two degrees of freedom dead beat control system with robustness this paper deals with the design of a two degrees of freedom tdf dead beat controller with both optimal robustness and minimum settling time based on the parametrization of all stabilizing tdf controllers optimal robustness and minimum time control are achieved simultaneously the minimum time dead beat control is constructed for arbitrary real rational reference input at the same time optimal robustness is achieved under the constraint that the error between reference input and output asymptotically vanishes for any plant perturbation that does not violate the internal stability it is proved that under the same robustness criterion irrespective of its length of settling time the optimal robustness of the tdf system is always superior to that of the one degree of freedom odf system as long as its settling time is finite and they become identical only when the settling time of the odf system goes to infinity a numerical example is given to illustrate the theoretical results

inference in dynamic models containing surprise variables abstract some new results on calculating moving average representation mar coefficients and their limiting distribution from estimated vector arma processes are presented the technique is applied to the problem of estimating the coefficients of unanticipated or surprise variables in a single equation for a multi period expectations horizon the method naturally conditions the expectations on all past values of the process and avoids the necessity of using two step regression procedures and adjusting the resulting standard errors

robust stability of additively perturbed interconnected systems the concept of generalized block diagonal dominance is used to derive robust stability results for additively perturbed interconnected systems these results characterize the robustness of interconnected systems by putting upper bounds on the spectral norms of the various subblocks of admissible perturbations

consistent estimation of equations with composite moving average disturbance terms abstract the paper examines the circumstances under which an equation with a composite ma disturbance term can be consistently estimated by single equation non linear least squares the composite disturbance may arise as a result of the dependent or an explanatory variable being unobservable either because it is subject to measurement error or because it is a desired or expected variable it may also arise as a result of substituting out an explanatory variable from an equation or because a vector ma process is specified for the structural form of a linear simultaneous equation model the argument of the paper relies on some results relating to the sum of finite ma processes presented in nelson 1975a and darroch and mcdonald 1981

global stabilization with almost disturbance decoupling of a class of uncertain non linear systems in this paper we study the global stabilization of a class of non linear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy the class of non linear systems considered could be viewed as a generalization of uniform rank multivariable linear systems which have the property that all their infinite zeros are of the same order although the plants considered are non linear the compensator developed here is linear our compensator which achieves global exponential stability and almost disturbance decoupling of the output requires only output feedback rather than full state feedback model uncertainty is dealt with either by restricting the uncertain elements to particular subspaces satisfying the so called matching conditions and or by treating a family of plants for which a single controller simultaneously globally exponentially stabilizes all the plants in while achieving almost disturbance decoupling of the output

optimal stochastic control for performance and stability robustness a design method for discrete time control systems that maintain stability with minimum performance degradation in the presence of a variety of deterministic and stochastic perturbation disturbances is presented deterministic perturbation and modeling errors are represented by maximum deviations from a nominal linear discrete time system and stochastic perturbations are modeled by generalization of the sector bound nonlinearity concept to the stochastic case based on the given bounds on deterministic and stochastic perturbations an upper bound on the quadratic performance index which is useful in assessing the performance deterioration according to the feedback gain used is found then the optimal feedback gain which minimizes this bound on the performance index is derived in the time invariant case the existence of a stabilizing property of the bound optimal controller which is obtained by minimizing an average cost per stage is shown

independent parameterization of two degree of freedom compensators in general robust tracking systems consideration is given to a general robust tracking problem in which the controlled object is a linear multivariable system having measured variables that are not necessary coincident with the output variables to be controlled a necessary and sufficient condition for the two degree of freedom compensator to achieve a robust tracking system with internal stability is given an existence condition is derived for such a compensator and the class of all such compensators is parameterized so that two specifications with respect to responses for reference commands and feedback properties can be satisfied independently by the two free parameters

stability robustness of lq optimal regulators for the performance index with cross product terms suggested are the guaranteed stability margins of lq optimal regulators for the performance index with cross product terms using modified return difference equality sufficient conditions to guarantee the required stability margins are presented as well as the conditions to guarantee the stability margins of standard lq optimal regulators an example for lq optimal control of a dc motor system is given to demonstrate how the weighting matrices can be chosen to guarantee the required stability margins

a multiloop generalization of the circle criterion for stability margin analysis in order to provide a theoretical tool well suited for use in characterizing the stability margins e g gain and phase margins of multiloop feedback systems multiloop input output stability results generalizing the circle stability criterion are considered generalized conic sectors with centers and radii determined by linear dynamical operators are employed to enable an engineer to specify the stability margins which he desires as a frequency dependent convex set of modeling errors including nonlinearities gain variations and phase variations which the system must be able to tolerate in each feedback loop without instability the resulting stability criterion gives sufficient conditions for closed loop stability in the presence of such frequency dependent modeling errors even when the modeling errors occur simultaneously in all loops so for example stability is assured as loop gains and phases vary throughout a set of nonzero measure whose boundaries are frequency dependent the stability conditions yield an easily interpreted scalar measure of the amount by which a muitiloop system exceeds or falls short of its stability margin specifications

optimal disturbance reduction in linear multivariable systems this paper presents a computational solution to an important optimization problem arising in optimal sensitivity theory the approach is to treat the multivariable problem exactly as the scalar problem in that stability constraints are handled via interpolation the resulting computations are easily implemented using existing methods

stability and performance robustness for multivariable linear systems abstract this paper deals with both aspects of stability and performance robustness of linear systems in the time domain a linear time invariant feedback control law which yields the largest set of parameter variations is first determined it is then used as an initial guess for designing a robust control law which produces satisfactory performance for each of several operating points of the system given a priori the stability robustness properties of the resulting control law is also studied the proposed approach is applied to an example yielding larger stability bounds including satisfactory performance in comparison with recently reported results

on the inequality of cover and hart in nearest neighbor discrimination when x1 1 xn n are independent identically distributed random vectors from ird x 0 1 distributed as x and when is estimated by its nearest neighbor estimate 1 then cover and hart have shown that p 1 n 2e x 1 x 2r 1 r where r is the bayes probability of error and x p 1 x x they have conditions on the distribution of x we give two proofs one due to stone and a short original one of the same result for all distributions of x if ties are carefully taken care of we also show that p 1 x1 1 xn n converges in probability to a constant for all distributions of x thereby strengthening results of wagner and fritz

on the loop transfer recovery one method of model based compensator design for linear multivariate systems consists of state feedback design and observer design athans 1971 a key step in recent work in multivariate synthesis involves selecting an observer gain so the final loop transfer function is the same as the state feedback loop transfer function doyle and stein 1979 goodman 1984 this is called loop transfer recovery ltr this paper shows how identification of the eigenstructure of the compensators that achieve ltr makes possible a design procedure for observer gain luenberger 1971 this procedure is based on the eigenstructure assignment of the observers the sufficient condition for ltr and the stability of the closed loop system is that the plant be minimum phase the limitation of this method might arise when the plant has multiple transmission zeros

robustness of discrete time systems for unstructured stochastic perturbations several stochastic stability robustness measures are presented for nominally exponentially stable linear discrete time systems with unstructured perturbations having second moment bounds dependence of these measures on the stability degree of the nominal system and other parameters used in the procedure is illustrated by using the time evolution of the second moment of the system state and stochastic lyapunov stability results positive super martingale convergence theorems the ability of nominally exponentially stable systems to maintain stability in the presence of unstructured stochastic linear and nonlinear perturbations is demonstrated quantitative results are given to determine the maximum modeling uncertainty which can be tolerated in design upper bounds on the second moments of stochastic perturbations to maintain the mean square and almost sure stability of these systems in the presence of unstructured perturbations are obtained

optimal pole shifting for continuous multivariable linear systems a method for shifting the real parts of the open loop poles to any desired positions while preserving the imaginary parts is presented the method is based on the mirror image property which has been reported by molinari in other words molinari s results are extended and then a recursive approach is developed in each step of this approach it is required to solve a first order or a second order linear matrix lyapunov equation for shifting one real pole or two complex conjugate poles respectively the presented method yields a solution which is optimal with respect to a quadratic performance index the attractive feature of this method is that it enables solutions to complex problems to be easily found without solving any non linear algebraic riccati equation

design of robust state feedback laws existence criteria and computational methods are presented for finding stabilizing state feedback laws for systems with uncertain state or control matrices the uncertainties are modelled as sector bounded non linearities and feedback laws ensuring global asymptotic closed loop stability are obtained using lyapunov e direct method the algorithms essentially amount to repeatedly solving a parameter dependent riccati equation until the maximal solution becomes positive definite

robust stabilizability for a class of transfer functions this paper is concerned with the robust stabilizability for single input single output plants robust stabilizability means that a fixed controller can stabilize simultaneously all the plants in a given class which is characterized by a frequency dependent uncertainty band function around the transfer function of a nominal model a necessary and sufficient condition for robust stabilizability is derived based on the well known nevanlinna pick theory in classical analysis it is shown that the values of the uncertainty band function should be restricted within a certain range at the unstable poles of the nominal model in order for the class to be robustly stabilizable a procedure of synthesizing a robust stabilizer is given and the parametrization of all the robust stabilizers is also shown

choice of the smoothing parameter and efficiency of k nearest neighbor classification abstract a simulation study was performed to investigate the sensitivity of the k nearest neighbor nn k rule of classification to the choice of k the optimal choice of k was found to be a function of the dimension of the sample space the size of the space the covariance structure and the sample proportions the nearest neighbor rules chosen using the k suggested by the simulations had correct classification rates at least as high as those rates for the linear discriminant function and the logistic regression method in particular the rule became more efficient as the difference in the covariance matrices increased and also when the difference in sample proportion was large an adaptive rule which selects k by iteratively maximizing the local mahalanobis distance is shown to be efficient thus abrogating the need to know the underlying population variance covariance structure

repetitive control system a new type servo system for periodic exogenous signals a control scheme called repetitive control is proposed in which the controlled variables follow periodic reference commands a high accuracy asymptotic tracking property is achieved by implementing a model that generates the periodic signals of period l into the closed loop system sufficient conditions for the stability of repetitive control systems and modified repetitive control systems are derived by applying the small gain theorem and the stability theorem for time lag systems synthesis algorithms are presented by both the state space approach and the factorization approach in the former approach the technique of the kalman filter and perfect regulation is utilized while coprime factorization over the matrix ring of proper stable rational functions and the solution of the hankel norm approximation are used in the latter one

parametrization of stabilizing controllers for multivariable servo systems with two degrees of freedom a necessary and sufficient condition for the existence of a servo controller is derived using the fractional representation approach for the plant whose measured variables are not necessarily coincident with its controlled outputs an independent parametrization of the servo controllers and the attainable transfer characteristics is proposed the possible classes of all controllers with integrity in the error channel or measured output channel is also clarified using the derived parametrization

a feedback theory of two degree of freedom optimal wiener hopf design the design of linear two degree of freedom stabilizing controllers is treated in a quadratic cost setting the class of all such controllers which give finite cost is established and the tradeoff possible between optimum performance tracking cost sensitivity and stability margins is discussed

robustness results in linear quadratic gaussian based multivariable control designs the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity in particular robustness results associated with multivariable control systems designed on the basis of linear quadratic lq and the linear quadratic gaussian lqg design methodologies are presented

large sample estimation and testing procedures for dynamic equation systems abstract joint two step estimation procedures which have the same asymptotic properties as the maximum likelihood ml estimator are developed for the final equation transfer function and structural form of a multivariate dynamic model with normally distributed vector moving average errors the ml estimator under fixed and known initial values is obtained by iterating the procedure until convergence the asymptotic distribution of the two step estimators is used to construct large sample testing procedures for the different forms of the model

on the asymptotic probability of error in nonparametric discrimination let x y x 1 y 1 cdots x n y n be independent identically distributed random vectors from r d times 0 1 and let hat y be the k nearest neighbor estimate of y from x and the x i y i s we show that for all distributions of x y the limit of l n p hat y neq y exists and satisfies lim n rightarrow infty l n leq 1 a k r ast a k frac alpha sqrt k k 3 25 big 1 frac beta sqrt k 3 big k text odd k geq 5 where r ast is the bayes probability of error and alpha 0 3399 cdots and beta 0 9749 cdots are universal constants this bound is shown to be best possible in a certain sense

lqg controller synthesis with plant and noise spectral uncertainties in this paper we consider the problem of robust controller synthesis with plant and noise spectral uncertainties in lqg optimal systems we frame an algorithm for synthesizing the robust controller to minimize the least favourable cost functional j via specifying the weighting matrices q and r the wiener hopf technique in the lqg optimal system the saddle point theory and a property of the contractive operator are employed to solve this problem

loop shaping design related to lqg ltr for siso minimum phase plants one method of model based compensator design for linear systems consists of two stages state feedback design and observer design a key issue in recent work in multivariable synthesis involves selecting the observer state feedback gain so that the final loop transfer function is the same as the state feedback observer loop transfer function this is called loop transfer recovery ltr athans and stein 1987 kazerooni and houpt 1986 kazerooni et al 1985 doyle and stein 1981 this paper shows how identification of the internal mechanism of the ltr provides simple design rules with little algebra for single input single output siso systems in the siso case the lqg ltr reduces to computation of a compensator that shapes the loop transfer function by i cancelling the zeros of the plant with the compensator poles and ii locating a new set of zeros for the compensator to shape the loop transfer function

on robust asymptotic tracking perturbations on coprime factors and parameterization of all solutions the robust asymptotic tracking problem is analyzed in this paper relative to unstructured perturbations on each coprime factor of the transfer functions from the control input to the measured and controlled outputs in each case necessary and sufficient conditions for the existence of solutions are presented which are explicitly given in terms of problem data under such conditions explicit parameterizations are given of all controllers which achieve robust asymptotic tracking in terms of free rational proper and stable matrices

feedback representation of precompensators the general case using the transfer approach we give under internal stability conditions a necessary and sufficient condition of equivalence between open loop precom pensation and a closed loop configuration that consists of dynamic output feedback and inside loop precompensation our result is the generalization of hammer s result hammer 1983 to the general case this result emphases the use of skew prime relationships the parametrization of this problem s solutions will throw new light on multipurpose controllers

two degree of freedom dead beat control system with robustness multivariable case abstract a design procedure for two degree of freedom tdf dead beat controllers for multivariable systems is presented based on the parametrization of all stabilizing tdf controllers a minimal time dead beat control system with optimal robustness is constructed for an arbitrary reference input the optimal robustness is achieved under the constraint of robust tracking a comparison of a tdf system with a one degree of freedom odf system reveals that under the same robustness criterion the optimal robustness of the tdf system is always superior to that of the odf system irrespective of its settling time it is also shown that the optimal robustness of the odf system becomes identical to that of the tdf only when the settling time of the odf system goes to infinity some numerical examples are given to illustrate the theoretical results

right half plane poles and zeros and design tradeoffs in feedback systems this paper expresses limitations imposed by right half plane poles and zeros of the open loop system directly in terms of the sensitivity and complementary sensitivity functions of the closed loop system the limitations are determined by integral relationships which must be satisfied by these functions the integral relationships are interpreted in the context of feedback design

a class discriminality measure based on feature space partitioning this paper presents a new class discriminability measure based on an adaptive partitioning of the feature space according to the available class samples it is intended to be used as a criterion in a classifier independent feature selection procedure the partitioning is performed according to a binary splitting rule and appropriate stopping criteria results from several tests withc gaussian and non gaussian multidimensional and multicalss computer generated samples were very similar to those obtained using a bayes error criterion function i e the optimal feature subsets selected by both criterion functions were the same the main advantage of the new measure is that it is computationally efficient

large sample estimation and testing procedures for dynamic equation systems abstract in 1980 palm and zellner presented a number of joint or system estimation and testing procedures for the final equations transfer functions and structural equations of a multivariate dynamic model with normally distributed vector moving average errors in this paper we show that there is a flaw in their argument which renders most of the procedures invalid possible alternative procedures are described

robustness with simultaneous pole and zero movement across the jω axis in this paper we present some new tests for assessing the robustness of the stability property of a feedback design the tests offer a wider scope of application than those previously described in the literature the main result is a robustness test which can be used to assess closed loop stability when the nominal plant model and perturbed plant model representing uncertainty have different numbers of poles and zeros in the right half plane this test also indicates over which frequencies good sensitivity and robust stability are compatible objectives and over which frequencies a compromise has to be made contrary to popular belief if there are no uncertain zeros which can move across the imaginary axis then good sensitivity and robust stability are compatible objectives over the same frequencies

the majorant lyapunov equation a nonnegative matrix equation for robust stability and performance of large scale systems a new robust stability and performance analysis technique is developed the approach involves replacing the state covariance by its block norm matrix i e the nonnegative matrix whose elements are the norms of subblocks of the covariance matrix partitioned according to subsystem dynamics a bound i e majorant for the block norm matrix is given by the majorant lyapunov equation a lyapunov type nonnegative matrix equation existence uniqueness and computational tractability of solutions to the majorant lyapunov equation are shown to be completely characterized in terms of m matrices two examples are considered for a damped simple harmonic oscillator with uncertain but constant natural frequency the majorant lyapunov equation predicts unconditional stability and for a pair of nominally uncoupled oscillators with uncertain coupling the majorant lyapunov equation shows that the range of nondestabilizing couplings is proportional to the frequency separation between the oscillators a result not predictable from quadratic or vector lyapunov functions

a probabilistic nearest neighbour method for statistical pattern recognition summary nearest neighbour algorithms are among the most popular methods used in statistical pattern recognition the models are conceptually simple and empirical studies have shown that their performance is highly competitive against other techniques however the lack of a formal framework for choosing the size of the neighbourhood k is problematic furthermore the method can only make discrete predictions by reporting the relative frequency of the classes in the neighbourhood of the prediction point we present a probabilistic framework for the k nearest neighbour method that largely overcomes these difficulties uncertainty is accommodated via a prior distribution on k as well as in the strength of the interaction between neighbours these prior distributions propagate uncertainty through to proper probabilistic predictions that have continuous support on 0 1 the method makes no assumptions about the distribution of the predictor variables the method is also fully automatic with no user set parameters and empirically it proves to be highly accurate on many bench mark data sets

algebraic theory of linear multivariable feedback systems this paper presents an algebraic theory for analysis and design of linear multivariable feedback systems the theory is developed in an algebraic setting sufficiently general to include as special cases continuous and discrete time systems both lumped and distributed designs are implemented by construction of a controller with two vector inputs and one vector output use of controllers of this type is shown to generate convenient stability results and convenient global parametrizations of all i o maps and all disturbance to output maps achievable for a given plant by a stabilizing compensator these parametrizations are then used to show that any such i o map and any such disturbance to output map may be simultaneously realized by choice of an appropriate controller in the special case of lumped systems it is shown that the design theory can be reduced to manipulations involving polynomial matrices only the resulting design procedure is thus shown to be more efficient computationally finally the problem of asymptotically tracking a class of input signals is considered in the general algebraic setting it is shown that the classical results on asymptotic tracking can be generalized to this setting additionally sufficient conditions for robustness of asymptotic tracking and robustness of stability are developed