multiple criterion control a convex programming approach the performance of linear dynamic systems with respect to a non linear increasing value function that aggregates convex functionals is investigated within a convex programming framework the methodology developed in this paper combines fundamental properties of convex sets in order to decompose the multicriterion control problem into a two level structure the upper level of this structure comprises only decision making aspects of the problem and involves the solution of a relaxed and static multicriterion problem the lower level of the structure comprises in turn only optimal control aspects of the problem the overall procedure is easily implemented the solution of the aggregated problem is obtained as the limit of a sequence of optimal control problems that preserve their original solution properties relationships between the approach adopted here and existing solution techniques are discussed the solutions of the classical minimax and salukvadze problems are obtained as special cases of the proposed approach

the shortest path problem with two objective functions abstract we present methods to find the shortest path in a network where each path is associated with two objectives we describe how to obtain the nondominated paths and the extreme nondominated paths and compare the expected complexity of the methods an improvement in efficiency can be obtained when quasiconcave or quasiconvex utility functions are assumed in the first case we describe how to find the optimal extreme nondominated path and bounds for the optimal path value then the optimal path can be located by calculating the k th shortest path in the second case we suggest a branch and bound method to solve the problem

covariance controllers for linear continuous time systems abstract necessary and sufficient conditions are given for the existence of a controller of specified order n c which will assign a specified matrix value x to the covariance of the closed loop system if a solution exists the entire set of stabilizing controllers that assign x are parameterized by a certain skew symmetric matrix

infinite ternary square free words concatenated from permutations of a single word abstract we answer a question of harju an infinite square free ternary word with an n stem factorization exists for any n 13 we show that there are square free uniform ternary morphisms of length k for every k 23 this resolves almost completely a problem of the author and rampersad

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

h 2 optimal control with an h constraint the state feedback case in this paper we consider a mixed hz optimal control problem it is assumed that the plant as well as the feedback controller are finite dimensional and linear time invariant and that the plant state is available for feedback more specifically among all the state feedback controllers that minimize the he norm of a closed loop transfer matrix we give necessary and sufficient conditions for the existence of a controller that also satisfies a prescribed h norm bound on some other closed loop transfer matrix when these conditions are met the solution to the above problem is also a global solution to the contrained optimization problem of minimizing an he norm performance measure subject to an h norm constraint we also give state space formulae for computing the solutions some easily checkable sufficient conditions for the existence of solutions are given finally we give an example in which all solutions to the constrained optimization problem are necessarily dynamic i e there is no static gain solution even though plant state is available for feedback

some inequalities for information divergence and related measures of discrimination inequalities which connect information divergence with other measures of discrimination or distance between probability distributions are used in information theory and its applications to mathematical statistics ergodic theory and other scientific fields we suggest new inequalities of this type often based on underlying identities as a consequence we obtain certain improvements of the well known pinsker inequality our study depends on two measures of discrimination called capacitory discrimination and triangular discrimination the discussion contains references to related research and comparison with other measures of discrimination e g ali silvey csiszar 1996 1966 divergences and in particular the hellinger distance

adaptive differential dynamic programming for multiobjective optimal control an efficient numerical solution scheme entitled adaptive differential dynamic programming is developed in this paper for multiobjective optimal control problems with a general separable structure for a multiobjective control problem with a general separable structure the optimal weighting coefficients for various performance indices are time varying as the system evolves along any noninferior trajectory recognizing this prominent feature in multiobjective control the proposed adaptive differential dynamic programming methodology combines a search process to identify an optimal time varying weighting sequence with the solution concept in the conventional differential dynamic programming convergence of the proposed adaptive differential dynamic programming methodology is addressed

cardinality constrained linear quadratic optimal control as control implementation often incurs not only a variable cost associated with the magnitude or energy of the control but also a setup cost we consider a discrete time linear quadratic lq optimal control problem with a limited number of control implementations termed in this technical note the cardinality constrained linear quadratic optimal control cclq we first derive a semi analytical feedback policy for cclq problems using dynamic programming dp due to the exponential growth of the complexity in calculating the action regions however dp procedure is only efficient for cclq problems with a scalar state space recognizing this fact we develop then two lower bounding schemes and integrate them into a branch and bound bnb solution framework to offer an efficient algorithm in solving general cclq problems adopting the devised solution algorithm for cclq problems we can solve efficiently the linear quadratic optimal control problem with setup costs

square free words obtained from prefixes by permutations an infinite square free word w over a three letter alphabet t is said to have a k stem s if w sw 1w 2 where for each i there exists a permutation p i of t which extended to a morphism gives w i p i s we show that there exists an infinite k stem word for k 1 2 3 9 and 13 k 19 but not for 4 k 8 and 10 k 12 the problem whether k stem words exist for each k 20 remains open

avoiding large squares in infinite binary words we consider three aspects of avoiding large squares in infinite binary words first we construct an infinite binary word avoiding both cubes xxx and squares yy with y 4 our construction is somewhat simpler than the original construction of dekking second we construct an infinite binary word avoiding all squares except 02 12 and 01 2 our construction is somewhat simpler than the original construction of fraenkel and simpson in both cases we also show how to modify our construction to obtain exponentially many words of length n with the given avoidance properties finally we answer an open question of prodinger and urbanek from 1979 by demonstrating the existence of two infinite binary words each avoiding arbitrarily large squares such that their perfect shuffle has arbitrarily large squares

on the minimax solution of multiple linear quadratic problems multiple linear quadratic problems are studied a set of coupling riccati equations is derived for vector valued cost to go a minimax solution of multiobjective convex problems is proven to be an equalizer strategy this permits the development of a new algorithm for finding the minimax solution for multiple linear quadratic problems

cost smoothing in discrete time linear quadratic control a smooth cost distribution can be a desirable feature in optimal control design when concerning even distribution of control energy and uniform resource allocation this consideration is formulated in this paper for discrete time linear systems where a square cost variation term is attached to a primal quadratic performance index in an additive form an analytical control law is obtained for the resulting non linear quadratic and nonseparable optimal control problem using a multilevel solution scheme investigating the trade off between minimizing the primal quadratic performance index and minimizing the square cost variation term offers some useful insights into multiobjective design of control systems

the multiple linear quadratic gaussian problem in this paper we define and solve the multiple linear quadratic gaussian lqg problem for discrete time systems using salukvadze s ideal point method which treats dynamic but deterministic multicriteria optimization problems the solution consists in designing a scalar regulator where the weighting matrices are replaced by the sums of their counterparts in the individual criteria the resulting control is optimal in the sense that it minimizes the difference between the cost of the implemented policy from the cost that would occur if we optimized each criterion separately and added the outcomes all the nice properties of the scalar lqg regulator are enjoyed by the multicriteria regulator as well extension to the continuous time case is straightforward yielding identical results

computation of generalized h 2 optimal controllers the generalized h 2 optimal control problem for a linear time invariant system is one in which the conventional h 2 norm is replaced by an operator norm the closed loop system is described in terms of a mapping between the space of time domain input disturbances in l 2 and the space of time domain regulated outputs in l a minimum of this norm is then sought over all stabilizing controllers it is shown that optimal controllers for such problems have the structure of a kalman filter with estimated state feedback where the feedback gains are obtained from the solution to a weighted lqr problem a computational algorithm is presented to determine the weights in this lqr problem and examples are given which demonstrate various problems which may arise in obtaining the optimal weights in particular it is shown that the generalized h 2 problem may involve the solution to a singular lqr problem

multiobjective h sub 2 h sub spl infin control for a linear time invariant system with several disturbance inputs and controlled outputs we show how to minimize the nominal h sub 2 norm performance in one channel while keeping bounds on the h sub 2 norm or h sub spl infin norm performance implying robust stability in the other channels this multiobjective h sub 2 h sub spl infin problem in an infinite dimensional space is reduced to sequences of finite dimensional convex optimization problems we show how to compute the optimal value and how to numerically detect the existence of a rational optimal controller if it exists we reveal how the novel trick of optimizing the trace norm of the youla parameter over certain convex constraints allows one to design a nearly optimal controller whose youla parameter is of the same order as the optimal one

a general theory for the wiener hopf design of multivariable control systems multivariable control system design in a quadratic cost setting is treated for a completely general configuration the class of all controllers is determined for which the general configuration is internally asymptotically stable and a quadratic cost functional is finite this controller class is parameterized in terms of an arbitrary real rational strictly proper matrix z s which is analytic in the closed right hand side of the s plane the choice z identical to 0 gives the controller which minimizes the quadratic cost functional

a theory of state covariance assignment for discrete systems in many regulation control problems it is desired to design the controller so that various system states have acceptable root mean squared values this is a multiple objective problem one way to satisfy these objectives is to assign a specified state covariance to the system this paper introduces and solves the following problem 1 characterize the entire set of state covariances which may be assigned to a linear discrete time system by state feedback and 2 find the set of all state feedback gains which will assign an admissible state covariance to the system extensions are also presented for state estimate feedback

direct variance design a multiobjective control theory a theory for designing linear state feedback controllers to directly accommodate variance constraints imposed on the system states is offered such controllers guarantee an average closed loop response to gaussian input disturbances the method provides a mechanism for directly assigning all variance values the diagonal elements of the covariance matrix to the closed loop system the theory may be viewed as offering direct access to a new set of design variables the state variances

a convergent algorithm for the output covariance constraint control problem this paper considers the optimal control problem of minimizing control effort subject to multiple performance constraints on output covariance matrices y i of the form y i leq overline y i where overline y i is given the contributions of this paper are a set of conditions that characterize global optimality and an iterative algorithm for finding a solution to the optimality conditions this iterative algorithm is completely described up to a user specified parameter we show that under suitable assumptions on problem data the iterative algorithm converges to a solution of the optimality conditions provided that this parameter is properly chosen both discrete and continuous time problems are considered

multivariate information bottleneck the information bottleneck ib method is an unsupervised model independent data organization technique given a joint distribution p x y this method constructs a new variable t that extracts partitions or clusters over the values of x that are informative about y algorithms that are motivated by the ib method have already been applied to text classification gene expression neural code and spectral analysis here we introduce a general principled framework for multivariate extensions of the ib method this allows us to consider multiple systems of data partitions that are interrelated our approach utilizes bayesian networks for specifying the systems of clusters and which information terms should be maintained we show that this construction provides insights about bottleneck variations and enables us to characterize the solutions of these variations we also present four different algorithmic approaches that allow us to construct solutions in practice and apply them to several real world problems

successive method for general multiple linear quadratic control problem in discrete time a successive method is proposed for the general multiple linear quadratic control problem in discrete time a family of auxiliary parametric linear quadratic control problems is constructed such that its solution sequence converges to the optimal solution of the original problem theoretical analysis for the computational procedure and global convergence of the successive method is provided the successive method utilizes the special structure of the problem thus being computationally efficient and being able to furnish a closed loop optimal control law

pareto suboptimal controllers in multi objective disturbance attenuation problems abstract a multi objective disturbance attenuation problem is considered as a novel framework for control and filtering problems under multiple exogenous disturbances there are n potentially possible disturbance inputs of a system on each of which may act a disturbance from a certain class a disturbance attenuation level is defined for each channel as an induced norm of the operator mapping signals of the corresponding class to the objective output of the system necessary conditions of the pareto optimality are derived it is established that the optimal solutions with respect to a multi objective cost parameterized by weights from an n dimensional simplex are pareto suboptimal solutions and their relative losses compared to the pareto optimal ones do not exceed 1 n n these results are extended to the case when the disturbances acting on different inputs are combined into coalitions the approach is applied to multiple classes of l 2 bounded and impulsive disturbances for which the h 0 optimal controllers as the pareto suboptimal solutions are synthesized in terms of linear matrix inequalities lmis illustrative examples demonstrate the effectiveness of the approach proposed

minimax control of linear stochastic systems with noise uncertainty the problem of linear quadratic gaussian control of multivariable linear stochastic systems with uncertain second order statistical properties is considered uncertainty is modeled by allowing process and observation noise spectral density matrices to vary arbitrarily within given classes and a minimax control formulation is applied to the quadratic objective functional general theorems proving the existence and characterization of saddle point solutions to this problem are presented and the relationship of these results to earlier results on minimax state estimation are discussed to illustrate the analytical results the specific example of regulating a double integrator plant is treated in detail

multilevel dynamic programming for general multiple linear quadratic control in discrete time systems abstract this paper extends the reach of dynamic programming to general multiple linear quadratic control problems in discrete time systems where the overall objective is a nonlinear function of multiple quadratic performance indices a multilevel dynamic programming solution procedure is proposed to obtain an analytical linear control law for this nonseparable control problem at the lower level the formulated auxiliary lagrangian problem is of a parametric linear quadratic structure and is solved by dynamic programming the weighting vector in the auxiliary lagrangian problem is adjusted by the upper level iteratively this two level process repeats until an optimal condition is satisfied

square free shuffles of words let u v denote the set of all shuffles of the words u and v it is shown that for each integer n 3 there exists a square free ternary word u of length n such that u u contains a square free word this property is then shown to also hold for infinite words i e there exists an infinite square free word u on three letters such that u can be shuffled with itself to produce an infinite square free word w u u

multiple objective optimal control of linear systems the quadratic norm case control of a linear system to meet requirements embodied in multiple performance criteria is recognized as the typical design problem the authors study the design of control when every criterion of interest takes the form of an h sub 2 norm defined over certain exogenous inputs and controlled outputs of the system the objective is to find all stabilizing controllers that are noninferior with respect to the defined objectives that is to find the set of pareto optimal controllers the novel feature is the use of the youla parametrization to represent the admissible controllers this representation enables the authors to show that each criterion and hence their weighted sum is convex over the class of admissible controllers since the set of admissible controllers is itself convex the pareto optimal controllers can be determined by the standard scalarization technique it is concluded that in general the controller order is higher than the order of the plant

on general multiple linear quadratic control problems general multiple linear quadratic control problems are studied where the overall objective is a nonlinear function of multiple quadratic performance indices a multilevel solution procedure is proposed to obtain an analytical linear control law for this nonseparable control problem the auxiliary lagrangian problem formulated at the lower level is of a parametric linear quadratic structure in which the weighting vector is adjusted by the upper level until a derived optimal condition is met

matrix criterion robust linear quadratic control problem this paper studies a robust linear quadratic lq control problem with multiple quadratic performance indices specifically a linear model is assumed to be available for each of a prespecified set of operating points of a system a vector valued quadratic control performance index is given at each operating point it is then desired to find the constant feedback gains of a linear controller to obtain satisfactory control performance over all the operating points this is a realistic case involving the minimization of a vector criterion of vector criteria i e a matrix valued criterion the matrix valued criterion gives insight into standard robust lq design and leads to several related vector minimization problems and to natural procedures for computing a satisfactory non inferior solution to the matrix valued minimization problem

recognizing binary shuffle squares is np hard abstract a shuffle of two words is formed by interleaving the characters into a new word keeping the characters of each word in order a word is a shuffle square if it is a shuffle of two identical words deciding whether a word is a shuffle square has been proved to be np complete independently by buss and soltys 5 and rizzi and vialette 20 the former proving the result for alphabets as small as 9 letters we prove in this paper that deciding whether a binary word is a shuffle square is np complete

learning decision trees with taxonomy of propositionalized attributes we consider the problem of exploiting a taxonomy of propositionalized attributes in order to learn compact and robust classifiers we introduce propositionalized attribute taxonomy guided decision tree learner pat dtl an inductive learning algorithm that exploits a taxonomy of propositionalized attributes as prior knowledge to generate compact decision trees since taxonomies are unavailable in most domains we also introduce propositionalized attribute taxonomy learner pat learner that automatically constructs taxonomy from data pat dtl uses top down and bottom up search to find a locally optimal cut that corresponds to the literals of decision rules from data and propositionalized attribute taxonomy pat learner propositionalizes attributes and hierarchically clusters the propositionalized attributes based on the distribution of class labels that co occur with them to generate a taxonomy our experimental results on uci repository data sets show that the proposed algorithms can generate a decision tree that is generally more compact than and is sometimes comparably accurate to those produced by standard decision tree learners

iterative parametric minimax method for a class of composite optimization problems this paper considers a class of composite optimization problems that are often difficult to solve directly due to large dimension nonlinearity nonseparability and or nonconvexity of the problem an iterative parametric minimax method is proposed in which the original optimization problem is embedded into a weighted minimax formulation the resulting auxiliary parametric optimization problems at the lower level often have simple structures that are readily tackled by efficient solution strategies such as the decomposition scheme in dynamic programming and in the primal dual method the analytical expression of the partial derivatives of systems performance indices with respect to the weighting vector in the parametric minimax formulation is derived the gradient method can be thus adopted at the upper level to adjust the value of the weighting vector the solution of the weighted minimax formulation converges to the optimal solution of the original problem in a multilevel iteration process an application of the proposed iterative parametric minimax method is demonstrated in constrained reliability optimization problems

gradient projection and local region search for multiobjective optimisation this paper presents a new method for multiobjective optimisation based on gradient projection and local region search the gradient projection is conducted through the identification of normal vectors of an efficient frontier the projection of the gradient of a nonlinear utility function onto the tangent plane of the efficient frontier at a given efficient solution leads to the definition of a feasible local region in a neighbourhood of the solution within this local region a better efficient solution may be sought to implement such a gradient based local region search scheme a new auxiliary problem is developed if the utility function is given explicitly this search scheme results in an iterative optimisation algorithm capable of general nonseparable multiobjective optimisation otherwise an interactive decision making algorithm is developed where the decision maker dm is expected to provide local preference information in order to determine trade off directions and step sizes optimality conditions for the algorithms are established and the convergence of the algorithms is proven a multiobjective linear programming molp problem is taken for example to demonstrate this method both graphically and analytically a nonlinear multiobjective water quality management problem is finally examined to show the potential application of the method to real world decision problems

theory and applications of generalized dynamic programming an overview abstract extensions of dynamic programming dp into generalized preference structures such as exist in multicriteria optimization have invariably assumed sufficient structure to ensure the validity of bellman s principle of optimality or the presence of monotonicity hence ensuring the validity of the functional equations of dp often however the only reasonable formulation of problem in terms of the size of the resulting state space is one for which neither monotonicity nor the strong principle of optimality is satisfied generalized dp based on a weaker principle of optimality is a generalization of dp that produces optimal solutions even in the absence of monotonicity it is shown both to subsume conventional dp and to provide an alternative means of implementing mitten s preference order dp this paper provides an overview of generalized dp and its applications to date summarizing our computational experiences in the process

multiobjective model predictive control this paper proposes a novel model predictive control mpc scheme based on multiobjective optimization at each sampling time the mpc control action is chosen among the set of pareto optimal solutions based on a time varying state dependent decision criterion compared to standard single objective mpc formulations such a criterion allows one to take into account several often irreconcilable control specifications such as high bandwidth closed loop promptness when the state vector is far away from the equilibrium and low bandwidth good noise rejection properties near the equilibrium after recasting the optimization problem associated with the multiobjective mpc controller as a multiparametric multiobjective linear or quadratic program we show that it is possible to compute each pareto optimal solution as an explicit piecewise affine function of the state vector and of the vector of weights to be assigned to the different objectives in order to get that particular pareto optimal solution furthermore we provide conditions for selecting pareto optimal solutions so that the mpc control loop is asymptotically stable and show the effectiveness of the approach in simulation examples

on multiple criteria stationary linear quadratic control multiple control criteria and design specifications are in general present in control systems design in this study all pareto optimal solutions are characterized for a large class of multiple criteria stationary linear quadratic control problems in terms of associated scalar criterion linear quadratic control problem solutions based on a supporting hyperplane argument and thus the results are fully constructive this argument which was used to establish these results is believed to be new

brief linear quadratic control revisited infinite horizon linear quadratic control is re examined and generalized to include a class of non stationary disturbances this revision is achieved by defining a generalized infinite horizon linear quadratic control problem using a flexible functional analytic signal description specifically an instantaneous linear quadratic output feedback problem is considered in this way it is shown that the solution to the generalized linear quadratic problem is equivalent to the solution of the corresponding standard linear quadratic problem with disturbance and noise covariance matrices having in the generalized problem a different more general meaning than in the standard problem in the generalized problem these covariance matrices are majorizing matrices that have a precise meaning even in the non stationary signal case this result justifies in a nice way the wide practice of interpreting the disturbance and noise covariance matrices in linear quadratic control as design variables

a bicriteria stationary lq control problem abstract this note gives a simple derivation of the minimal loss vectors and the pareto optimal solutions to a certain bicriteria stationary lq control problem

extension of dynamic programming to nonseparable dynamic optimization problems abstract the use of dynamic programming is extended to a general nonseparable class where multiobjective optimization is used as a separation strategy the original nonseparable dynamic optimization problem is first embedded into a separable albeit multiobjective optimization problem where multiobjective dynamic programming using the envelope approach is used as a solution scheme under certain conditions the optimal solution of the original nonseparable problem is proven to be attained by a noninferior solution

multiple objective optimization approach to adaptive and learning control this paper formulates a new approach to the classical learning adaptive control problem our approach is based on two key observations 1 the inherent conflict between control and identification as they compete for the only available resource namely the input to the plant 2 when designing and optimizing the performance of a control system the current task as well as the repertoire of other typical future tasks which the system may encounter during its life time should be considered our approach is formulated for a general nonlinear time varying plant thus unlike existing adaptive control theory the theory for a linear time invariant system evolves as a special case of the general case the design for the full lifetime of the system creates a methodology that specifies what current actions should be taken in addition to the tracking of the current reference trajectory at the expense of some performance degradation in the current task so as to improve the performance of future tasks this is

on the convexity of some divergence measures based on entropy functions three measures of divergence between vectors in a convex set of a n dimensional real vector space are defined in terms of certain types of entropy functions and their convexity property is studied among other results a classification of the entropies of degree alpha is obtained by the convexity of these measures these results have applications in information theory and biological studies

performance first control for discrete time lqg problems performance first control for discrete time lqg is considered in this paper to minimize the probability that the performance index exceeds a preselected threshold via constructing a closed loop feedback control law this problem can be converted into a mean variance control problem which can be solved by developing a nested form of the variance and using polynomial optimization as a solution scheme

computational methods for parametric lq problems a survey iterative methods for finding the optimal constant feedback gains for parametric lq problems notably for optimal constant output feedback problems are surveyed the connections of several methods to loss function expansions are discussed with important implications to the understanding of their convergence properties especially the descent anderson moore method levine athans like methods and the newton method are considered convergence results are also included the initialization problem and the output feedback stabilization problem are also discussed furthermore it is shown that the concepts and methods surveyed in this paper are useful in solving many realistic generalized parametric lq problems as well notably so called robust parametric lq problems

uniformly growing k th power free homomorphisms a string is called kth power free if it does not have xk as a nonempty substring for all nonnegative rational numbers k kth power free strings and kth power free homomorphisms are investigated and the shortest uniformly growing square free k 2 and cube free k 3 homomorphisms mapping into least alphabets with three and two letters are introduced it is shown that there exist exponentially many square free and cube free strings of each length over these alphabets sharpening the kth power freeness to the repetitive threshold rt n of n letter alphabets we provide arguments for the nonexistence of various rt n th power free homomorphisms

multiple models multiplicative noise and linear quadratic control algorithmic aspects numerical solution of certain linear quadratic lq control problems for robust design is addressed an iterative method is suggested and analysed for solving a minimax multiple model lq control problem a convergent iterative method is studied for finding the constant feedback gains of a given linear controller so as to solve a spectral radius functional minimization problem for multiple plants furthermore a convergent iterative method is proposed for solving the maximum entropy parametric lq control problem with multiplicative noise

brief paper robust multi objective feedback design with linear guaranteed cost bounds this paper considers the problem of designing a state feedback control law which minimizes multiple quadratic performance objectives in the presence of uncertain linear plant dynamics vector optimization techniques are used to minimize upper bounds on each performance objective guaranteed cost by exploiting the linear uncertainty bound introduced by bernstein 1987 the vector optimization problem is scalarized and pareto optimal solutions are computed the theory is applied to a numerical example with two quadratic performance measures

hierarchical control for large scale systems with general multiple linear quadratic structure abstract a class of large scale linear control systems where the overall objective function is a nonlinear function of multiple quadratic performance indices is investigated in this paper this type of large scale control problem with a general multiple linear quadratic structure is nonseparable in the sense of conventional hierarchical control hierarchical control is extended in this paper to large scale nonseparable control problems where multiobjective optimization is used as a separation strategy the large scale general multiple linear quadratic control problem is embedded under certain conditions into a family of the weighted lagrangian formulation the weighted lagrangian formulation is separable with respect to subsystems and can be effectively solved using the interaction prediction approach at the two lower levels in the proposed three level solution structure at the third level the weighting vector for the weighted lagrangian formulation is adjusted iteratively to search the optimal weighting vector with which the optimal control of the original large scale nonseparable control problem is attained one feature of this hierarchical control scheme is a derived analytical solution for the large scale general multiple linear quadratic control

quantifying inductive bias ai learning algorithms and valiant s learning framework abstract we show that the notion of inductive bias in concept learning can be quantified in a way that directly relates to learning performance in the framework recently introduced by valiant our measure of bias is based on the growth function introduced by vapnik and chervonenkis and on the vapnik chervonenkis dimension we measure some common language biases including restriction to conjunctive concepts conjunctive concepts with internal disjunction k dnf and k cnf concepts we also measure certain types of bias that result from a preference for simpler hypotheses using these bias measurements we analyze the performance of the classical learning algorithm for conjunctive concepts from the perspective of valiant s learning framework we then augment this algorithm with a hypothesis simplification routine that uses a greedy heuristic and show how this improves learning performance on simpler target concepts improved learning algorithms are also developed for conjunctive concepts with internal disjunction k dnf and k cnf concepts we show that all our algorithms are within a logarithmic factor of optimal in terms of the number of examples they require to achieve a given level of learning performance in the valiant framework our results hold for arbitrary attribute based instance spaces defined by either tree structured or linear attributes

generalized dynamic programming for stochastic combinatorial optimization in stochastic versions of combinatorial optimization problems the objective is to maximize or minimize a function of random variables for many problems of this type conventionally applied dynamic programming dp may fail to generate an optimal solution due to the potential violation of the monotonicity assumption of dp we develop a generalization of dp that guarantees optimality even in the absence of monotonicity we illustrate the methodology on a version of the stochastic traveling salesman problem for which a previously proposed dp algorithm e kao is potentially suboptimal due to the violation of monotonicity m sniedovich using generalized dp we are able to modify the algorithm to guarantee optimality

optimal multivariable controller design using an itse performance index this article deals with the design of optimal controllers and as an embedded problem with the computation of achievable performance bounds in the control of non minimum phase unstable multi input multi output systems the cost function comprises a time weighted measure of the tracking error itse and an incremental quadratic penalisation of the control effort the proposed methodology relies on the properties of a frequency domain generalisation of the itse index the solution to the optimisation problem can be computed using orthonormal basis function expansions and a closed form expression is found for the optimal coefficients of the expansion numerical examples are presented to illustrate the results