a new indirect adaptive control scheme for time varying plants structures are developed for the control and estimation parts of the indirect adaptive scheme which are more appropriate for time varying plants in contrast to the usual pointwise schemes the new controller structure can meet the control objective exactly for a wide class of plants with smooth but otherwise unrestricted parameter variations on the other hand the possibly available knowledge of the form or frequency of variation of the fast parameters is included in the new estimator structure so that for successful estimation the overall plant is not restricted to varying slowly with time the new estimator and control law are combined using the certainty equivalence principle to develop an indirect adaptive control scheme meeting the control objective for plants with time varying parameters whose fast varying parts are of known form and unknown parts are slow in the mean

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

supervisory control of families of linear set point controllers 2 robustness a simply structured high level controller called a supervisor has recently been proposed in part i of this article ibid vol 41 1996 for the purpose of orchestrating the switching of a sequence of candidate set point controllers into feedback with an imprecisely modeled siso process so as to cause the output of the process to approach and track a constant reference input the process is assumed to be modeled by an siso linear system whose transfer function is in the union of a number of subclasses each subclass being small enough so that one of the candidate controllers would solve the set point tracking problem if the process transfer function was to be one of the subclass members this paper proves that without any further modification the same supervisor described in part i can also perform this function in the face of norm bounded unmodeled dynamics and moreover that none of the signals within the overall system can grow without bound in response to bounded disturbance and noise inputs whether they are constant or not

brief adaptive control for linear slowly time varying systems using direct least squares estimation in this paper we propose a least squares based non recursive identification algorithm capable of dealing with slowly time varying parameters the minimized criterion is an l 2 norm of the identification error with forgetting factor the proposed estimation algorithm does not require explicit knowledge on the noise bound or the region where the true parameters lie finally a pole placement hybrid controller is designed and the system s state is shown to be bounded

phase locked patterns and amplitude death in a ring of delay coupled limit cycle oscillators we study the existence and stability of phase locked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical hopf bifurcation the coupling is limited to nearest neighbors and is linear we analyze a model set of discrete dynamical equations using the method of plane waves the resultant dispersion relation which is valid for any arbitrary number of oscillators displays important differences from similar relations obtained from continuum models we discuss the general characteristics of the equilibrium states including their dependencies on various system parameters we next carry out a detailed linear stability investigation of these states in order to delineate their actual existence regions and to determine their parametric dependence on time delay time delay is found to expand the range of possible phase locked patterns and to contribute favorably toward their stability the amplitude death state is studied in the parameter space of time delay and coupling strength it is shown that death island regions can exist for any number of oscillators n in the presence of finite time delay a particularly interesting result is that the size of an island is independent of n when n is even but is a decreasing function of n when n is odd

multirhythmicity generated by slow variable diffusion in a ring of relaxation oscillators and noise induced abnormal interspike variability the deterministic and noise dependent dynamics of a ring of three ohmically coupled electronic relaxation oscillators are considered by means of numerical simulations each isolated oscillator is described by a set of two ordinary differential equations with very different characteristic times the emergence of the limit cycle via the hopf bifurcation results from the n shaped current versus voltage characteristic of the nonlinear resistor the phase diagram is calculated for a ring of three such oscillators in the presence of small detuning special attention is focused on two parameter areas one near a transition to the homogeneous and the other near the inhomogeneous stable steady state along with other nontrivial limit cycles essentially asymmetrical limit cycles termed dynamic traps may arise in these two areas a dynamic trap is a regime in which one or two oscillators do not perform full amplitude oscillations and correspondingly do not generate spikes the interspike interval isi distribution in the presence of noise is calculated as a function of the coupling strength in both areas of the parameter plane the distributions are extremely polymodal near the homogeneous steady state even if the in phase limit cycle is dominating the origins of this abnormal enhancement of isi variability are discussed in detail a similar analysis shows that nontrivial periodic attractors are observable in the vicinity of the inhomogeneous stable steady states only if the level of noise is relatively low in this case the dominance of the in phase limit cycle basin results in an almost unimodal distribution of interspike intervals

brief paper input to state stability of switched systems and switching adaptive control in this paper we prove that a switched nonlinear system has several useful input to state stable iss type properties under average dwell time switching signals if each constituent dynamical system is iss this extends available results for switched linear systems we apply our result to stabilization of uncertain nonlinear systems via switching supervisory control and show that the plant states can be kept bounded in the presence of bounded disturbances when the candidate controllers provide iss properties with respect to the estimation errors detailed illustrative examples are included

reaction cattaneo systems with fluctuating relaxation time a reaction cattaneo equation with fluctuating relaxation time of the diffusive flux has been explored it has been shown that depending on the strength of fluctuations the dynamical system exhibits new oscillatory solutions as a result of hopf and double hopf bifurcations leading to spatiotemporal patterns this analysis has been applied to two model nonlinear systems

adaptive control of linear time varying plants a new model reference controller structure the problem of developing a control law which can force the output of a linear time varying plant to track the output of a stable linear time invariant reference model is discussed it is shown that the standard model reference controller used for linear time invariant plants cannot guarantee zero tracking error in general when the plant is time varying a new model reference controller is proposed which guarantees stability and zero tracking error for a general class of linear time varying plants with known parameters when the time varying plant parameters are unknown but vary slowly with time it is shown that the new controller can be combined with a suitable adaptive law so that all the signals in the closed loop remain bounded for any bounded initial conditions and the tracking error is small in the mean the assumption of slow parameter variations in the adaptive case can be relaxed if some information about the frequency or the form of the fast varying parameters is available a priori such information can be incorporated in an appropriately designed adaptive law so that stability and improved tracking performance is guaranteed for a class of plants with fast varying parameters

brief adaptive control of linear time varying systems single input single output uncertain linear time varying systems are considered which are affected by unknown bounded additive disturbances the uncertain time varying parameters are required to be smooth and bounded but are neither required to be sufficiently slow nor to have known bounds the output which is the only measured variable is required to track a given smooth bounded reference trajectory the undisturbed system is assumed to be minimum phase and to have known and constant relative degree known sign of the high frequency gain known upper bound on the system order an adaptive output feedback control algorithm is designed which assures i boundedness of all closed loop signals ii arbitrarily improved transient performance of the tracking error iii asymptotically vanishing tracking error when parameter time derivatives are l 1 signals and disturbances are l 2 signals

dissipativity theory for switched systems a framework of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up each subsystem of a switched system is associated with a storage function to describe the energy stored in the subsystem and is associated with a supply rate that represents energy coming from outside the subsystem when the subsystem is active the exchange of energy between the active subsystem and an inactive subsystem is characterized by cross supply rates stability is reached when all supply rates can be made negative as long as the total exchanged energy between the active subsystem and any inactive subsystems is finite in some sense two special forms of dissipativity passivity and l 2 gain are addressed for both cases asymptotic stability is guaranteed under certain negative output feedback plus asymptotic zero state detectability switched passivity conditions and switched l 2 gain inequalities are respectively derived which are generalizations of classical ones feedback invariance of passivity and a small gain theorem are also given

analyzing the stability of switched systems using common zeroing output systems this paper introduces the notion of common zeroing output systems czos to analyze the stability of switched systems the concept of czos allows one to verify weak zero state detectability it characterizes a common behavior of any individual subsystem when the output signal for each subsystem is approaching zero heuristically speaking it removes the effect of switching behavior and thus enables one to analyze stability properties in systems with complex switching signals with the help of czos the krasovskii lasalle theorem can be extended to switched nonlinear time varying systems with both arbitrary switching and more general restricted switching cases for switched nonlinear time invariant systems the needed detectability condition is further simplified leading to several new stability results particularly when a switched linear time invariant system is considered it is possible to generate a recursive method which combines a krasovskii lasalle result and a nested matrosov result to find a czos if it exists the power of the proposed czos is demonstrated by consensus problems in literature to obtain a stronger convergence result with weaker conditions

optimal policy for minimizing risk models in markov decision processes we consider the minimizing risk problems in discounted markov decisions processes with countable state space and bounded general rewards we characterize optimal values for finite and infinite horizon cases and give two sufficient conditions for the existence of an optimal policy in an infinite horizon case these conditions are closely connected with lemma 3 in white 1993 which is not correct as wu and lin 1999 point out we obtain a condition for the lemma to be true under which we show that there is an optimal policy under another condition we show that an optimal value is a unique solution to some optimality equation and there is an optimal policy on a transient set

multimodal regimes in a compartmental model of the dopamine neuron we study chains of strongly electrically coupled relaxation oscillators modeling dopamine neurons when individual oscillators are in the regime close to an andronov hopf bifurcation ahb the coupled system exhibits a variety of oscillatory behavior we show that the proximity of individual oscillators to the ahb has a significant impact on the system dynamics in a wide range of parameters it manifests itself through a family of stable multimodal periodic solutions that are composed out of large amplitude relaxation oscillations and small amplitude oscillations this family of solutions has a rich bifurcation structure the waveform and the period vary greatly across the family the structure and bifurcations of the stable periodic solutions of the coupled system are investigated using numerical and analytic techniques

finite data rate feedback stabilization of switched and hybrid linear systems we study the problem of asymptotically stabilizing a switched linear control system using sampled and quantized measurements of its state the switching is assumed to be slow enough in the sense of combined dwell time and average dwell time each individual mode is assumed to be stabilizable and the available data rate is assumed to be large enough but finite our encoding and control strategy is rooted in the one proposed in our earlier work on non switched systems and in particular the data rate bound used here is the data rate bound from that earlier work maximized over the individual modes the main technical step that enables the extension to switched systems concerns propagating over approximations of reachable sets through sampling intervals during which the switching signal is not known a novel algorithm is developed for this purpose our primary focus is on systems with time dependent switching switched systems but the setting of state dependent switching hybrid systems is also discussed

optimization models for the first arrival target distribution function in discrete time the study of expectation optimality criteria standard criteria has constituted most previous work in the area of markov decision processes mdps however the optimal policies obtained from such models are not reliable when considering a single or a few decision processes since only the average performance over many trials is guaranteed to be optimal in fact the expectation optimality criteria are insufficient to characterize the w x variability risk features of practical problems 1 5 a typical requirement for a long term application for example unmanned space flight and satellites is to have a 0 95 or greater probability of being operational at the end of a 10 year period whereas a typical requirement for space shuttle aircraft flight control and military systems is to have a reliability of 0 97 at the end of a 3 h time period likewise chemical reactions must

multimodal oscillations in systems with strong contraction one and two parameter families of flows in r 3 near an andronov hopf bifurcation ahb are investigated in this work we identify conditions on the global vector field which yield a rich family of multimodal orbits passing close to a weakly unstable saddle focus and perform a detailed asymptotic analysis of the trajectories in the vicinity of the saddle focus our analysis covers both cases of sub and supercritical ahb for the supercritical case we find that the periodic orbits born from the ahb are bimodal when viewed in the frame of coordinates generated by the linearization about the bifurcating equilibrium if the ahb is subcritical it is accompanied by the appearance of multimodal orbits which consist of long series of nearly harmonic oscillations separated by large amplitude spikes we analyze the dependence of the interspike intervals which can be extremely long on the control parameters in particular we show that the interspike intervals grow logarithmically as the boundary between regions of sub and supercritical ahb is approached in the parameter space we also identify a window of complex and possibly chaotic oscillations near the boundary between the regions of sub and supercritical ahb and explain the mechanism generating these oscillations this work is motivated by the numerical results for a finite dimensional approximation of a free boundary problem modeling solid fuel combustion c 2007 elsevier b v all rights reserved

supervisory control of uncertain linear time varying systems we consider the problem of adaptively stabilizing linear plants with unknown time varying parameters in the presence of noise disturbances and unmodeled dynamics using the supervisory control framework which employs multiple candidate controllers and an estimator based switching logic to select the active controller at every instant of time time varying uncertain linear plants can be stabilized by supervisory control provided that the plant s parameter varies slowly enough in terms of mixed dwell time switching and average dwell time switching the noise and disturbances are bounded and small enough in terms of l infinity norms and the unmodeled dynamics are small enough in the input to state stability sense this work extends previously reported works on supervisory control of linear time invariant systems with constant unknown parameters to the case of linear time varying uncertain systems a numerical example is included and limitations of the approach are discussed

optimal threshold probability in undiscounted markov decision processes with a target set we consider risk minimizing problems in undiscounted markov decisions processes with a target set we formulate the problem as an infinite horizon case with a recurrent class we show that an optimal value function is a unique solution to an optimality equation and there exists an stationary optimal policy also we give several value iteration methods and a policy improvement method

synchronization in light controlled oscillators we have built light controlled oscillators lcos that mimic gregarious fireflies in the sense that their interactions are episodic and almost pulse like the ability of the lcos to synchronize their light emission constitutes a good experimental setup to validate different models of populations of integrate and fire oscillators and to analyze the role of the interactions and the spatial distribution of the lcos experimental measurements on two and three interacting lcos enable us to find synchronization ranges despite intrinsic differences among the oscillators we develop a mathematical model that we have used to solve analytically the simplified case of two identical oscillators in which we have found synchronous and anti synchronous states we have constructed the phase response curve for an lco finally we solved the model numerically finding that it reproduces our different experimental results with two lcos master slave interaction and mutual interaction and three interacting lcos in a linear configuration

adaptive control of a class of slowly time varying plants abstract an adaptive control system of the type considered earlier by the author which is designed to be stable under the assumption that the unknown plant parameters are constant is shown to maintain stability when the plant parameters are slowly time varying

adaptive control of time varying linear systems the authors present a global bounded input bounded state stability theory for a class of continuously adapting controllers applied to time varying linear systems this gives theoretical support to the application of many of the algorithms used in practice a key feature of the analysis is that no persistence of excitation requirement is needed

robust state dependent switching of linear systems with dwell time a state dependent switching law that obeys a dwell time constraint and guarantees the stability of a switched linear system is designed sufficient conditions are obtained for the stability of the switched systems when the switching law is applied in presence of polytopic type parameter uncertainty a lyapunov function in quadratic form is assigned to each subsystem such that it is non increasing at the switching instants during the dwell time this function varies piecewise linearly in time after the dwell the system switches if the switching results in a decrease in the value of the lf the method proposed is also applicable to robust stabilization via state feedback it is further extended to guarantee a bound on the l2 gain of the switching system it is also used in deriving state feedback control law that robustly achieves a prescribed l2 gain bound

robust adaptive control a slowly varying systems approach in this paper we characterize a class of indirect adaptive controllers that can stabilize a time invariant system subjected to both parametric and l to l bounded unstructured uncertainty pertaining to this class of controllers a particular indirect adaptive scheme is proposed and an a priori computable upper bound on the size of the unstructured uncertainty for which stability is ensured is provided

adaptive control of a class of slowly time varying systems with modeling uncertainties in a recent work a new linear adaptive controller based on certainty equivalence and backstepping design which promises a level of transient and asymptotic performance comparable to that of the tuning functions adaptive backstepping controller without using high order nonlinearities was proposed for linear time invariant systems the proposal was supplemented with robustness and performance analysis in the presence of modeling uncertainties in this note the same idea is used to develop a new linear adaptive controller for slowly time varying systems with modeling uncertainties the new adaptive control scheme guarantees robustness with respect to modeling errors via normalizing damping parameter projection and static normalization use of normalizing damping is essential in protecting the linearity of the system which plays a key role in reaching the stability and robustness results

total and partial amplitude death in networks of diffusively coupled oscillators networks of weakly nonlinear oscillators are considered with diffusive and time delayed coupling averaging theory is used to determine parameter ranges for which the network experiences amplitude death whereby oscillations are quenched and the equilibrium solution has a large domain of attraction the amplitude death is shown to be a common phenomenon which can be observed regardless of the precise nature of the nonlinearities and under very general coupling conditions in addition when the network consists of dissimilar oscillators there exist parameter values for which only parts of the network are suppressed sufficient conditions are derived for total and partial amplitude death in arbitrary network topologies with general nonlinearities coupling coefficients and connection delays

robust adaptive regulation with minimal prior knowledge a robust adaptive regulator is designed under minimal prior knowledge namely the order of a nominal plant model in a well defined sense the involved robustness means that the closed loop stability is guaranteed in the presence of some class of time varying parameters and unmodeled dynamics the main design feature of the proposed adaptive regulator consists in its self excitation capability together with an appropriate identification stabilization time splitting unlike in the available literature concerning robust adaptive control the involved self excitation is established independently of the parameter estimator properties the use of the robustness oriented modifications as deadzone and parameter projection or contraction which are aimed at achieving the parameter estimates boundedness is no longer required beforehand thereby reducing the underlying prior knowledge

percentile performance criteria for limiting average markov decision processes addresses the following basic feasibility problem for infinite horizon markov decision processes mdps can a policy be found that achieves a specified value target of the long run limiting average reward at a specified probability level percentile related optimization problems of maximizing the target for a specified percentile and vice versa are also considered the authors present a complete and discrete classification of both the maximal achievable target levels and of their corresponding percentiles the authors also provide an algorithm for computing a deterministic policy corresponding to any feasible target percentile pair next the authors consider similar problems for an mdp with multiple rewards and or constraints this case presents some difficulties and leads to several open problems an lp based formulation provides constructive solutions for most cases

brief hysteresis based switching algorithms for supervisory control of uncertain systems we address the problem of controlling a linear system with unknown parameters ranging over a continuum by means of switching among a finite family of candidate controllers we present a new hysteresis based switching logic designed specifically for this purpose and derive a bound on the number of switches produced by this logic on an arbitrary time interval the resulting switching control algorithm is shown to provide stability and robustness to arbitrary bounded noise and disturbances and sufficiently small unmodeled dynamics

localized and asynchronous patterns via canards in coupled calcium oscillators in this paper we consider the mechanism for localized behavior in coupled calcium oscillators described by the canonical two pool model localization occurs when the individual cells oscillate with amplitudes of different orders of magnitude our analysis and computations show that a combination of diffusive coupling heterogeneity and the underlying canard structure of the oscillators all contribute to the localized behavior two key quantities characterize the different states of the system by representing the effects of both the autonomous and the non autonomous terms which are due to the coupling by highlighting the influence of the canard phenomenon these quantities identify stabilizing and destabilizing effects of the coupling on the localized behavior we compare our analysis with computations describing multi mode states and asynchronized large oscillations in addition to the localized states

stabilization of nonholonomic integrators via logic based switching this paper explains how to stabilize a nonholonomic integrator using a hybrid control law employing switching and logic results concerning asymptotic stability and exponential convergence to the origin are derived the notion of a positively invariant set is extended to hybrid systems and sufficient conditions for invariance are presented the verification of these conditions does not require the computation of the state trajectories and their use goes beyond the analysis of the system presented in this paper

lyapunov conditions for input to state stability of impulsive systems this paper introduces appropriate concepts of input to state stability iss and integral iss for impulsive systems i e dynamical systems that evolve according to ordinary differential equations most of the time but occasionally exhibit discontinuities or impulses we provide a set of lyapunov based sufficient conditions for establishing these iss properties when the continuous dynamics are iss but the discrete dynamics that govern the impulses are not the impulses should not occur too frequently which is formalized in terms of an average dwell time adt condition conversely when the impulse dynamics are iss but the continuous dynamics are not there must not be overly long intervals between impulses which is formalized in terms of a novel reverse adt condition we also investigate the cases where i both the continuous and discrete dynamics are iss and ii one of these is iss and the other only marginally stable for the zero input while sharing a common lyapunov function in the former case we obtain a stronger notion of iss for which a necessary and sufficient lyapunov characterization is available the use of the tools developed herein is illustrated through examples from a micro electro mechanical system mems oscillator and a problem of remote estimation over a communication network

threshold probability of non terminal type in finite horizon markov decision processes abstract we consider a class of problems concerned with maximizing probabilities given stage wise targets which generalizes the standard threshold probability problem in markov decision processes the objective function is the probability that at all stages the associatively combined accumulation of rewards earned up to that point takes its value in a specified stage wise interval it is shown that this class reduces to the case of the nonnegative valued multiplicative criterion through an invariant imbedding technique we derive a recursive formula for the optimal value function and an effective method for obtaining the optimal policies

minimizing a threshold probability in discounted markov decision processes necessary and sufficient conditions are found for the characteristic functions of a finite number of given sets to be linearly independant

associative dynamic programs abstract in this paper we consider finite stage stochastic dynamic programs with associative reward systems an invariant imbedding technique yields a dynamic program with a terminal reward system on an augmented state space according to the associativity we clarify the validity of three possible recursive equations one parametrized equation and two non parametrized ones each of the additive multiplicative and multiplicative additive dynamic programs admits the three recursive equations further the corresponding composite relations among three optimum value functions hold however minimum maximum and fractional dynamic programs admit only the parametrized recursive equation they do not admit the two non parametrized equations further the corresponding relations among the three optimum value functions do not hold

minimizing risk models in markov decision processes with policies depending on target values abstract this paper studies the minimizing risk problems in markov decision processes with countable state space and reward set the objective is to find a policy which minimizes the probability risk that the total discounted rewards do not exceed a specified value target in this sort of model the decision made by the decision maker depends not only on system s states but also on his target values by introducing the decision maker s state we formulate a framework for minimizing risk models the policies discussed depend on target values and the rewards may be arbitrary real numbers for the finite horizon model the main results obtained are i the optimal value functions are distribution functions of the target ii there exists an optimal deterministic markov policy and iii a policy is optimal if and only if at each realizable state it always takes optimal action in addition we obtain a sufficient condition and a necessary condition for the existence of finite horizon optimal policy independent of targets and we give an algorithm computing finite horizon optimal policies and optimal value functions for an infinite horizon model we establish the optimality equation and we obtain the structure property of optimal policy we prove that the optimal value function is a distribution function of target and we present a new approximation formula which is the generalization of the nonnegative rewards cases an example which illustrates the mistakes of previous literature shows that the existence of optimal policy has not been proved really in this paper we give an existence condition which is a sufficient and necessary condition for the existence of an infinite horizon optimal policy independent of targets and we point out that whether there exists an optimal policy remains an open problem in the general case