conditions for the equivalence of internal and external stability for distributed parameter systems conditions are given on a controlled observed distributed parameter system under which external stability also known as input output stability implies internal stability which is the exponential stability of the underlying semigroup generator it is shown that when the system satisfies a general definition of stabilizability and detectability external stability is equivalent to internal stability unlike the case previous definitions of stabilizability and detectability a system which satisfies these does not necessarily have a spectrum decomposition therefore in order to check internal stability it is often sufficient to check the boundedness of the transfer function in the right half complex plane this is illustrated with a simple example

an adaptive tracking problem with a control input constraint abstract in this paper we consider the problem of controlling an uncertain linear time invariant lti continuous time plant when there is a control input constraint a switching controller is presented which will carry out asymptotic error regulation for constant reference and constant disturbance signals which are compatible with the control input constraint assuming that i the plant is asymptotically stable ii the plant has no transmission zeros at zero and iii the plant has as many inputs as outputs this controller is quite easy to implement especially in the single input single output siso case and is noise tolerant some examples including a model of a three input three output distillation column are included to illustrate the controller behaviour

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

admissibility of unbounded control operators for linear systems described by dot x t ax t bu t where a generates a semigroup on the state space x and b is an unbounded operator some necessary as well as some sufficient conditions are given for b to be admissible i e for any t the state x t should be in x and should depend continuously on the input u in l p this approach begins with an axiomatic description of such a system in terms of a functional equation the results are applied to the wave equation on a bounded interval

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

envelope theorems for arbitrary choice sets the standard envelope theorems apply to choice sets with convex and topological structure providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative this paper studies optimization with arbitrary choice sets and shows that the traditional envelope formula holds at any differentiability point of the value function we also provide conditions for the value function to be variously absolutely continuous left and right differentiable or fully differentiable these results are applied to mechanism design convex programming continuous optimization problems saddle point problems problems with parameterized constraints and optimal stopping problems

optimization of convex risk functions we consider optimization problems involving convex risk functions by employing techniques of convex analysis and optimization theory in vector spaces of measurable functions we develop new representation theorems for risk models and optimality and duality theory for problems with convex risk functions

regression analysis likelihood error and entropy in a regression with independent and identically distributed normal residuals the log likelihood function yields an empirical form of the mathcal l 2 norm whereas the normal distribution can be obtained as a solution of differential entropy maximization subject to a constraint on the mathcal l 2 norm of a random variable the mathcal l 1 norm and the double exponential laplace distribution are related in a similar way these are examples of an inter regenerative relationship in fact mathcal l 2 norm and mathcal l 1 norm are just particular cases of general error measures introduced by rockafellar et al finance stoch 10 1 51 74 2006 on a space of random variables general error measures are not necessarily symmetric with respect to ups and downs of a random variable which is a desired property in finance applications where gains and losses should be treated differently this work identifies a set of all error measures denoted by mathscr e and a set of all probability density functions pdfs that form inter regenerative relationships through log likelihood and entropy maximization it also shows that m estimators which arise in robust regression but in general are not error measures form inter regenerative relationships with all pdfs in fact the set of m estimators which are error measures coincides with mathscr e on the other hand m estimators are a particular case of l estimators that also arise in robust regression a set of l estimators which are error measures is identified it contains mathscr e and the so called trimmed mathcal l p norms

optimality conditions in portfolio analysis with general deviation measures optimality conditions are derived for problems of minimizing a general measure of deviation of a random variable with special attention to situations where the random variable could be the rate of return from a portfolio of financial instruments general measures of deviation go beyond standard deviation in satisfying axioms that do not demand symmetry between ups and downs the optimality conditions are applied to characterize the generalized master funds which elsewhere have been developed in extending classical portfolio theory beyond the case of standard deviation the consequences are worked out for deviation based on conditional value at risk and its variants in particular

robust stability of systems with integral control a number of necessary and sufficient conditions are derived which must be satisfied by the plant d c gain matrix of a linear time invariant system in order for an integral controller to exist for which the closed loop system is stable based on these results the robustness of integral control systems is analyzed i e the family of plants is defined which are stable when controlled with the same integral controller conditions for actuator sensor failure tolerance of systems with integral control are also given finally parallels are drawn between the results of this paper and the bifurcation theory of nonlinear systems

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

circle criteria small gain conditions and internal stability for infinite dimensional systems abstract an internal version of the small gain theorem is given for a class of plants including time delay and distributed systems more precisely it is shown that for a large class of infinite dimensional state space systems the small gain condition in l 2 is sufficient for internal stability furthermore it is proved that there exist unstable feedback systems of loop gain equal to one the internal version of the small gain theorem is used in order to establish that the circle criterion is sufficient for global exponential stability

transfer functions of regular linear systems part i characterizations of regularity we recall the main facts about the representation of regular linear systems essentially that they can be described by equations of the form x t ax t bu t y t cx t du t like finite dimensional systems but now a b and c are in general unbounded operators regular linear systems are a subclass of abstract linear systems we define transfer functions of abstract linear systems via a generalization of a theorem of foures and segal we prove a formula for the transfer function of a regular linear system which is similar to the formula in finite dimensions the main result is a simple to state but hard to prove necessary and sufficient condition for an abstract linear system to be regular in terms of its transfer function other conditions equivalent to regularity are also obtained the main result is a consequence of a new tauberian theorem which is of independent interest

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

sensitivity analysis in applications with deviation risk regret and error measures the envelope formula is obtained for optimization problems with positively homogeneous convex functionals defined on a space of random variables those problems include linear regression with general error measures and optimal portfolio selection with the objective function being either a general deviation measure or a coherent risk measure subject to a constraint on the expected rate of return the obtained results are believed to be novel even for markowitz s mean variance portfolio selection but are far more general and include explicit envelope relationships for the rates of return of portfolios that minimize lower semivariance mean absolute deviation deviation measures of cal l p type and semi cal l p type and conditional value at risk in each case the envelope theorem yields explicit estimates for the absolute value of the difference between deviation risk of optimal portfolios with the unperturbed and perturbed asset probability distributions in terms of a norm of the perturbation

bilinear analysis for kernel selection and nonlinear feature extraction this paper presents a unified criterion fisher kernel criterion fkc for feature extraction and recognition this new criterion is intended to extract the most discriminant features in different nonlinear spaces and then fuse these features under a unified measurement thus fkc can simultaneously achieve nonlinear discriminant analysis and kernel selection in addition we present an efficient algorithm fisher kernel analysis fka which utilizes the bilinear analysis to optimize the new criterion this fka algorithm can alleviate the ill posed problem existed in traditional kernel discriminant analysis kda and usually has no singularity problem the effectiveness of our proposed algorithm is validated by a series of face recognition experiments on several different databases

robust controller for boundary control systems some basic results of robust controller theory are generalized to distributed parameter systems with unbounded control and perturbation operators the theory presented is then applied to the construction of a flow adaptive robust controller for heat exchangers

tracking and disturbance rejection of mimo nonlinear systems with pi controller we study tracking and disturbance rejection of a class of mimo nonlinear systems with linear proportional plus integral pi compensator roughly speaking we show that if the given nonlinear plant is exponentially stable and has a strictly increasing dc steady state i o map then a simple pi compensator can be used to yield a stable unity feedback closed loop system which asymptotically tracks reference inputs that tend to constant vectors and asymptotically rejects disturbances that tend to constant vectors

subdifferential calculus rules in convex analysis a unifying approach via pointwise supremum functions we provide a rule to calculate the subdifferential set of the pointwise supremum of an arbitrary family of convex functions defined on a real locally convex topological vector space our formula is given exclusively in terms of the data functions and does not require any assumption either on the index set on which the supremum is taken or on the involved functions some other calculus rules namely chain rule formulas of standard type are obtained from our main result via new and direct proofs

robustness of linear systems abstract in this paper we consider linear systems which are stable and examine the robustness of this property the perturbations are assumed to have unbounded structure and we determine the smallest perturbation which destroys stability we begin with an abstract analysis of the problem but in later sections specialize to three types of systems those whose mild solutions are given in terms of 1 a strongly continuous semigroups 2 b resolvent operators integrodifferential systems 3 c evolution operators time varying systems for b a banach space l2 t0 t b denotes the space of all square integrable functions defined on t0 t with values in b for b1 b2 banach spaces t0 t denotes the space of strongly measurable functions f t0 t l b1 b2 with ess sup f b 1 t0 l b1 b2 denotes the space of strongly measurable functions f t0 l b1 b2 with f t 0 and k l1 t0

tuning of multivariable pi controllers for unknown delay differential systems a design method for tuning of multivariable pi controllers for possibly unknown linear time invariant delay differential systems is presented the plant is assumed to be stable with input and output delays and subject to step disturbances the multivariable pi controller may be tuned with the aid of open loop step responses the stability and robustness of the control law is discussed and an example is given to show the applicability of the controller

discrete time and sampled data low gain control of infinite dimensional linear systems in the presence of input hysteresis we introduce a general class of causal dynamic discrete time nonlinearities which have certain monotonicity and lipschitz continuity properties in particular the discretizations of a large class of continuous time hysteresis operators obtained by applying the standard sampling and hold operations belong to this class it is shown that closing the loop around a power stable linear infinite dimensional discrete time single input single output system subject to an input nonlinearity from the class under consideration and compensated by a discrete time integral controller guarantees asymptotic tracking of constant reference signals provided that a the positive integrator gain is sufficiently small and b the reference value is feasible in a very natural sense we apply this result in the development of sampled data low gain integral control for exponentially stable regular linear infinite dimensional continuous time systems subject to input hysteresis

discrete time low gain control of uncertain infinite dimensional systems using a frequency domain analysis it is shown that the application of a feedback controller of the form k z 1 or kz z 1 where k spl isin r to a power stable infinite dimensional discrete time system with square transfer function matrix g z will result in a power stable closed loop system which achieves asymptotic tracking of arbitrary constant reference signals provided that i all the eigenvalues of g 1 have positive real parts and ii the gain parameter k is positive and sufficiently small moreover if g 1 is positive definite we show how the gain parameter gain x can be tuned adaptively the resulting adaptive tracking controllers are universal in the sense that they apply to any power stable system with g 1 0 in particular they are not based on system identification or plant parameter estimation algorithms nor is the injection of probing signals required finally we apply these discrete time results to obtain adaptive sampled data low gain controllers for the class of regular systems a rather general class of infinite dimensional continuous time systems for which convenient representations are known to exist both in state space and in frequency domain we emphasize that our results guarantee not only asymptotic tracking at the sampling instants but also in the sampling interval

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