ensembles of fuzzy linear model trees for the identification of multioutput systems we address the task of discrete time modeling of nonlinear dynamic systems with multiple outputs using measured data in the area of control engineering this task is typically converted into a set of classical regression problems one for each output which can then be solved with any nonlinear regression approach fuzzy models in the takagi sugeno form are popular in this context we use lolimot which is a tree learning method to build fuzzy linear model trees in this paper we propose implement and empirically evaluate three extensions of fuzzy linear model trees first we consider and evaluate multioutput models second we propose to use ensembles of such models third we investigate the use of a search heuristic based on simulation error as opposed to one step ahead prediction error specific to the context of modeling dynamic systems finally we perform an empirical evaluation and compare these approaches on six multioutput case studies using both measured and simulated data with noise the case studies include modeling of the inverse dynamics of a robot arm as well as five additional process industry systems ensembles improve the performance of both single and multioutput trees while the heuristic specific to modeling dynamic systems only improves performance very slightly multioutput model trees exhibit comparable or worse predictive performance to a set of single output models while providing a more compact model overall we can recommend the use of bagging of single output lolimot models learned by using the simulation error as a search heuristic

disturbance localization with dead beat control for linear periodic discrete time systems in this paper the classical notion of a controlled invariant subspace together with its main properties is extended to the case of linear periodic discrete time systems and used for deriving necessary and sufficient solvability conditions for the disturbance localization problem and a synthesis procedure for the solution moreover the notions of outer and inner controllable subspaces are introduced and studied for the same class of system thus allowing the derivation of necessary and sufficient solvability conditions for the disturbance localization problem with output or state dead beat control and to give synthesis procedures for the solutions

convergent semidefinite programming relaxations for global bilevel polynomial optimization problems in this paper we consider a bilevel polynomial optimization problem where the objective and the constraint functions of both the upper and the lower level problems are polynomials we present methods for finding its global minimizers and global minimum using a sequence of semidefinite programming sdp relaxations and provide convergence results for the methods our scheme for problems with a convex lower level problem involves solving a transformed equivalent single level problem by a sequence of sdp relaxations whereas our approach for general problems involving a nonconvex polynomial lower level problem solves a sequence of approximation problems via another sequence of sdp relaxations

top down induction of first order logical decision trees a first order framework for top down induction of logical decision trees is introduced the expressivity of these trees is shown to be larger than that of the flat logic programs which are typically induced by classical ilp systems and equal to that of first order decision lists these results are related to predicate invention and mixed variable quantification finally an implementation of this framework the tilde system is presented and empirically evaluated

disturbance localization by measurement feedback for linear periodic discrete time systems abstract the recent notions of inner controllable outer controllable and outer reconstructible subspaces together with the extension of the notion of c a b pair of subspaces to the class of linear periodic discrete time systems are the main tools used in this paper in order to study the disturbance localization problem by measurement feedback for the same class of systems by means of these concepts the necessary and sufficient solvability conditions of such a problem and synthesis procedures of the solutions are found for three different cases i e with and without an additional requirement of output or state dead beat control

dead beat control of linear periodic discrete time systems in this paper the dead beat control of linear periodic discrete time systems subject to periodic disturbances is studied necessary and sufficient conditions are given for the existence of a linear periodic controller such that both output dead beat control under periodic disturbances and state dead beat control under no disturbance are performed moreover synthesis procedures of the controller as well as of state dead beat observers are given which can be applied also to a class of bilinear systems

supervised hierarchical clustering in fuzzy model identification this paper presents a new supervised hierarchical clustering algorithm suhiclust for fuzzy model identification the presented algorithm solves the problem of global model accuracy together with the interpretability of local models as valid linearizations of the modeled nonlinear system the algorithm combines the advantages of supervised hierarchical algorithms which are based on heuristic tree construction algorithms together with the advantages of fuzzy product space clustering the high flexibility of the validity functions that is obtained by fuzzy clustering combined with supervised learning results in an efficient partitioning algorithm which is independent of initialization and results in a parsimonious fuzzy model furthermore the usability of suhiclust is very undemanding because it delivers in contrast with many other methods reproducible results in order to get reasonable results the user only has to set either a threshold for the maximum number of local models or a value for the maximum allowed global model error as a termination criterion for fine tuning the interpolation smoothness controls the degree of regularization the performance is illustrated on both analytical examples and benchmark problems from the literature

a new sequential optimality condition for constrained nonsmooth optimization we introduce a sequential optimality condition for locally lipschitz constrained nonsmooth optimization verifiable just using derivative information and which holds even in the absence of any con

exact output control for a family of linear plants with parameter uncertainties a family of linear continuous time plants parametrized by a vector of unknown parameters taking values in a known finite set is considered the problem investigated consists in finding a linear discrete time compensator that independently of the actual value of the parameter vector guarantees zero continuous time steady state output error with respect to a given continuous time external reference it is shown that the problem admits a solution in the class of periodic controllers

bilevel optimal control problems with pure state constraints and finite dimensional lower level this paper focuses on the development of optimality conditions for a bilevel optimal control problem with pure state constraints in the upper level and a finite dimensional parametric optimization problem in the lower level after transforming the problem into an equivalent single level problem we concentrate on the derivation of a necessary optimality condition of pontryagin type we point out some major difficulties arising from the bilevel structure of the original problem and its pure state constraints in the upper level leading to a degenerated maximum principle in the absence of constraint qualifications hence we use a partial penalization approach and a well known regularity condition for optimal control problems with pure state constraints to ensure the nondegeneracy of the derived maximum principle finally we illustrate the applicability of the derived theory by means of a small example

bilevel optimization on the structure of the feasible set we consider bilevel optimization from the optimistic point of view let the pair x y denote the variables the main difficulty in studying such problems lies in the fact that the lower level contains a global constraint in fact a point x y is feasible if y solves a parametric optimization problem l x in this paper we restrict ourselves to the special case that the variable x is one dimensional we describe the generic structure of the feasible set m moreover we discuss local reductions of the bilevel problem as well as corresponding optimality criteria finally we point out typical problems that appear when trying to extend the ideas to higher dimensional x dimensions this will clarify the high intrinsic complexity of the general generic structure of the feasible set m and corresponding optimality conditions for the bilevel problem u

is bilevel programming a special case of a mathematical program with complementarity constraints bilevel programming problems are often reformulated using the karush kuhn tucker conditions for the lower level problem resulting in a mathematical program with complementarity constraints mpcc clearly both problems are closely related but the answer to the question posed is no even in the case when the lower level programming problem is a parametric convex optimization problem this is not obvious and concerns local optimal solutions we show that global optimal solutions of the mpcc correspond to global optimal solutions of the bilevel problem provided the lower level problem satisfies the slater s constraint qualification we also show by examples that this correspondence can fail if the slater s constraint qualification fails to hold at lower level when we consider the local solutions the relationship between the bilevel problem and its corresponding mpcc is more complicated we also demonstrate the issues relating to a local minimum through examples

deadbeat error control of discrete multivariable systemsdagger abstract the main objective of this paper is to delineate conditions under which deadbeat error control can be achieved between a plant output and a discrete reference input signal all facets of this problem are considered in the linear multivariable case i e when the reference is any non diminishing signal whether the plant is truly discrete or a discretized continuous one and whether the initial conditions are zero or unknown the results presented can also be used to resolve the case of known non zero initial conditions on the state of the plant as well as the compensator

globally optimal fuzzy decision trees for classification and regression a fuzzy decision tree is constructed by allowing the possibility of partial membership of a point in the nodes that make up the tree structure this extension of its expressive capabilities transforms the decision tree into a powerful functional approximant that incorporates features of connectionist methods while remaining easily interpretable fuzzification is achieved by superimposing a fuzzy structure over the skeleton of a cart decision tree a training rule for fuzzy trees similar to backpropagation in neural networks is designed this rule corresponds to a global optimization algorithm that fixes the parameters of the fuzzy splits the method developed for the automatic generation of fuzzy decision trees is applied to both classification and regression problems in regression problems it is seen that the continuity constraint imposed by the function representation of the fuzzy tree leads to substantial improvements in the quality of the regression and limits the tendency to overfitting in classification fuzzification provides a means of uncovering the structure of the probability distribution for the classification errors in attribute space this allows the identification of regions for which the error rate of the tree is significantly lower than the average error rate sometimes even below the bayes misclassification rate

the realization problem for linear periodic systems abstract the realization problem for discrete time linear periodic systems is considered deep insight on the various complicated aspects of minimal quasi minimal and uniform realization is provided based on the knowledge of the structural properties of discrete time periodic systems the results hinge on the lifting isomorphism between such systems and time invariant ones

how stringent is the linear independence assumption for mathematical programs with complementarity constraints the linear independence constraint qualifications licq plays an important role in the analysis of mathematical programs with complementarity constraints mpccs and is a vital ingredient to convergence analyses of sqp type or smoothing methods cf e g fukushima and pang 1999 luo et al 1996 scholtes and sta hr 1999 scholtes 2001 sta hr 2000 we will argue in this paper that licq is not a particularly stringent assumption for mpccs our arguments are based on an extension of jongen s 1977 genericity analysis to mpccs his definitions of nondegenerate critical points and regular programs extend naturally to mpccs and his genericity results generalize straightforwardly to mpccs in standard form an extension is not as straightforward for mpccs with the particular structure induced by lower level stationarity conditions for variational inequalities or optimization problems we show that licq remains a generic property for this class of mpccs

output dead beat controllers and function dead beat observers for linear periodic discrete time systems in this paper two problems are considered that of finding a possibly dynamic linear periodic controller such that both the regulated output and the control input of a linear periodic discrete time system become and remain zero and that of designing a dead beat observer of a linear function of the state of the system for both these problems necessary and sufficient conditions for the existence of a solution are given and synthesis procedures of both the controller and the observer are provided by the sufficiency proofs such conditions are very simple and concise when expressed in terms of controllable and or unreconstructible states

on using the elastic mode in nonlinear programming approaches to mathematical programs with complementarity constraints we investigate the possibility of solving mathematical programs with complementarity constraints mpccs using algorithms and procedures of smooth nonlinear programming although mpccs do not satisfy a constraint qualification we establish sufficient conditions for their lagrange multiplier set to be nonempty mpccs that have nonempty lagrange multiplier sets and satisfy the quadratic growth condition can be approached by the elastic mode with a bounded penalty parameter in this context the elastic mode transforms mpcc into a nonlinear program with additional variables that has an isolated stationary point and local minimum at the solution of the original problem which in turn makes it approachable by sequential quadratic programming sqp algorithms one such algorithm is shown to achieve local linear convergence once the problem is relaxed under stronger conditions we also prove superlinear convergence to the solution of an mpcc using an adaptive elastic mode approach for an sqp algorithm recently analyzed in an mpcc context in r fletcher s leyffer s sholtes and d ralph local convergence of sqp methods for mathematical programs with equilibrium constraints tech report na 210 university of dundee dundee uk 2002 our assumptions are more general since we do not use a critical assumption from that reference in addition we show that the elastic parameter update rule will not interfere locally with the superlinear convergence once the penalty parameter is appropriately chosen

multiobjective identification of takagi sugeno fuzzy models the problem of identifying the parameters of the constituent local linear models of takagi sugeno fuzzy models is considered in order to address the tradeoff between global model accuracy and interpretability of the local models as linearizations of a nonlinear system two multiobjective identification algorithms are studied particular attention is paid to the analysis of conflicts between objectives and we show that such information can be easily computed from the solution of the multiobjective optimization this information is useful to diagnose the model and tune the weighting priorities of the multiobjective optimization moreover the result of the conflict analysis can be used as a constructive tool to modify the fuzzy model structure including membership functions in order to meet the multiple objectives simple illustrative examples as well as experimental results show the usefulness of the method

structural properties of multirate sampled data systems a complete analysis of the structural properties of multirate sampled data systems is considered in this paper necessary and sufficient conditions for the reachability controllability and stabilizability and for the dual notions are given in terms of simple rank tests these results obtained by the structural theory of periodic systems generalize to the multirate case the well known conditions of the single rate case

on deadbeat controllers the possibility of achieving a deadbeat regulation and tracking in linear multivariable systems independently of their initial conditions is investigated necessary and sufficient conditions for the existence of various deadbeat controllers are established in a constructive way a detailed analysis of the control sequence generated by any deadbeat controller is then presented

parametrized solution of the periodic dead beat control problem the dead beat control problem for linear periodic discrete time systems in presence of unmeasurable disturbances and external reference signals is considered using a polynomial method a parametrization of all causal output feedback controllers solving the problem is provided

a complete fuzzy decision tree technique in this paper a new method of fuzzy decision trees called soft decision trees sdt is presented this method combines tree growing and pruning to determine the structure of the soft decision tree with refitting and backfitting to improve its generalization capabilities the method is explained and motivated and its behavior is first analyzed empirically on 3 large databases in terms of classification error rate model complexity and cpu time a comparative study on 11 standard uci repository databases then shows that the soft decision trees produced by this method are significantly more accurate than standard decision trees moreover a global model variance study shows a much lower variance for soft decision trees than for standard trees as a direct cause of the improved accuracy

bilevel programming for generating discrete representations in multiobjective optimization the solution to a multiobjective optimization problem consists of the nondominated set that portrays all relevant trade off information the ultimate goal is to identify a decision maker s most preferred solution without generating the entire set of nondominated solutions we propose a bilevel programming formulation that can be used to this end the bilevel program is capable of delivering an efficient solution that maps into a given set provided that one exits if the decision maker s preferences are known a priori they can be used to specify the given set alternatively we propose a method to obtain a representation of the nondominated set when the decision maker s preferences are not available this requires a thorough search of the outcome space the search can be facilitated by a partitioning scheme similar to the ones used in global optimization since the bilevel programming formulation either finds a nondominated solution in a given partition element or determines that there is none a representation with a specified coverage error level can be found in a finite number of iterations while building a discrete representation the algorithm also generates an approximation of the nondominated set within the specified error factor we illustrate the algorithm on the multiobjective linear programming problem

deadbeat ripple free tracking with disturbance rejection a polynomial approach the deadbeat ripple free tracking problem for sampled data systems is considered it is assumed that both the state and the output of the continuous time plant to be controlled are affected by external disturbances a polynomial approach is adopted and solvability conditions are given both in terms of the sampled system and of the original continuous time one

design of ripple free multivariable robust servomechanisms the application of standard robust servomechanism theory to sampled data systems guarantees asymptotic tracking at sampling instances and between sampling instants the output will normally contain ripple in this note the robust servomechanism theory is extended to sampled data systems and a technique is proposed for ripple free tracking of sinusoids and polynomials it is shown that a continuous internal model is necessary and sufficient to provide ripple free response

genetic programming for model selection of tsk fuzzy systems this paper compares a genetic programming gp approach with a greedy partition algorithm lolimot for structure identification of local linear neuro fuzzy models the crisp linear conclusion part of a takagi sugeno kang tsk fuzzy rule describes the underlying model in the local region specified in the premise the objective of structure identification is to identify an optimal partition of the input space into gaussian axis orthogonal fuzzy sets the linear parameters in the rule consequent are then estimated by means of a local weighted least squares algorithm lolimot is an incremental tree construction algorithm that partitions the input space by axis orthogonal splits in each iteration it greedily adds the new model that minimizes the classification error gp performs a global search for the optimal partition tree and is therefore able to backtrack in case of sub optimal intermediate split decisions we compare the performance of both methods for function approximation of a highly non linear two dimensional test function and an engine characteristic map

brief paper multivariable closed loop deadbeat control a polynomial matrix approach the closed loop deadbeat servo problem cdsp considered in this paper consists of the synthesis of a linear output feedback controller such that the control signal and tracking error both vanish after a finite period of time for every reference sequence from a prespecified class and for every initial state of a plant and the controller the closed loop structure is determined by studying necessary and sufficient conditions for deadbeat tracking performance a new theorem asserts that if an open loop deadbeat control strategy exists for every initial state of the plant and every reference function from a given class then cdsp is solvable and all desired control laws are found in an explicit parametric form by solving simple unilateral linear equations in polynomial matrices on the basis of this theorem a design algorithm is developed asymptotic stability of the closed loop system exhibiting deadbeat properties is demonstrated a numerical example is given to illustrate the usefulness and computational efficiency of the new design algorithm presented