nonlinear control of constrained linear systems via predictive reference management a method based on conceptual tools of predictive control is described for solving set point tracking problems wherein pointwise in time input and or state inequality constraints are present it consists of adding to a primal compensated system a nonlinear device called command governor cg whose action is based on the current state set point and prescribed constraints the cg selects at any time a virtual sequence among a family of linearly parameterized command sequences by solving a convex constrained quadratic optimization problem and feeds the primal system according to a receding horizon control philosophy the overall system is proved to fulfill the constraints be asymptotically stable and exhibit an offset free tracking behavior provided that an admissibility condition on the initial state is satisfied though the cg can be tailored for the application at hand by appropriately choosing the available design knobs the required online computational load for the usual case of affine constraints is well tempered by the related relatively simple convex quadratic programming problem

estimation of a fuzzy regression model using fuzzy distances regression analysis is a powerful statistical tool that has many applications in different areas the problem of regression analysis under a fuzzy environment has been treated in the literature from different points of view and considering a variety of input output data crisp or fuzzy however we realize that in general most research papers have a conflict between the solution of the fuzzy regression problem using crisp distances minimizing a real error function and the interpretation of fuzzy data as possibility distributions the main aim of this paper is to develop a methodology to solve this problem introducing a fuzzy partial order and a family of fuzzy distance measures on the whole set of fuzzy numbers the new approach allows us to obtain linear and nonlinear models that reach the lowest fuzzy error the estimation process in general can be considered easier to apply in practice and it is not limited to triangular fuzzy numbers numerical examples are provided to illustrate the usefulness and applicability of these results and comparisons with existing methodologies show that the performance of the proposed solution is very satisfactory

asymptotic behaviour of optimal spectral planar domains with fixed perimeter we consider the problem of minimizing the kth dirichlet eigenvalue of planar domains with fixed perimeter and show that as k goes to infinity the optimal domain converges to the ball with the same perimeter we also consider this problem within restricted classes of domains such as n polygons and tiling domains for which we show that the optimal asymptotic domain is that which maximises the area for fixed perimeter within the given family i e the regular n polygon and the regular hexagon respectively physically the above problems correspond to the determination of the shapes within a given class which will support the largest number of modes below a given frequency

feedback system design the tracking and disturbance rejection problems the problem of designing a compensator for a specified plant which simultaneously stabilizes the resultant feedback system and causes it to track a prescribed family of inputs and or reject prescribed disturbances is considered a set of linear design equations in the space of stable systems is formulated in a general linear systems setting and an explicit parameterization of the resultant solution space is obtained for a class of generalized multivariate systems the theory is illustrated with several single and multivariate examples

upper bounds for the neumann eigenvalues on a bounded domain in euclidean space abstract let k be the the kth eigenvalue for the neumann boundary value problem with respect to the laplace operator on a bounded domain with piecewise smooth boundary in rn weyl s asymptotic formula states that k c n k v 2 n we aim to give an upper bound for partial sums jk 1 j of eigenvalues our bound depends only on the volume of and is to some extent asymptotically correct for any domain because of the analogy between the problems of obtaining lower bounds for dirichlet eigenvalues and upper bounds for neumann eigenvalues cf g polya proc london math soc 3 11 1961 419 433 we can adapt the technique used by li and yau commun math phys 88 1983 309 318 for the task of estimating dirichlet eigenvalues

a generalization of hukuhara difference and division for interval and fuzzy arithmetic we propose a generalization of the hukuhara difference first the case of compact convex sets is examined then the results are applied to generalize the hukuhara difference of fuzzy numbers using their compact and convex level cuts finally a similar approach is suggested to attempt a generalization of division for real intervals and fuzzy numbers applications to solving interval and fuzzy linear equations and fuzzy differential equations are shown

the l2 anti windup problem for discrete time linear systems definition and solutions abstract the anti windup problem for discrete time linear systems is formalized in terms of the l 2 norm of the deviation of the actual response of the system with saturation and anti windup compensation from the ideal unconstrained response we show that paralleling continuous time results a r teel n kapoor the l 2 anti windup problem its definition and solution in proceedings of the 4th ecc brussels belgium july 1997 the problem is globally solvable if and only if the plant is non exponentially unstable and it is robustly globally solvable if and only if the plant is exponentially stable we provide a constructive solution whenever the problem is solvable also offered is a high performance global solution for exponentially stable plants based on receding horizon control illustrative simulations are included

design of compensators for robust tracking and disturbance rejection in this paper the design of compensators to achieve robust asymptotic tracking and disturbance rejection is presented by solving a set of linear algebraic equations both plant entered and input entered disturbances are considered the design requires less computation than the existing ones

on the computation of reference signal constraints for guaranteed tracking performance abstract this paper concerns the problem of determining constraints on reference signals for tracking systems such that the tracking performance can be guaranteed within a specified tolerance for any reference signal satisfying the constraints we first consider the problem of computing derivative constraints which are linear constraints on the vector valued reference signal and its time derivatives and present an off line algorithm for computing inner approximations to supremal derivative constraint sets based on the hyperplane method for generating inner and outer approximations to the reachable set of states for the controlled system no simulation is required we then consider planning problems in which a finite number of parameters are selected to generate the reference signal the derivative constraints are mapped into this parameter space the simplicial approximation method is proposed as a method for computing an approximation to the set of admissible parameters the resulting linear parameter constraints characterize a class of reference signals which can be successfully executed by the tracking system thereby permitting supervisory planning and control to be carried out in the reference signal parameter space without simulating detailed models of the underlying system dynamics we illustrate the computational algorithm and the application of derivative and parameter constraints for the problem of generating trajectories for a two axis computer numerical control cnc cutting tool

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

aggregation of subjective evaluations based on discrete fuzzy numbers in this paper aggregation functions defined on the set of all discrete fuzzy numbers whose support is a subset of consecutive natural numbers are introduced and the particular cases of uninorms and nullnorms are studied in detail these aggregation functions are constructed from discrete aggregation functions defined on a finite chain and they are applied to the aggregation of subjective evaluations

a new problem in control system design and circuit design an optimisation problem arising in the design of circuits and control systems is formulated and an outer approximation algorithm for solving it is presented the problem is characterized by constraints that must be satisfied for all functions in a given subset of a function space it is shown that an outer approximation type algorithm increases the number of variables and constraints at each iteration a practical algorithm will require a constraint dropping scheme

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

on the schrodinger equation and the eigenvalue problem if k is thekth eigenvalue for the dirichlet boundary problem on a bounded domain in n h weyl s asymptotic formula asserts that lambda k sim c n left frac k v d right 2 n hence sum limits i 1 k lambda i sim frac nc n n 2 k frac n 2 n v d 2 n we prove that for any domain and for all sum limits i 1 k lambda i geqq frac nc n n 2 k frac n 2 n v d 2 n a simple proof for the upper bound of the number of eigenvalues less than or equal to for the operator v x defined on n n 3 in terms of int limits mathbb r n v alpha n 2 is also provided

lyapunov approximation of reachable sets for uncertain linear systems a method is presented for calculating an approximation to the reachable set from the origin of a class of linear control systems the method involves the construction of a lyapunov like function and ultimately requires the numerical solution of a simple optimization problem advantages of the method are that it is applicable to n dimensional systems and does not require calculation of orbits or a choice of boundary conditions further the system need not be completely controllable for the method to be applicable however while the method ensures that the reachable set lies within a specified set a closeness of fit criterion is not available

approximating reachable sets for a class of linear control systems we present a technique for overestimating the reachable set from the origin for a class of n dimensional linear control systems the proposed box method is based upon decomposing the system into one and two dimensional subsystems for which bounds on the new variables can readily be found using these bounds enables the construction of a n dimensional parallelepiped containing the reachable set of the original system examples of this procedure are given as well as a comparison to an overapproximation afforded by a lyapunov approach

asymptotic behaviour of extremal averages of laplacian eigenvalues we study the convergence of extrema of averages of eigenvalues of the dirichlet laplacian on domains in mathbb r n under both measure and surface measure restrictions in the former case we prove that the sequence of averages to the power n 2 is sub additive and determine the first term in its asymptotics in the high frequency limit in the latter case we show that the sequence of minimisers converges to the ball as the frequency goes to infinity similar results hold for neumann boundary conditions

comparison of fuzzy numbers using a fuzzy distance measure a new approach for ranking fuzzy numbers based on a distance measure is introduced a new class of distance measures for interval numbers that takes into account all the points in both intervals is developed first and then it is used to formulate the distance measure for fuzzy numbers the approach is illustrated by numerical examples showing that it overcomes several shortcomings such as the indiscriminative and counterintuitive behavior of several existing fuzzy ranking approaches

a simple method for computation of fuzzy linear regression we propose a new method for computation of fuzzy regression that is simple and gives good solutions we consider two cases first when only the dependent variable is fuzzy our approach is given and is compared with those suggested in the literature secondly when both dependent and independent variables are fuzzy our approach is extended and compared with those given in the literature in each case a simple example is used to compare the competing approaches

optimal rejection of persistent bounded disturbances in this paper we formulate the problem of optimal disturbance rejection in the case where the disturbance is generated as the output of a stable system in response to an input which is assumed to be of unit amplitude but is otherwise arbitrary the objective is to choose a controller that minimizes the maximum amplitude of the plant output in response to such a disturbance mathematically this corresponds to requiring uniformly good disturbance rejection over all time since the problem of optimal tracking is equivalent to that of optimal disturbance rejection if a feedback controller is used see 7 sect 5 6 the theory presented here can also be used to design optimal controllers that achieve uniformly good tracking over all time rather than a tracking error whose l 2 norm is small as is the case with the currently popular h infty theory the present theory is a natural counterpart to the existing theory of optimal disturbance rejection the so called h infty theory which is based on the assumption that the disturbance to be rejected is generated by a stable system whose input is square integrable and has unit energy it is shown that the problem studied here has quite different features from its predecessor complete solutions to the problem are given in several important cases including those where the plant is minimum phase or when it has only a single unstable zero in other cases procedures are given for obtaining bounds on the solution and for obtaining suboptimal controllers

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

fuzzy random variables abstract in this paper we define the concepts of fuzzy random variable and the expectation of a fuzzy random variable the new definition of expectation generalizes the integral of a set valued function we derive some properties of these new concepts by considering a suitable generalization of the hausdorff metric we derive the lebesgue dominated convergence type theorem

optimal spectral rectangles and lattice ellipses we consider the problem of minimizing the k th eigenvalue of rectangles with unit area and dirichlet boundary conditions this problem corresponds to finding the ellipse centred at the origin with axes on the horizontal and vertical axes with the smallest area containing k integer lattice points in the first quadrant we show that as k goes to infinity the optimal rectangle approaches the square and correspondingly the optimal ellipse approaches the circle we also provide a computational method for determining optimal rectangles for any k and relate the rate of convergence to the square with the conjectured error term for gauss s circle problem

extremal eigenvalues of the laplacian on euclidean domains and closed surfaces we investigate properties of the sequences of extremal values that could be achieved by the eigenvalues of the laplacian on euclidean domains of unit volume under dirichlet and neumann boundary conditions respectively in a second part we study sequences of extremal eigenvalues of the laplace beltrami operator on closed surfaces of unit area