superinduction for pattern groups abstract it is well known that the representation theory of the finite group of unipotent upper triangular matrices u n over a finite field is a wild problem by instead considering approximately irreducible representations supercharacters one obtains a rich combinatorial theory analogous to that of the symmetric group where we replace partition combinatorics with set partitions this paper studies diaconis isaacs concept of superinduction in pattern groups while superinduction shares many desirable properties with usual induction it no longer takes characters to characters we begin by finding sufficient conditions guaranteeing that superinduction is in fact induction it turns out for two natural embeddings of u m in u n superinduction is induction we conclude with an explicit combinatorial algorithm for computing this induction analogous to the pieri formulas for the symmetric group

brief low gain integral control of continuous time linear systems subject to input and output nonlinearities continuous time low gain integral control strategies are presented for tracking of constant reference signals for finite dimensional continuous time asymptotically stable single input single output linear systems subject to a globally lipschitz and non decreasing input nonlinearity and a locally lipschitz non decreasing and affinely sector bounded output nonlinearity both non adaptive but possibly time varying and adaptive integrator gains are considered in particular it is shown that applying error feedback using an integral controller ensures asymptotic tracking of constant reference signals provided that a the steady state gain of the linear part of the plant is positive b the positive integrator gain is ultimately sufficiently small and c the reference value is feasible in a very natural sense the classes of actuator and sensor nonlinearities under consideration contain standard nonlinearities important in control engineering such as saturation and deadzone

brief paper output regulation for linear distributed parameter systems using finite dimensional dual observers in this article the solution of the output regulation problem is considered for linear infinite dimensional systems where the outputs to be controlled cannot be measured it is shown that this problem can be solved by a finite dimensional dual observer that is directly implementable so that the separation principle can be applied for the stabilization as in finite dimensions a parametric design of these dual observers is proposed for riesz spectral systems that allows to achieve a low controller order and a desired control performance for the closed loop system the presented results are illustrated by determining a finite dimensional regulator for an euler bernoulli beam with kelvin voigt damping that achieves tracking for steplike reference inputs and that asymptotically rejects sinusoidal disturbances

robust controller for systems with exponentially stable strongly continuous semigroups abstract the theory of robust controllers is extended to the case where we have boundary and or distributed control and the system operator is an infinitesimal generator of a strongly continuous exponentially stable semigroup an example on hyperbolic systems is presented

integral control of infinite dimensional linear systems subject to input saturation closing the loop around an exponentially stable single input single output regular linear system subject to a globally lipschitz and nondecreasing actuator nonlinearity and compensated by an integral controller is shown to ensure asymptotic tracking of constant reference signals provided that a the steady state gain of the linear part of the plant is positive b the positive integrator gain is sufficiently small and c the reference value is feasible in a very natural sense the class of actuator nonlinearities under consideration contains standard nonlinearities important in control engineering such as saturation and deadzone

bounds for invariance pressure abstract this paper provides an upper bound for the invariance pressure of control sets with nonempty interior and a lower bound for sets with finite volume in the special case of the control set of a hyperbolic linear control system on r d this yields an explicit formula further applications to linear control systems on lie groups and to inner control sets are discussed

a supercharacter analogue for normality diaconis and isaacs define in 8 diaconis and isaacs 2008 a supercharacter theory for algebra groups over a finite field by constructing certain unions of conjugacy classes called superclasses and certain reducible characters called supercharacters this work investigates the properties of algebra subgroups h g which are unions of some set of the superclasses of g we call such subgroups supernormal after giving a few useful equivalent formulations of this definition we show that products of supernormal subgroups are supernormal and that all normal pattern subgroups are supernormal we then classify the set of supernormal subgroups of un q the group of unipotent upper triangular matrices over the finite field fq and provide a formula for the number of such subgroups when q is prime following this we give supercharacter analogues for clifford s theorem and mackey s method of little groups specifically we show that a supercharacter restricted to a supernormal subgroup decomposes as a sum of supercharacters with the same degree and multiplicity we then describe how the supercharacters of an algebra group of the form un uh ua where ua is supernormal and a2 0 are parametrized by uh orbits of the supercharacters of ua and the supercharacters of the stabilizer subgroups of these orbits

supercharacter formulas for pattern groups c andre and n yan introduced the idea of a supercharacter theory to give a tractable substitute for character theory in wild groups such as the unipotent uppertriangular group u n f q in this theory superclasses are certain unions of conjugacy classes and supercharacters are a set of characters which are constant on superclasses this paper gives a character formula for a supercharacter evaluated at a superclass for pattern groups and more generally for algebra groups

riesz basis approach to the stabilization of a flexible beam with a tip mass using an abstract condition of riesz basis generation of discrete operators in the hilbert spaces we show in this paper that a sequence of generalized eigenfunctions of an euler bernoulli beam equation with a tip mass under boundary linear feedback control forms a riesz basis for the state hilbert space in the meanwhile an asymptotic expression of eigenvalues and the exponential stability are readily obtained the main results of siam j control optim 36 1998 pp 1962 1986 are concluded as a special case and the additional conditions imposed there are removed

supercharacters and superclasses for algebra groups we study certain sums of irreducible characters and compatible unions of conjugacy classes in finite algebra groups these groups generalize the unimodular upper triangular groups over a finite field and the supercharacter theory we develop extends results of carlos andre and ning yan that were originally proved in the upper triangular case this theory sometimes allows explicit computations in situations where it would be impractical to work with the full character table we discuss connections with the kirillov orbit method and with gelfand pairs and we give conditions for a supercharacter or a superclass to be an ordinary irreducible character or conjugacy class respectively we also show that products of supercharacters are positive integer combinations of supercharacters

integral control of linear systems with actuator nonlinearities lower bounds for the maximal regulating gain closing the loop around an exponentially stable single input single output regular linear system subject to a globally lipschitz and nondecreasing actuator nonlinearity and compensated by an integral controller is known to ensure asymptotic tracking of constant reference signals provided that 1 the steady state gain of the linear part of the plant is positive 2 the positive integrator gain is sufficiently small and 3 the reference value is feasible in a very natural sense here lower bounds are derived for the maximal regulating gain for various special cases including systems with nonovershooting step response and second order systems with a time delay in the input or output the lower bounds are given in terms of open loop frequency step response data and the lipschitz constant of the nonlinearity and are hence readily obtainable

robust multivariable pi controller for infinite dimensional systems a robust multivariable controller is introduced for a class of distributed parameter systems the system to be controlled is given as dot x ax bu y cx in a banach space the purpose of the control which is based on the measurement y is to stabilize and regulate the system so that y t rightarrow y r as t rightarrow infty where y r is a constant reference vector under the assumptions that operator a generates a holomorphic stable semigroup b is linear and bounded c is linear and a bounded and the input and output spaces are of the same dimension a necessary and sufficient condition is found for the existence of a robust multivariable controller this controller appears to be a multivariable pi controller also a simple necessary criterion for the existence of a decentralized controller is derived the tuning of the controller is discussed and it is shown that the i part of the controller can be tuned on the basis of step responses without exact knowledge of the system s parameters the presented theory is then used as an example to control the temperature profile of a bar with the dirichlet boundary conditions

low gain integral control of well posed linear infinite dimensional systems with input and output nonlinearities abstract time varying low gain integral control strategies are presented for asymptotic tracking of constant reference signals in the context of exponentially stable well posed linear infinite dimensional single input single output systems subject to globally lipschitz nondecreasing input and output nonlinearities it is shown that applying error feedback using an integral controller ensures that the tracking error is small in a certain sense provided that a the steady state gain of the linear part of the system is positive b the reference value r is feasible in an entirely natural sense and c the positive gain function t k t is ultimately sufficiently small and not of class l 1 under a weak restriction on the initial data it is shown that a b and c ensure asymptotic tracking if additionally the impulse response of the linear part of the system is a finite signed borel measure the global lipschitz assumption on the output nonlinearity may be considerably relaxed

time varying and adaptive integral control of infinite dimensional regular linear systems with input nonlinearities closing the loop around an exponentially stable single input single output regular linear system subject to a globally lipschitz nondecreasing actuator nonlinearity and compensated by an integral controller with time dependent gain k t is shown to ensure asymptotic tracking of a constant reference signal r provided that a the steady state gain of the linear part of the system is positive b the reference value r is feasible in an entirely natural sense and c the function t mapsto k t monotonically decreases to zero at a sufficiently slow rate this result forms the basis of a simple adaptive control strategy that ensures asymptotic tracking under conditions a and b

dichotomy theorem for control sets abstract we introduce two notions of equi invariant sets and unstable sets for control systems and show that a control set with dense interior is either equi invariant or unstable this is the analogy to the well known dichotomy theorem for topological transitive dynamical systems an illustrative example is given to show that both of the two situations can occur

on robust pi control of infinite dimensional systems a pi controller is applied to a class of linear multivariable infinite dimensional minimum phase systems satisfying a generalized relative degree one condition it is shown that the closed loop system is stable and tracks asymptotically constant reference signals in the presence of asymptotically constant disturbances provided that the controller gains are sufficiently large it turns out that the closed loop system has nice robustness properties under high gain conditions in particular robustness criteria for external and internal stability are given if the closed loop system is subjected to perturbations induced by nonlinearities in the feedback loop the analysis is based on frequency domain as well as state space methods

stability analysis and numerical simulations of a one dimensional open channel hydraulic system abstract this paper is dedicated to the qualitative analysis as well as numerical simulations of a one dimensional open channel hydraulics system which is commonly used in hydraulic engineering to model the unsteady flow dynamics in a river first an output feedback control is proposed next the closed loop system is proved to possess a unique solution in a functional space furthermore the spectrum and resolvent sets of the system operator are characterized then stability results are stated and proved according to a smallness assumption on the feedback gain the proof invokes lyapunov direct method last but not least we adopt the chebychev collocation method that uses backward euler method and the gauss lobatto points to provide numerical simulations in order to ascertain the correctness of the theoretical outcomes

supercharacter theories of semiextraspecial p groups and frobenius groups abstract in this paper we describe all supercharacter theories of semiextraspecial p groups and frobenius groups we first review the constructions which will classify these supercharacter theories we then show that the supercharacter theories of these groups as well as the more general camina pairs must have nontrivial c normal subgroups next we examine the superclass structure to show that the supercharacter theory can be constructed from supercharacter theories of subgroups of the group and its quotient groups we can apply this to count the number of supercharacter theories for the group

a robust pi controller for infinite dimensional systems in this paper we deal with single input single output systems of the form on a separable hilbert space h where the operator a is the generator of an exponentially stable c0 semigroup on h b h c is a a admissible linear operator and w is an arbitrary constant disturbance vector in h we propose a low gain pi controller which stabilizes and regulates the system such that for a given reference constant yr y t tends to yr independently of w as t our result generalizes the previous one of pohjolainen 1982 in that the semigroup is not necessarily holomorphic a numerical example will be given to illustrate the application of the theory

a riesz basis methodology for proportional and integral output regulation of a one dimensional diffusive wave equation in this article we consider a dam river system modeled by a diffusive wave equation this model is commonly used in hydraulic engineering to describe dynamic behavior of the unsteady flow in a river for shallow water when the flow variations are not important in order to stabilize and regulate the system we propose a proportional and integral boundary controller contrary to many physical systems we end up with a nondissipative closed loop system with noncollocated actuators and sensors we show that the closed loop system is a riesz spectral system and generates an analytic semigroup then we shall be able to assign the spectrum of the closed loop system in the open left half plane to ensure its exponential stability as well as the output regulation independently of any known or unknown constant perturbation these results are illustrated by several numerical examples

a note on topological feedback entropy and invariance entropy abstract for discrete time control systems notions of entropy for invariance are compared one is based on feedbacks and the other one on open loop control functions under a strong invariance condition it is shown that they are essentially equivalent several modifications are also discussed

caratheodory pesin structures associated with control systems abstract we introduce five caratheodory pesin c p structures for control systems and show that the invariance entropy studied by colonius and kawan 2009 and the topological feedback entropy in colonius et al 2013 are just quantities generated by some special c p structures that give the characteristics of dimension types for these classical control entropies we explore some basic properties of these control entropies and investigate the relationships among these quantities in addition we also obtain a sufficient condition for the existence of a generator for the invariance entropy which was posed by kawan 2013 p 87 as an open question

an analog of nilpotence arising from supercharacter theory abstract the goal of this paper is to generalize several group theoretic concepts such as the center and commutator subgroup central series and ultimately nilpotence to a supercharacter theoretic setting and to use these concepts to show that there can be a strong connection between the structure of a group and the structure of its supercharacter theories we then use these concepts to show that the upper and lower annihilator series of j can be described in terms of certain central series for the algebra group g 1 j defined by s when s is the algebra group supercharacter theory defined by diaconis isaacs

adaptive low gain integral control of multivariable well posed linear systems the principle of low gain integral control for finite dimensional systems is well known more recently low gain integral control results have been obtained for classes of infinite dimensional systems in this paper we show that integral control with a simple and natural adaptation of the integrator gain achieves tracking of constant reference signals for every exponentially stable multivariable well posed infinite dimensional linear system whose steady state gain matrix has its spectrum in the open right half plane our results considerably extend improve and simplify previous work by the authors siam j control optim 35 1997 pp 78 116

low gain control of uncertain regular linear systems it is well known that closing the loop around an exponentially stable finite dimensional linear time invariant plant with square transfer function matrix bg s compensated by a controller of the form k s gamma 0 where k in bbb r and gamma 0 in bbb r mm will result in an exponentially stable closed loop system which achieves tracking of arbitrary constant reference signals provided that i all the eigenvalues of bg 0 gamma 0 have positive real parts and ii the gain parameter k is positive and sufficiently small in this paper we consider a rather general class of infinite dimensional linear systems called regular systems for which convenient representations are known to exist both in time and in frequency domain the purpose of the paper is twofold i we extend the above result to the class of exponentially stable regular systems and ii we show how the parameters k and gamma 0 can be tuned adaptively the resulting adaptive tracking controllers are not based on system identification or parameter estimation algorithms nor is the injection of probing signals required

exponential stabilization of laminated beams with structural damping and boundary feedback controls we study the boundary stabilization of laminated beams with structural damping which describes the slip occurring at the interface of two layered objects by using an invertible matrix function with an eigenvalue parameter and an asymptotic technique for the first order matrix differential equation we find out an explicit asymptotic formula for the matrix fundamental solutions and then carry out the asymptotic analyses for the eigenpairs furthermore we prove that there is a sequence of generalized eigenfunctions that forms a riesz basis in the state hilbert space and hence the spectrum determined growth condition holds furthermore exponential stability of the closed loop system can be deduced from the eigenvalue expressions in particular the semigroup generated by the system operator is a c 0 group due to the fact that the three asymptotes of the spectrum are parallel to the imaginary axis

nondissipative torque and shear force controls of a rotating flexible structure this paper is concerned with the feedback stabilization problem of a rotating disk with a flexible beam attached to its center we propose a torque control applied on the disk and a shear force control exerted at the free end of the beam which lead to a nondissipative closed loop system despite this situation we prove that the system can be nonuniformly exponentially stabilized provided that the angular velocity of the disk is less than the square root of the first eigenvalue of the self adjoint positive operator of the open loop system this result is illustrated by a set of numerical simulations