reduced order feedback control of distributed parameter systems via singular perturbation methods abstract implementable feedback control of distributed parameter systems must often be based on reduced order models due to the infinite dimensional nature of the actual open loop system the behavior of controllers designed via reduced order models obtained with singular perturbation techniques is analyzed when such controllers are used in the actual distributed parameter system the closed loop stability is in question the results presented here provide bounds on the smallness of the singular perturbation parameter to ensure stable operation such a priori bounds may be used to evaluate potential reduced order controllers for distributed parameter systems

singularly perturbed difference equations in optimal control problems a linear regular problem involving singularly perturbed difference equations is considered the basic features of singularly perturbed systems order reduction separation of time scales boundary layers etc are highlighted application to the numerical treatment of control problems involving stiff differential equations is discussed

a fourier spectral discontinuous galerkin method for time dependent 3 d schrodinger poisson equations with discontinuous potentials in this paper we propose a high order fourier spectral discontinuous galerkin method for time dependent schrodinger poisson equations in 3 d spaces the fourier spectral galerkin method is used for the two periodic transverse directions and a high order discontinuous galerkin method for the longitudinal propagation direction such a combination results in a diagonal form for the differential operators along the transverse directions and a flexible method to handle the discontinuous potentials present in quantum heterojunction and supperlattice structures as the derivative matrices are required for various time integration schemes such as the exponential time differencing and crank nicholson methods explicit derivative matrices of the discontinuous galerkin method of various orders are derived numerical results using the proposed method with various time integration schemes are provided to validate the method

on the robustness of output feedback control methods to modeling errors singular perturbation analysis is employed to study the robustness of output feedback control schemes for linear time invariant systems the effect of designing the control strategy using a model that neglects unknown parasitic elements is considered it is shown that such a strategy may in general be destabilizing even when the neglected modes are asymptotically stable special structures that will not permit this situation and will guarantee asymptotic stability are illustrated

subsystems time scales and multimodeling through a couple of naive examples the control theorists are invited to re examine the role of modeling in the study of large scale dynamic systems instead of assuming the existence of n diagonally dominant blocks it is possible to justify one strongly coupled slow core and n weakly coupled fast subsystems this structure is exhibited with a physically meaningful choice of state variables the controls are introduced following the recent concept of multimodeling

the equivalence of time scale decomposition techniques used in the analysis and design of linear systems linear system models can be decomposed into reduced order fast and slow subsystems using spectrum separating solutions to dual riccati type equations eigenspace power iterations provide globally convergent iterative schemes for obtaining these solutions from this basis an equivalence of previous decomposition techniques is then achieved including the classic two time scale asymptotic series decomposition of singularly perturbed systems the result is a unified theory for the decomposition of time scales in linear systems applicable to both continuous and discrete time models

direct singular perturbation analysis of high gain and cheap control problems a new and direct approach to the analysis and design of high gain feedback and cheap control problems is developed transformation of such singular problems to singular perturbation models of conventional type early at the onset of analysis or design allows a direct application of the readily available singular perturbation literature the approach permits a simple characterization of a multivariable root loci under a high gain feedback and b asymptotic behavior of optimal closed loop poles state and control trajectories performance index and optimal transfer function as the control cost coefficient in the performance index goes to zero

convergence in the boundary layer for singularly perturbed equations a singularly perturbed linear finite dimensional ordinary differential equation is considered on the half line 0 the reduced system is assumed to have a unique solution in the sense of distributions it is proved that under reasonable conditions the solution of the full system converges to that of the reduced in the distributional sense and the order of the limiting distribution is computed an application to the optimal linear quadratic regulator with cheap control is described

paper optimal control of markov chains admitting strong and weak interactions this paper is devoted to the study of an optimal control problem for a markov chain with generator b ea where e is a small parameter it is shown that an approximate solution can be calculated by a policy improvement algorithm involving computations relative to an aggregated problem the dimension of which is given by n the number of ergodic sets for the b matrix together with a family of decentralized problems the dimensions of which are given by the number of elements in each ergodic set for the b matrix

on a class of optimal control problems with an almost cost free solution for a class of linear singular optimal control problems with a nonunique singular arc the solution of the corresponding nearly singular problem is analyzed and a limit solution based on formal singular perturbations is derived a rigorous proof of the correctness of the result is given by constructing a convergent power series satisfying the riccati equation of the nearly singular problem

perturbation analysis of a system of quasi variational inequalities for optimal stochastic scheduling optimal scheduling of continuously evolving dynamical systems involves the analysis of certain partial differential inequalities on solution dependent domains these are the quasi variatlonai inequalities qvi s introduced for such problems by a bensoussan and j l lions they arise naturally in such applications as inventory control and unit commitment scheduling in electric energy systems qvi s are in these contexts the analog of the dynamic programming partial differential equations of r bellman for continuous control problems analytical treatment of qvi s involves not only the solution of partial differential inequalities but also the simultaneous analysis of the free boundaries of the domain of the solution in effect the optimal return function is the solution of the inequalities and the optimal control switching policy is defined by the free boundaries this paper considers a system of two singularly perturbed second order quasi variational inequalities with a turning point in a bounded domain in r1 asymptotic approximations for the free boundaries are derived using standard perturbation analysis for boundary value problems also local regularity properties of the limit solution are obtained the results are illustrated by a parametric study of a simple model of commitment scheduling for a single unit in a power generation system

composite controls for singularly perturbed systems the controllability and the stabilizability invariance of the reduced system slow subsystem of the nonlinear singularly perturbed system due to a class of fast feedback controls is shown the general type composite control for the nonlinear singularly perturbed system is proposed and its application for the synthesis problem is considered

asymptotic stability of nonlinear multiparameter singularly perturbed systems sufficient conditions are derived to guarantee the asymptotic stability of a class of nonlinear singularly perturbed systems with several perturbation parameters of the same order estimates of the region of attraction and bounds on the small parameters are obtained

applications of singular perturbation techniques to control problems this paper discusses typical applications of singular perturbation techniques to control problems in the last fifteen years the first three sections are devoted to the standard model and its time scale stability and controllability properties the next two sections deal with linear quadratic optimal control and one with cheap near singular control then the composite control and trajectory optimization are considered in two sections and stochastic control in one section the last section returns to the problem of modeling this time in the context of large scale systems the bibliography contains more than 250 titles

robustness of absolute stability the stability of a class of single input single output singularly perturbed systems formed by a linear time invariant feedforward block with a sector bounded time varying feedback is considered it is shown that if the reduced order slow subsystem is absolutely stable and the parasitics are asymptotically stable and sufficiently fast then the full system is absolutely stable bounds on the singular perturbation parameter for uniform asymptotic stability and absolute stability are obtained

a reduction process for perturbed markov chains given a perturbed markov chain with generator a varepsilon a 0 varepsilon a 1 varepsilon 2 a 2 cdots it is shown that to each time scale t t varepsilon t varepsilon 2 cdots is associated a reduced markov chain this process of reduction has only finitely many steps it is given in a recursive way and each reduced chain admits as state space the recurrent classes of the reduced chain defined at the previous stage it is shown that if lambda is an eigenvalue different from zero of the generator of the kth reduced chain with multiplicity p then a varepsilon admits p eigenvalues lambda varepsilon such that lambda varepsilon varepsilon k lambda o varepsilon k a basis of ker a 0 resp ker a 0 which is robust to the perturbation is constructed

infinite time regulators for singularly perturbed difference equations linear quadratic regulators for singularly perturbed difference equations are considered asymptotic behaviour of the optimal solution as the perturbation parameter tends to zero is studied the composite feedback control strategy of continuous time singularly perturbed systems is extended to the new problem

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

masker first advantage for cues in informational masking the detectability of a pure tone signal may be reduced by adding a small number of randomly drawn masker tones remote from the signal frequency an effect attributed to informational masking a pretrial cue consisting of either the upcoming signal or masker releases informational masking but a pretrial cue of the signal plus masker stimulus does not in these experiments the relative potency of pre and posttrial cues in releasing informational masking was examined in separate conditions the masker alone and signal plus masker stimuli were cues the results indicated a masker first advantage i e sensitivity was superior when a masker cue preceded a yes no trial interval compared to a when a signal plus masker preceded the trial and b when either cue type followed the yes no trial interval a masker first advantage was also obtained when the results from a two interval forced choice same different task were examined in contrast a masker first advantage was not obtained when the frequency of the signal to be detected was random for detection tasks using random multi tone maskers there may be differences in processing efficiency depending on the order in which stimuli are presented the masker first advantage may depend in part on observers maintaining their attention at the signal frequency

a multimodel approach to stochastic nash games a decentralized filtering and control scheme is presented for obtaining low order nash equilibrium strategies for decision makers using different models of the same large scale system multiparameter singular perturbations are employed to capture the multimodel nature of the fast dynamic subsystems interconnected through slow dynamic variables the small parameters are appropriately scaled so that the variables in both time scales are well defined the decision makers have decentralized information structures and are constrained to use only finite dimensional compensators of a specified dimension it is shown that the proposed scheme is in fact the asymptotic limit of the exact solution as the small parameters go to zero

singular perturbation of the popov kaiman yakubovich lemma absolute stability of linear time invariant single input single output lti siso singularly perturbed systems with a time varying feedback element is examined via the popov kalman yakubovich pky lemma if the reduced order slow subsystem is absolutely stable then so is the full system provided the parasitics are sufficiently fast and stable

disturbance decoupling by high gain feedback asymptotic disturbance decoupling add a concept which is suitable for the study of the effects of high gain feedback on disturbance decoupling is introduced in this note we show that the conditions for add are the conditions for exact disturbance decoupling due to wonham and morse for a reduced order system