almost invariant subspaces an approach to high gain feedback design part ii almost conditionally invariant subspaces in part i of this paper almost controlled invariant subspaces were studied in this part we will consider their duals the almost conditionally invariant subspaces these concepts give immediately by dualization of the almost disturbance decoupling control by state feedback the solution of the almost disturbance decoupled estimation problem finally we consider the problem of approximate disturbance decoupling by measurement feedback and it is shown that this problem is solvable to any arbitrary degree of accuracy if and only if 1 almost disturbance decoupling by state feedback and 2 almost disturbance decoupled estimation of the to be controlled output are both possible

proof of a conjecture of wohltmann on target path controllability we prove that a sufficient condition for target path controllability as defined by h w wohltmann is also necessary

nonstationary discrete time deterministic and stochastic control systems bounded and unbounded cases this paper is about nonstationary nonlinear discrete time deterministic and stochastic control systems with borel state and control spaces with either bounded or unbounded costs the control problem is to minimize an infinite horizon total cost performance index using dynamic programming arguments we show that under suitable assumptions the optimal cost functions satisfy optimality equations which in turn give a procedure to find optimal control policies we also prove the convergence of value iteration or successive approximations functions several examples illustrate our results under different sets of assumptions

a technique for establishing completeness results in theorem proving with equality it is proved that an automatic theorem proving system consisting of resolution paramodulation factoring equality reversal simplification and subsumption removal is complete in first order logic with equality when restricted to equality units the system is similar to the knuth bendix procedure for deriving consequences from equalities however our proofs of completeness are restricted to the case in which the ordering on words terms or atoms that is required in this type of process is order isomorphic to the positive integers the completeness of resolution and paramodulation without the functionally reflexive axioms is a simple corollary of our result the methods used are based upon the familiar ideas associated with semantic trees and should be helpful in showing that other theorem proving systems with equality are complete

stabilizability and detectability of discrete time time varying systems stabilizability and detectability for discrete time varying systems are discussed these concepts are introduced by decomposing the state space of the system into three orthogonal subspaces this allows an intuitive interpretation and shows the difficulties which occur when general stabilizability and detectability properties are derived a counterexample is given to show that a previously published claim that the time varying discrete time kalman filter is exponentially stable under the conditions of uniform stabilizability and uniform detectability is incorrect

investigation of an adaptive sampling method for data interpolation using radial basis functions an adaptive sampling method is presented for optimizing the location of data points in parameter space for multidimensional data interpolation the method requires a small number of points to begin and achieves a compromise between space filling updates and local refinement in areas where the data are nonlinear as measured by the laplacian a smooth separation function quantifies the sample spacing and this is blended with the laplacian to form a criterion on which to assess potential new sample positions validation results are presented using two dimensional analytic test cases which demonstrate that the method can recover known optimal designs and gives improvement over data independent approaches in addition a detailed analysis of the various model parameters is presented initial findings are very promising and it is hoped that further work using the method to generate an aerodynamic database using cfd simulations will lead to a reduction in the number of points required for a given modelling accuracy

bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments abstract this article is concerned with prediction of a function y t over a multidimensional domain t given the function values at a set of sites t 1 t 2 t n in t and with the design that is with the selection of those sites the motivating application is the design and analysis of computer experiments where t determines the input to a computer model of a physical or behavioral system and y t is a response that is part of the output or is calculated from it following a bayesian formulation prior uncertainty about the function y is expressed by means of a random function y which is taken here to be a gaussian stochastic process the mean of the posterior process can be used as the prediction function t and the variance can be used as a measure of uncertainty this kind of approach has been used previously in bayesian interpolation and is strongly related to the kriging methods used in geostatistics here emphasis is placed on product linear and product cubic correlation func

control aspects of linear discrete time varying systems results for time invariant linear systems concerning controllability reachability output controllability stabilizability and target path controllability are extended to time varying systems for the extensions which are already known in the literature elementary proofs are given moreover necessary and sufficient conditions are given for the strong admissibility of a target path

comments on functional reproducibility of time varying input output systems recent results on solvability developed as part of a conjecture of k a grasse siam j contr optimiz vol 26 p 230 249 1988 on the necessity of certain rank conditions is answered for an important class of systems a simpler description of the derivative arrays is presented an alternative way of computing the control producing a given output is presented

nonstationary discrete time deterministic and stochastic control systems with infinite horizon this article is about nonstationary nonlinear discrete time deterministic and stochastic control systems with borel state and control spaces possibly noncompact control constraint sets and unbounded costs the control problem is to minimise an infinite horizon total cost performance index using dynamic programming arguments we show that under suitable assumptions the optimal cost functions satisfy optimality equations which in turn give a procedure to find optimal control policies

refutational theorem proving using term rewriting systems abstract in this paper we propose a new approach to theorem proving in first order logic based on the term rewriting method first for propositional calculus we introduce a canonical term rewriting system for boolean algebra this system enables us to transform the first order predicate calculus into a form of equational logic and to develop several complete strategies both clausal and nonclausal for first order theories based on the knuth bendix completion procedure more importantly our strategies can deal with predicate logic and built in equational theories in a uniform and effective way we also describe an implementation and comparisons with some other first order theorem proving methods

a geometric approach to the singular filtering problem we consider the least squares filtering problem for a stationary gaussian process when the observation is not fully corrupted by white noise the so called singular case an optimal estimator is constructed consisting of an integrating part which is as in the regular case computed from a spectral factorization or an equivalent matrix problem and a differentiating part whose parameters are computed from a single matrix equation this improves on older results which either work under restrictive assumptions or describe the solution only as the result of some nested algorithm

fuzzy term rewriting system abstract this paper provides an approach to treat fuzzy equality in first order logic specially in a theory in which only equality occurs as a predicate symbol namely equational theory fuzzy term rewriting systems frs that is the set of left to right directional equations are also discussed finally a fuzzy recognition algorithm is presented by applying frs which shows its potential use

target path controllability of linear time varying dynamical systems the purpose of this paper is to derive necessary and sufficient conditions for target path controllability tpc of time varying dynamical systems and to relate the results to those of brockett and mesarovic in 1965 it is shown that conditions for tpc in w p 1 by means of lp controls are easy to verify but are very strong tpc implies that the number of target variables is less than or equal to the number of control variables

comparison of adaptive sampling methods for generation of surrogate aerodynamic models a surrogate modeling strategy using effective interpolation and sampling methods facilitates a reduction in the number of computational fluid dynamics simulations required to construct an aerodynamic model to a specified accuracy in this paper two adaptive sampling strategies are compared for generating surrogate models based on kriging and radial basis function interpolation respectively the relationships between the two model formulations are discussed and three test cases are considered including analytic functions and recovery of aerodynamic coefficients for two example applications longitudinal flight mechanics analysis for the dlr f12 aircraft and structural loads analysis of an rae2822 airfoil for the airfoil example models of cl cd and cm were constructed with the two sampling strategies using euler boundary layer coupled computational fluid dynamics and a three dimensional flight envelope of incidence mach and reynolds number the two sampling approaches direct some samples toward

orderings for term rewriting systems abstract methods of proving that a term rewriting system terminates are presented they are based on the intuitive notion of simplification orderings orderings in which any term that is syntactically simpler than another is smaller than the other as a consequence of kruskal s tree theorem any nonterminating system must be self embedding in the sense that it allows for the derivation of some term from a simpler one thus termination is guaranteed if every rule in the system is a reduction in some simplification ordering most of the orderings that have been used for proving termination are indeed simplication orderings using this notion often allows for much easier proofs a particularly useful class of simplification orderings the recursive path orderings is defined examples of the use of simplication orderings in termination proofs are given

reproducibility of linear and nonlinear input output systems a control system may be viewed as effecting a transformation under fixed initial conditions of the input the control to the output the controls are to be chosen from a given family of functions and consequently the outputs are members of a set of functions this viewpoint may be extended in various ways for example the initial conditions may be allowed to vary within a given set alternatively one may start with a set of possible outputs and try to find one or more allowed controls and permissible initial conditions which will yield the set of outputs put concretely one can ask when a spacecraft starting at one of a set of initial conditions and steered by one of a set of prescribed controls can be made to follow any one of a family of curves with preassigned velocity this roughly is what is meant by reproducibility reproducibility has been studied extensively by a number of investigators 1 5 10 111 here we obtain necessary and sufficient conditions for the reproducibility of linear time varying as well as time invariant input output systems and

singular optimal control a geometric approach linear quadratic singular optimal control problem is solved for nonminimum phase and noninvertible systems a state space decomposition is obtained and a reduced order nonsingular subproblem is solved the optimal stabilizing input of the singular problem has been found when there are no transmission zeros on the imaginary axis

path controllability of linear input output systems the varied definitions used in four studies of path controllability of linear input output systems are given their similarities and differences examined and some of their corresponding results compared and discussed

detectability and stabilizability of time varying discrete time linear systems the concepts of detectability and stabilizability are explored for time varying systems we study duality invariance under feedback an extended version of the lemma of lyapunov existence of stabilizing feedback laws linear quadratic filtering and control and the existence of approximate canonical forms

controlled markov decision processes with avar criteria for unbounded costs in this paper we consider the control problem with the average value at risk avar criteria of the possibly unbounded l1 costs in infinite horizon on a markov decision process mdp with a suitable state aggregation and by choosing a priori a global variable s heuristically we show that there exist optimal policies for the infinite horizon problem for possibly unbounded costs