadratic functional in state control and their expectations we obtain the explicit optimal solution as well as the optimal cost the corresponding optimal solution is linear in state and its expectation which is characterized by the riccati differential equations rdes the results are obtained by showing that after applying the completion of squares method the remaining exponentiated stochastic integral and additional rde terms can be eliminated together by taking expectation since they constitute the associated radon nikodym derivative as an extension of the problem the leq zero sum differential game is considered for which we obtain the explicit optimal solution saddle point equilibrium as well as the optimal cost