ranks of boolean matrices abstract we denote by m n 0 1 the set of all n n boolean matrices for any boolean matrix x in m n 0 1 has row rank r and column rank s and we denote it by rank k r s let v be the set of all x in m n 0 1 such that rank x n s where n is fixed and s is not fixed we find the lower bound s for x in v

technical communique who needs qp for linear mpc anyway conventional mpc uses quadratic programming qp to minimise on line a cost over n linearly constrained control moves however stability constraints often require the use of large n thereby increasing the on line computation rendering the approach impracticable in the case of fast sampling here we explore an alternative that requires a fraction of the computational cost which increases only linearly with n and propose an extension which in all but a small class of models matches to within a fraction of a percent point the performance of the optimal solution obtained through qp the provocative title of the paper is intended to point out that the proposed approach offers a very attractive alternative to qp based mpc

stability analysis for switched boolean networks under arbitrary switching signals this note investigates the stability of switched boolean networks sbns under arbitrary switching signal by using the tool of semi tensor product of matrices first an algebraic expression is given for the sbn via the semi tensor product based on it a necessary and sufficient condition is presented for the switching point reachability of the system second using the switching point reachability the pointwise stabilizability is studied and a necessary and sufficient condition is obtained finally the global stability of sbns under arbitrary switching signal is investigated and an easily verifiable necessary and sufficient condition is presented two illustrative examples are presented to show that the main results are effective in analyzing the stability of sbns

a framework for robustness analysis of constrained finite receding horizon control a framework for robustness analysis of input constrained finite receding horizon control is presented under the assumption of quadratic upper bounds on the finite horizon costs we derive sufficient conditions for robust stability of the standard discrete time linear quadratic receding horizon control formulation this is achieved by recasting conditions for nominal and robust stability as an implication between quadratic forms lending itself to s procedure tools which are used to convert robustness questions to tractable convex conditions robustness with respect to plant model mismatch as well as for state measurement error is shown to reduce to the feasibility of linear matrix inequalities simple examples demonstrate the approach

fuzzy matrices of permanent one abstract we study the n n fuzzy matrices of permanent one hall matrices which are generalizations of the reflexive fuzzy matrices we give some necessary and sufficient conditions for a hall matrix to have a generalized inverse in the semigroup hn of n n hall matrices as applications we also study the fuzzy linear maps and the principal left ideals of hn

the determinant and adjoint of a square fuzzy matrix abstract the theory of the determinant and adjoint of a square fuzzy matrix will be studied also we define the circular fuzzy matrices and show that some properties of a square fuzzy matrix such as reeflexivity transitivity circularity are carried over to the adjoint of the matrix finally we show how to construct a transitive fuuzzy matrix from a given one through the adjoint matrix

a linear programming oriented procedure for quadratic stabilization of uncertain systems abstract this paper gives a new necessary and sufficient condition for linear quadratic stabilization of linear uncertain systems when both the dynamic as well as the control matrix are subject to uncertainty a constructive numerical procedure is defined to check the condition and it furthermore provides a stabilizing linear feedback gain some experiments are presented

brief paper controllability of boolean control networks with time delays in states this paper investigates the controllability of boolean networks with time invariant delays in states after a brief introduction on converting the logic dynamics to discrete time delay systems the controllability via two kinds of controls is studied one kind of control is generated by boolean control networks another kind of control is free boolean sequences in both cases necessary and sufficient conditions of the controllability of boolean control networks are proved finally examples are given to illustrate the efficiency of the obtained results

factorizations of matrices over semirings in this paper as a generalization of prime boolean matrices and prime fuzzy matrices we study semiprime matrices over chain semirings using the relationship between semiprime matrices and their row spaces we show that a nonmonomial matrix with full semiring rank can be expressed as a product of elementary matrices and semiprime matrices furthermore we show that a nonmonomial regular matrix with full semiring rank can be expressed as a product of elementary matrices

stabilizing receding horizon h sub spl infin controls for linear continuous time varying systems in this note new matrix inequality conditions on the terminal weighting matrices are proposed for linear continuous time varying systems under these conditions nonincreasing and nondecreasing monotonicities of the saddle point value of a dynamic game are shown to be guaranteed it is proved that the proposed terminal inequality conditions ensure the closed loop stability of the receding horizon h sub spl infin control rhhc the stabilizing rhhc guarantees the h sub spl infin norm bound of the closed loop system the proposed terminal inequality conditions for the monotonicity of the saddle point value and the closed loop stability include most well known existing terminal conditions as special cases the results for time invariant systems are obtained correspondingly from those in the time varying case

a predictive control scheme for systems with variable time delay this article deals with the robust control design problem for linear time invariant systems affected by variable feedback delay constraints on the system state are considered in the system description the starting point is the construction of a predictive control law which guarantees the existence of a nonempty robust positive invariant rpi set with respect to the closed loop dynamics subsequently an iterative algorithm is proposed in order to obtain an approximation of the maximal rpi set the problem can be treated in the framework of piecewise affine systems due to the explicit formulations of the control law obtained via multiparametric programming

disturbance decoupling of boolean control networks disturbance decoupling problem ddp of boolean control networks is considered using semi tensor product of matrices and the matrix expression of logical functions a working procedure is proposed to solve the problem this procedure consists of two key design steps first how to convert a system into an output friendly coordinate frame an algorithm is provided to calculate the output friendly subspaces secondly it was shown how to find proper controllers to solve the problem if it is solvable a state variable separation form is introduced to guide the design of controllers based on the design technique necessary and sufficient conditions are obtained for the solvability of ddp

lq tracking controls with fixed terminal states and their application to receding horizon controls in this paper finite horizon linear quadratic tracking controls fhlqtc with fixed terminal states are proposed in recursive forms for linear time invariant lti discrete and continuous time systems the proposed fhlqtcs are to minimize finite horizon quadratic cost functions while driving the terminal state exactly to the given fixed reference value the fhlqtcs in this paper are applied to the receding horizon linear quadratic tracking controls rhlqtc with guaranteed stability it is shown through simulation that the proposed fhlqtc moves the terminal state exactly to the given destination and the proposed rhlqtc follows the given reference signal well while guaranteeing stability

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

properties of generalized predictive control control design using long range prediction based on a dynamic model of the plant has become an important contender for high performance applications the model can be derived analytically but more typically it is provided by simple experiments or in the adaptive context by recursive estimation many methods have been proposed in the literature depending on the assumed model structure and the choice of cost function here the approach called generalized predictive control or gpc is reviewed of special interest is the derivation of prediction equations using an observer polynomial and a demonstration that the selection of particular horizons the costing horizons and the control horizon leads to well understood basic techniques such as dead beat pole placement and lq simulated examples show that gpc is suitable for controlling a complex plant such as unstable inverse unstable systems and how the observer polynomial independently tailors the response to the disturbances preprogrammed set points as with robot trajectory control and actuator nonlinearities can also be catered for a discussion of adaptive applications of gpc to several industrial process concludes that the method is easy to use and effective

a linear framework on the distributed model predictive control of positive systems abstract this paper investigates the distributed model predictive control dmpc for positive systems with interval and polytopic uncertainties respectively different from the traditional quadratic dmpc a new linear dmpc framework is established for positive systems first a linear cooperative cost function performance index function is introduced for the dmpc of positive systems accordingly some linear constraint conditions are imposed on the systems then a linear co positive lyapunov function is constructed using the linear lyapunov function the dmpc controllers are designed for interval positive systems and polytopic positive systems respectively the controller of each subsystem contains not only the state information of the subsystem but also the state information of other correlated subsystems linear programming based optimization algorithm is addressed to compute the controller parameters to guarantee the feasibility and stability of the systems a cone invariant set is proposed finally two case studies are provided to illustrate the effectiveness of the theoretical findings

unique solvability of max min fuzzy equations and strong regularity of matrices over fuzzy algebra a matrix is said to have strongly linearly independent columns or in the case of square matrices to be strongly regular if for some vector b the system a x b has a unique solution we formulate a necessary and sufficient condition for a linear system of equations over a fuzzy algebra to have a unique solution and prove the equivalence of strong regularity and trapezoidal property moreover an algorithm for testing these properties is reviewed

a maximum principle for single input boolean control networks boolean networks have recently been attracting considerable interest as computational models for genetic and cellular networks we consider a mayer type optimal control problem for a single input boolean network and derive a necessary condition for a control to be optimal this provides an analog of pontryagin s maximum principle for single input boolean networks

on a convex parameter space method for linear control design of uncertain systems this paper presents a new procedure for continuous and discrete time linear control systems design it consists of the definition of a convex programming problem in the parameter space that when solved provides the feedback gain one of the most important features of the procedure is that additional design constraints are easily incorporated in the original formulation yielding solutions to problems that have raised a great deal of interest within the last few years this is precisely the case of the decentralized control problem and the quadratic stabilizability problem of uncertain systems with both dynamic and input uncertain matrices in this last case necessary and sufficient conditions for the existence of a linear stabilizing gain are provided and to the authors knowledge this is one of the first numerical procedures able to handle and solve this interesting design problem for high order continuous time or discrete time linear models the theory is illustrated by examples

multiplicative update rules for concurrent nonnegative matrix factorization and maximum margin classification the state of the art classification methods which employ nonnegative matrix factorization nmf employ two consecutive independent steps the first one performs data transformation dimensionality reduction and the second one classifies the transformed data using classification methods such as nearest neighbor centroid or support vector machines svms in the following we focus on using nmf factorization followed by svm classification typically the parameters of these two steps e g the nmf bases coefficients and the support vectors are optimized independently thus leading to suboptimal classification performance in this paper we merge these two steps into one by incorporating maximum margin classification constraints into the standard nmf optimization the notion behind the proposed framework is to perform nmf while ensuring that the margin between the projected data of the two classes is maximal the concurrent nmf factorization and support vector optimization are performed through a set of multiplicative update rules in the same context the maximum margin classification constraints are imposed on the nmf problem with additional discriminant constraints and respective multiplicative update rules are extracted the impact of the maximum margin classification constraints on the nmf factorization problem is addressed in section vi experimental results in several databases indicate that the incorporation of the maximum margin classification constraints into the nmf and discriminant nmf objective functions improves the accuracy of the classification

moving horizon control of linear systems with input saturation and plant uncertainty part 2 disturbance rejection and tracking we present a moving horizon feedback system based on constrained optimal control algorithms for linear plants with input saturation the system is a non conventional sampled data system its sampling periods vary from sampling instant to sampling instant and the control during the sampling time is not constant but determined by the solution of an open loop optimal control problem in part 1 we showed that the proposed moving horizon control system is robustly stable in this paper we show that it is capable of asymptotically suppressing a class of l bounded disturbances that are restricted to a subspace and of asymptotically following a class of reference inputs that are continuously differentiable bounded in magnitude and slope and restricted to a subspace

moving horizon control of linear systems with input saturation and plant uncertainty part 1 robustness we present a moving horizon feedback system based on constrained optimal control algorithms for linear plants with input saturation the system is a non conventional sampled data system its sampling periods vary from sampling instant to sampling instant and the control during the sampling time is not constant but determined by the solution of an open loop optimal control problem this is a two part paper in this part we show that the proposed moving horizon control system is robustly stable whether the state of the plant is measurable or not in the second part we show that the proposed moving horizon control system is capable of following a class of reference inputs and suppressing a class of disturbances experimental results show that the behaviour of the moving horizon control system is superior to that resulting from some alternative control laws

receding horizon controls for input delayed systems this paper presents a receding horizon control rhc for an unconstrained input delayed system to begin with we derive a finite horizon optimal control for a quadratic cost function including two final weighting terms the rhc is easily obtained by changing the initial and final times of the finite horizon optimal control a linear matrix inequality lmi condition on two final weighting matrices is proposed to meet the cost monotonicity under which the optimal cost on the horizon is monotonically nonincreasing with time and hence the asymptotical stability is guaranteed only if an observability condition is met it is shown through simulation that the proposed rhc stabilizes the input delayed system effectively and its performance can be tuned by adjusting weighting matrices with respect to the state and the input

state feedback stabilization for boolean control networks state feedback stabilization for boolean control networks is investigated in this technical note based on the algebraic representation of logical dynamics in terms of the semi tensor product of matrices a necessary and sufficient condition is derived for the existence of a globally stabilizing state feedback controller and a general control design approach is proposed when global stabilization is feasible via state feedback instead of designing the logical form of a stabilizing feedback law directly we first construct its algebraic representation and then convert the algebraic representation back to the logical form an example is worked out to illustrate the proposed design procedure

a fast algorithm for linear complex chebyshev approximations we propose a new algorithm for finding best minimax polynomial approximations in the complex plane the algorithm is the first satisfactory generalization of the well known remez algorithm for real approximations among all available algorithms ours is the only quadratically convergent one numerical examples are presented to illustrate rapid convergence

determinant theory for d 01 lattice matrices abstract we study determinant theory for d01 lattice matrices and consider the cayley hamilton theorem for these matrices a distributive lattice l is said to be d01 lattice if 0 1 l and 0 x 1 for all x l we prove that det ab det a det b det aadj a det a det adj a a where adj a denotes the adjoint matrix of a d01 lattice matrice a

observability reconstructibility and state observers of boolean control networks the aim of this paper is to introduce and characterize observability and reconstructibility properties for boolean networks and boolean control networks described according to the algebraic approach proposed by d cheng and co authors in the series of papers 3 6 7 and in the recent monography a complete characterization of these properties based both on the boolean matrices involved in the network description and on the corresponding digraphs is provided finally the problem of state observer design for reconstructible bns and bcns is addressed and two different solutions are proposed

fuzzy relation equations theory as a basis of fuzzy modelling an overview abstract we give a wide overview on the applications of fuzzy relation equations theory to decision making processes to the construction of preference relations and to knowledge engineering mainly fuzzy control and fuzzy pattern recognition general theoretical results and methodological aspects are pointed out

regular matrices in the semigroup of hall matrices abstract we study the regular matrices in the semigroup h n of hall matrices boolean matrices with positive permanent we study some necessary and sufficient conditions for a hall matrix to be regular in h n in terms of idempotent matrices adjoint matrices and identifying permutation matrices

optimal control of boolean control networks in this paper we address the optimal control problem for boolean control networks bcns we first consider the problem of finding the input sequences that minimize a given cost function over a finite time horizon the problem solution is obtained by means of a recursive algorithm that represents the analogue for bcns of the difference riccati equation for linear systems we prove that a significant number of optimal control problems for bcns can be easily reframed into the present setup in particular the cost function can be adjusted so as to include penalties on the switchings provided that we augment the size of the bcn state variable in the second part of the paper we address the infinite horizon optimal control problem and we provide necessary and sufficient conditions for the problem solvability the solution is obtained as the limit of the solution over the finite horizon 0 t and it is always achieved in a finite number of steps finally the average cost problem over the infinite horizon investigated in optimal control of logical control networks y zhao ieee trans autom control vol 56 no 8 pp 1766 1776 aug 2011 is addressed by making use of the results obtained in the previous sections

the riccati equation solution of the linear quadratic problem with constrained terminal state we represent the minimal cost and the optimal feedback for the linear quadratic optimal control problem with linear constraints on the terminal state in terms of a solution of the matrix riccati equation which is obtained as a limit of certain solutions representing the optimal cost for the unconstrained problem with penalized terminal state also we examine the convergence of the solution for the upper limit of the interval tending to infinity and the stabilizing effect of the limit control as a by product of our method we obtain some improvement of the known results for the unconstrained nonautonomous infinite interval problem

on the trade off between feasibility and performance in bilinear and state affine model based predictive control closed loop stabilizing model based predictive control mpc algorithms for discrete time bilinear and state affine models are presented stability of the closed loop is obtained through the use of an appropriate end point weighting and end point inequality constraint in this way the infinite horizon performance index is bounded from above by the objective function that is minimized in the mpc algorithm this paper presents an algorithm that aims at obtaining a large feasibility region by maximizing off line the region that is defined by the end point inequality constraint in order to improve the performance of the mpc algorithm the conservatism of the upper bound on the infinite horizon performance index is reduced in the on line computations

constrained infinite horizon model predictive control for fuzzy discrete time systems the problem of constrained infinite horizon model predictive control for fuzzy discrete systems is considered in this paper new sufficient conditions are proposed in terms of linear matrix inequalities based on the optimal solutions of these sufficient conditions at each sampling instant we design both parallel distributed compensation and nonparallel distributed compensation state feedback controllers which can guarantee that the resulting closed loop fuzzy discrete system is asymptotically stable in addition the fuzzy feedback controllers meet the specifications for the fuzzy discrete systems with both input and output constraints numerical examples are presented to demonstrate the effectiveness of the proposed techniques

a riccati approach for constrained linear quadratic optimal control an active set method is proposed for solving linear quadratic optimal control problems subject to general linear inequality path constraints including mixed state control and state only constraints a riccati based approach is developed for efficiently solving the equality constrained optimal control subproblems generated during the procedure the solution of each subproblem requires computations that scale linearly with the horizon length the algorithm is illustrated with numerical examples

representation of conformal maps by rational functions the traditional view in numerical conformal mapping is that once the boundary correspondence function has been found the map and its inverse can be evaluated by contour integrals we propose that it is much simpler and 10 1000 times faster to represent the maps by rational functions computed by the aaa algorithm to justify this claim first we prove a theorem establishing root exponential convergence of rational approximations near corners in a conformal map generalizing a result of d j newman in 1964 this leads to the new algorithm for approximating conformal maps of polygons then we turn to smooth domains and prove a sequence of four theorems establishing that in any conformal map of the unit circle onto a region with a long and slender part there must be a singularity or loss of univalence exponentially close to the boundary and polynomial approximations cannot be accurate unless of exponentially high degree this motivates the application of the new algorithm to smooth domains where it is again found to be highly effective

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

bisimulations of boolean control networks a framework for analyzing bisimulation relations of boolean control networks bcns is set up in this paper bisimulation relations are natural objectives in control systems theory a bisimulation relation between a pair of control systems defines a relation on their state spaces or state sets explaining how a trajectory or transition of one system can be paired with a trajectory or transition of the other system and vice versa the paper first formalizes the notion of bi simulation in bcns and presents detailed results characterizing bi simulation relations for bcns then as an application of the notion of bisimulation it considers the propagation of the fundamental properties of macro controllability and stabilizability through a bisimulation relation it thereby suggests the possibility that certain control properties of a bcn can be inferred by analyzing a potentially simpler bcn the analysis developed in this paper is based on the semitensor product approach which gives algorithms that have e

model predictive control for linear parameter varying constrained systems using ellipsoidal set prediction this paper proposes a new model predictive control mpc method for linear parameter varying systems with bounded parameter variation subject to input constraints the method adopts closed loop prediction and constructs ellipsoidal sets to predict the future states with reasonable computational effort then the information on the parameter variation rate is exploited to improve the accuracy of the prediction furthermore a relaxed terminal condition which guarantees the stability for infinite horizon is introduced to enlarge the stabilizable region it is shown that the feasibility of the mpc problem at the initial step ensures the stability of the closed loop system finally a simulation result illustrates the effectiveness of the proposed method

the extended symplectic pencil and the finite horizon lq problem with two sided boundary conditions this technical note introduces a new approach to the solution of a very general class of finite horizon optimal control problems for discrete time systems this approach provides a parametric expression for the optimal control sequences as well as the corresponding optimal state trajectories by exploiting a new decomposition of the so called extended symplectic pencil this decomposition provides an original strategy for a more direct solution of the problem with no need of the system theoretic hypotheses including regularity of the symplectic pencil that have always been assumed in the literature so far

aggregation algorithm towards large scale boolean network analysis the analysis of large scale boolean network dynamics is of great importance in understanding complex phenomena where systems are characterized by a large number of components the computational cost to reveal the number of attractors and the period of each attractor increases exponentially as the number of nodes in the networks increases this paper presents an efficient algorithm to find attractors for medium to large scale networks this is achieved by analyzing subnetworks within the network in a way that allows to reveal the attractors of the full network with little computational cost in particular for each subnetwork modeled as a boolean control network the input state cycles are found and they are composed to reveal the attractors of the full network the proposed algorithm reduces the computational cost significantly especially in finding attractors of short period or any periods if the aggregation network is acyclic also this paper shows that finding the best acyclic aggregation is equivalent to finding the strongly connected components of the network graph finally the efficiency of the algorithm is demonstrated on two biological systems namely a t cell receptor network and an early flower development network

brief nonlinear model predictive control with polytopic invariant sets ellipsoidal invariant sets have been widely used as target sets in model predictive control mpc these sets can be computed by constructing appropriate linear difference inclusions together with additional constraints to ensure that the ellipsoid lies within a given inclusion polytope the choice of inclusion polytope has a significant effect on the size of the target ellipsoid but the optimal inclusion polytope cannot in general be computed systematically this paper shows that use of polytopic invariant sets overcomes this difficulty allowing larger stabilizable sets without loss of performance in the interests of online efficiency consideration is focused on interpolation based mpc

ranks of fuzzy matrices applications in state reduction of fuzzy automata abstract in this paper we consider different types of ranks of fuzzy matrices over residuated lattices we investigate relations between ranks and prove that row rank column rank and schein rank of idempotent fuzzy matrices are equal in particular ranks and corresponding decompositions of fuzzy matrices representing fuzzy quasi orders are studied in detail we show that fuzzy matrix decomposition by ranks can be used in the state reduction of fuzzy automata moreover we prove that using rank decomposition of fuzzy matrices improves results of any state reduction method based on merging indistinguishable states of fuzzy automata

controller design for disturbance decoupling of boolean control networks we investigate a type of disturbance decoupling problem ddp of boolean control networks using the semi tensor product of matrices the dynamics of a boolean control network is expressed in its algebraic form under the framework of output friendly subspace we give a necessary and sufficient condition for the solvability of ddp by analyzing the redundant variables and we present a computationally feasible method to construct all the valid feedback control matrices the logical functions of each controller can be recovered from the obtained feedback control matrix finally an example is provided to show the effectiveness of the proposed method

orthogonal polynomials of equilibrium measures supported on cantor sets the equilibrium measure of a compact set is a fundamental object in logarithmic potential theory we compute numerically this measure and its orthogonal polynomials when the compact set is a cantor set defined by an iterated function system we first construct sequences of discrete measures via the solution of large systems of non linear equations that converge weakly to the equilibrium measure successively we compute their jacobi matrices via standard procedures enhanced for the scope numerical estimates of the convergence rate to the limit jacobi matrix are provided which show stability and efficiency of the whole procedure as a companion result we also compute jacobi matrices in two other cases equilibrium measures on finite sets of intervals and balanced measures of iterated function systems these algorithms can reach large polynomial orders therefore we study the asymptotic behavior of the orthogonal polynomials and by a natural extension of the concept of regular root asymptotics we derive an efficient scheme for the computation of complex green s functions and of related conformal mappings

an accelerated approach for solving fuzzy relation equations with a linear objective function in literature the optimization model with a linear objective function subject to fuzzy relation equations has been converted into a 0 1 integer programming problem by fang and li 1999 they proposed a jump tracking branch and bound method to solve this 0 1 integer programming problem in this paper we propose an upper bound for the optimal objective value based on this upper bound and rearranging the structure of the problem we present a backward jump tracking branch and bound scheme for solving this optimization problem a numerical example is provided to illustrate our scheme furthermore testing examples show that the performance of our scheme is superior to the procedure in the paper by fang and li several testing examples show that our initial upper bound is sharp

a primal dual potential reduction method for problems involving matrix inequalities we describe a potential reduction method for convex optimization problems involving matrix inequalities the method is based on the theory developed by nesterov and nemirovsky and generalizes gonzaga and todd s method for linear programming a worst case analysis shows that the number of iterations grows as the square root of the problem size but in practice it appears to grow more slowly as in other interior point methods the overall computational effort is therefore dominated by the least squares system that taust be solved in each iteration a type of conjugate gradient algorithm can be used for this purpose which results in important savings for two reasons first it allows us to take advantage of the special structure the problems often have e g lyapunov or algebraic riccati inequalities second we show that the polynomial bound on the number ofiterations remains valid even if the conjugate gradient algorithm is not run until completion which in practice can greatly reduce the computational effort per iteration we describe in detail how the algorithm works for optimization problems with l lyapunov inequaliues each of size m we prove an overall worst case operation count of o mssll5 the average case complexity appears to be closer to o m4ll5 this estimate is justified by extensive numerical experimentation and is consistent with other researchers experience with the practical performance of interior point algorithms for linear programming this result means that the computational cost of extending current control theory based on the solution of lyapunov or riccati equations to a theory that is based on the solution of multiple coupled lyapunov or riccati inequalities is modest

matrix approach to model matching of asynchronous sequential machines in this note we propose a matrix based approach for asynchronous sequential machines using semi tensor product of matrices we convert an asynchronous machine into a discrete time bilinear system and study its dynamics by investigating its structure matrices we give simple algorithms for cycle detection and reachability analysis and moreover provide a control design method for the model matching of two input state machines

method of centers for minimizing generalized eigenvalues abstract we consider the problem of minimizing the largest generalized eigenvalue of a pair of symmetric matrices each of which depends affinely on the decision variables although this problem may appear specialized it is in fact quite general and includes for example all linear quadratic and linear fractional programs many problems arising in control theory can be cast in this form the problem is nondifferentiable but quasiconvex so methods such as kelley s cutting plane algorithm or the ellipsoid algorithm of shor nemirovsky and yudin are guaranteed to minimize it in this paper we describe relevant background material and a simple interior point method that solves such problems more efficiently the algorithm is a variation on huard s method of centers using a self concordant barrier for matrix inequalities developed by nesterov and nemirovsky nesterov and nemirovsky have also extended their potential reduction methods to handle the same problem since the problem is quasiconvex but not convex devising a nonheuristic stopping criterion i e one that guarantees a given accuracy is more difficult than in the convex case we describe several nonheuristic stopping criteria that are based on the dual of a related convex problem and a new ellipsoidal approximation that is slightly sharper in some cases than a more general result to nesterov and nemirovsky the algorithm is demonstrated on an example determining the quadratic lyapunov function that optimizes a decay rate estimate for a differential inclusion

on the convergence of multiplicative update algorithms for nonnegative matrix factorization nonnegative matrix factorization nmf is useful to find basis information of nonnegative data currently multiplicative updates are a simple and popular way to find the factorization however for the common nmf approach of minimizing the euclidean distance between approximate and true values no proof has shown that multiplicative updates converge to a stationary point of the nmf optimization problem stationarity is important as it is a necessary condition of a local minimum this paper discusses the difficulty of proving the convergence we propose slight modifications of existing updates and prove their convergence techniques invented in this paper may be applied to prove the convergence for other bound constrained optimization problems

employing the algebraic riccati equation for a parametrization of the solutions of the finite horizon lq problem the discrete time case in this paper a new methodology is developed for the closed form solution of a generalized version of the finite horizon linear quadratic regulator problem for lti discrete time systems the problem considered herein encompasses the classical version of the lq problem with assigned initial state and weighted terminal state as well as the so called fixed end point version in which both the initial and the terminal states are sharply assigned the present approach is based on a parametrization of all the solutions of the extended symplectic system in this way closed form expressions for the optimal state trajectory and control law may be determined in terms of the boundary conditions by taking advantage of standard software routines for the solution of the algebraic riccati and stein equations our results lead to a simple and computationally attractive approach for the solution of the considered optimal control problem without the need of iterating the riccati difference equation

logical matrix factorization with application to topological structure analysis of boolean network this note investigates the logical matrix factorization with application to the topological structure analysis of boolean networks first the concepts of both factorization and rank are defined for logical matrices and two factorization problems are then studied using nonsingular logical matrix transformations several necessary and sufficient conditions for the factorization of a given logical matrix are presented second the logical matrix factorization is applied to the topological structure analysis of a given boolean network and a size reduced structure equivalent logical network is constructed for the given system it is shown that the topological structure including all the fixed points and cycles of the resulting size reduced logical network is the same as that of the original boolean network the study of an illustrative example shows that the new results presented in this note are effective in analyzing the topological structure of boolean networks

nonconvex optimization problem the infinite horizon linear quadratic control problem with quadratic constraints abstract we present a general method for the solution of the problem of minimization of a quadratic functional in a hilbert space over the intersection of some subspace and a set defined by special quadratic constraints many optimal control problems can be formulated in this abstract form as an example a stationary infinite horizon linear quadratic optimization problem with quadratic constraints is posed and solved

robust optimal feedback for terminal linear quadratic control problems under disturbances we consider a linear dynamic system in the presence of an unknown but bounded perturbation and study how to control the system in order to get into a prescribed neighborhood of a zero at a given final moment the quality of a control is estimated by the quadratic functional we define optimal guaranteed program controls as controls that are allowed to be corrected at one intermediate time moment we show that an infinite dimensional problem of constructing such controls is equivalent to a special bilevel problem of mathematical programming which can be solved explicitely an easy implementable algorithm for solving the bilevel optimization problem is derived based on this algorithm we propose an algorithm of constructing a guaranteed feedback control with one correction moment we describe the rules of computing feedback which can be implemented in real time mode the results of illustrative tests are given

a parametrization of the solutions of the finite horizon lq problem with general cost and boundary conditions a generalization of the finite horizon linear quadratic regulator problem is proposed for lti continuous time controllable systems in particular a formulation of the linear quadratic lq problem is considered with affine constraints on the initial and the terminal states and with general quadratic costs in the initial and terminal states the solution presented is simple and attractive from a computational point of view and is based on the solutions of an algebraic riccati equation and of a lyapunov equation that enable all the solutions of the hamiltonian differential equation to be parametrized in closed form

on reachability and controllability of switched boolean control networks this paper investigates the reachability and controllability of switched boolean control networks bcns by using the semi tensor product method first a kind of switching input state transfer graph is defined based on which and the algebraic expression of switched bcns we thus propose a new kind of switching input state incidence matrix that contains the complete information of the switching input state transfer graph second by the switching input state incidence matrix several necessary and sufficient conditions are obtained for the reachability and controllability of switched bcns finally an algorithm is established to find a switching sequence and a control scheme to realize the reachability of switched bcns in the shortest time the study of an illustrative example shows that the new results obtained in this paper are very effective in investigating the reachability and controllability of switched bcns

on linear programming and robust modelpredictive control using impulse responses abstract campo and morari have derived a linear programming problem with a potentially large number of constraints which is equivalent to a min max formulation for robust model predictive control of linear systems that formulation involves minimization with respect to the controls of the maximum with respect to the system s impulse response from a set of possible impulse responses of the infinity norm of the error between the predicted and required system output sequences here an alternative linear programming problem is derived which has a smaller number of constraints and is therefore potentially more convenient for on line control

the complex structured singular value a tutorial introduction to the complex structured singular value is presented with an emphasis on the mathematical aspects of the based methods discussed here have been useful for analysing the performance and robustness properties of linear feedback systems several tests for robust stability and performance with computable bounds for transfer functions and their state space realizations are compared and a simple synthesis problem is studied uncertain systems are represented using linear fractional transformations lfts which naturally unify the frequency domain and state space methods

on robust stability and set invariance of switched linear parameter varying systems in this paper we address the problem of robust stability and set invariance of switched linear parameter varying lpv systems affected by bounded disturbances a switched lpv system is a collection of single lpv subsystems with a switching rule that decides which subsystem is active at each time this framework is useful for lpv systems with large parameter variation range for which it may be difficult to assess or guarantee stability over the whole parameter range our first contribution is to derive a result for a single lpv system that extends and generalises previous work for switched systems our second and main contribution is to apply this seed result in the derivation of dwell time type conditions on the switched lpv switching rule which ensure robust closed loop stability and set invariance of the trajectories of the switched lpv system across the whole parameter range as an application of the results we consider the problem of reference tracking for lpv systems using switched lpv state fe

regular fuzzy matrices and fuzzy equations abstract there have been many researches on fuzzy relational equations in this paper under the general framework of fuzzy matrix theory we first introduce ranks and regularity properties of fuzzy matrices then for a regular matrix a mn f we study the generalized inverses of a and the solutions of a fuzzy equation x a b

on stability of constrained receding horizon control with finite terminal weighting matrix in this paper a new stabilizing receding horizon control based on a finite input and state horizon cost with a finite terminal weighting matrix is proposed for time varying discrete linear systems with constraints we propose matrix inequality conditions on the terminal weighting matrix under which closed loop stability is guaranteed for both cases of unconstrained and constrained systems with input and state constraints we show that such a terminal weighting matrix can be obtained by solving a linear matrix inequality lmi in the case of constrained time invariant systems an artificial invariant ellipsoid constraint is introduced in order to relax the conventional terminal equality constraint and to handle constraints using the invariant ellipsoid constraints a feasibility condition of the optimization problem is presented and a region of attraction is characterized for constrained systems with the proposed receding horizon control

a linear representation of dynamics of boolean networks a new matrix product called semi tensor product of matrices is reviewed using it a matrix expression of logic is proposed where a logical variable is expressed as a vector a logical function is expressed as a multiple linear mapping under this framework a boolean network equation is converted into an equivalent algebraic form as a conventional discrete time linear system analyzing the transition matrix of the linear system formulas are obtained to show a the number of fixed points b the numbers of cycles of different lengths c transient period for all points to enter the set of attractors and d basin of each attractor the corresponding algorithms are developed and used to some examples

inverses of l fuzzy matrices abstract inverses and generalized inverses of matrices over a brouwerian lattice are considered necessary and sufficient conditions for the existence of inverses g inverses thierrin vagner inverses minimum norm g inverses least squares g inverses and moore penrose inverses of matrices are obtained algorithms for finding all these types of generalized inverses are given

iteration algorithm for solving ax b in max min algebra abstract for solving the linear system a x b we introduce some iteration algorithms where a aij and b bi a given matrix and a column vector with elements from a brouwerian lattice and is a max min composite operation

predictive control for sector bounded nonlinear model and its application to solid oxide fuel cell systems in this paper a nonlinear model predictive control method is presented for solid oxide fuel cell systems for realistic modeling a sector bounded nonlinear model with input constraint is considered as a performance index we consider one horizon cost function that is represented by the weighted sum of state control input and nonlinear function by minimizing the upper bound of the cost function the optimized control input sequences are obtained for cost monotonicity a terminal inequality condition is derived in terms of a finite number of linear matrix inequalities lmis by using augmented vector feedback law which consists of state and sector bounded nonlinear function in order to show the effectiveness of the proposed method the sector bounded nonlinear model is derived for the solid oxide fuel cell systems and the system performance is verified by applying the proposed mpc algorithm to the systems

a fast method for solving certain integral equations of the first kind with application to conforma mapping abstract we describe a fast iterative method for solving fredholm integral equations of the first kind whose kernels have a logarithmic principal part the method is a fourier galerkin method and due to the singularity of the kernel the linear system of simultaneous equations is block diagonally dominant and can be solved rapidly by an iterative method we present examples of the computation of conformal mappings of simply and multiply connected domains

the smallest solution of max min fuzzy equations abstract the object of this paper is to study the smallest solution of a max min fuzzy equation we give some necessary and sufficient conditions for the existence of a unique minimal solution of the equation also a sufficient and necessary condition for the equation to have only one solution these results offer some solutions to an unsolved problem posed by guo si zhong et al 1

controllability and observability of boolean control networks with time variant delays in states this brief investigates the controllability and observability of boolean control networks with not necessarily bounded time variant delays in states after a brief introduction to converting a boolean control network to an equivalent discrete time bilinear dynamical system via the semi tensor product of matrices the system is split into a finite number of subsystems constructed forest with no time delays by using the idea of splitting time that is proposed in this brief then the controllability and observability of the system are investigated by verifying any so called controllability constructed path and any so called observability constructed paths in the above forest respectively which generalize some recent relevant results matrix test criteria for the controllability and observability are given the corresponding control design algorithms based on the controllability theorems are given we also show that the computing complexity of our algorithm is much less than that of the existing algorithms

sets of solution set equivalent coefficient matrices of fuzzy relation equations abstract a set of coefficient matrices which are equivalent to the solution set of a fuzzy relation equation is considered it is also shown that the cardinal numbers of solution sets of fuzzy relation equations for two constant vectors with the same partition on the index set are equal to each other

further contributions to the study of finite fuzzy relations equations abstract an interesting property of the schein rank of a fuzzy matrix stressed by k h kim and f w roush is formalized as definition of the basis of a set of fuzzy vectors defined over a commutative semiring with respect to another set of fuzzy vectors we apply this definition and another related concept in the setting of finite fuzzy relation equations in particular we give a sufficient condition for the existence of the smallest solution of a max min fuzzy equation

an interpolation strategy for discrete time bilinear mpc problems input output i o feedback linearization suffers from a number of restrictions which have limited its use in model based predictive control some of these restrictions do not apply to the case of bilinear systems but problems with input constraints and unstable zero dynamics persist this paper overcomes these difficulties by means of an interpolation strategy involved in this interpolation is a feasible and stabilizing trajectory which is computed through the use of invariant feasible sets and a more aggressive trajectory which can be chosen to be either the unconstrained optimal trajectory or any alternative one

quasi min max fuzzy model predictive control of direct methanol fuel cells abstract direct methanol fuel cells dmfcs are known as a promising power source in future in this paper we consider steering a dmfc plant to a desired operating point while optimizing the transient performance according to a quadratic cost function quasi min max fuzzy model predictive control fmpc with input constraints is proposed for the dmfc in order to reduce the computational burden for real time implementation a partial off line quasi min max fmpc is also proposed in this case a bank of invariant sets together with the corresponding feedback control laws are obtained by solving some linear matrix inequalities lmis off line leaving the online part a bisection search and a much simplified constrained optimization problem online computation complexity for both the quasi min max fmpc and the partial off line one is also analyzed simulation results are given to show the effectiveness of the proposed controllers

on polynomial approximation in the complex plane with application to conformal mapping we consider the selection of polynomial bases for polynomial approximation of analytic functions on bounded simply connected regions in the complex plane while a monomial basis may be very ill conditioned we show that a basis of lagrange polynomials with fejer points as nodes is well conditioned numerical examples where we compute polynomial approximations of conformal mappings conclude the paper

on the determination of boundary collocation points for solving some problems for the laplace operator abstract boundary collocation is a method for obtaining approximate solutions of boundary problems for linear partial differential equations for which complete families of particular solutions are explicitly known the method contains various decisions which are important for its performance such as choice of solution subspace choice of basis for the subspace and choice of collocation points using a model problem some particular strategies for the determination of collocation points are investigated

a heuristic method to compute the approximate postinverses of a fuzzy matrix this paper considers the problem of computing the approximate inverses of a fuzzy matrix under max min composition a polynomial time algorithm is proposed to construct an approximate postinverse by minimizing an evaluation function which balances two different distance measures the obtained approximate postinverse contains no zero columns unless the given fuzzy matrix itself contains zero rows subsequently the techniques for solving fuzzy relational equations are applied to obtain all the approximate postinverses of equal quality

convex liftings based robust control design this paper presents a new approach for control design of constrained linear systems affected by bounded additive disturbances and polytopic uncertainties this method hinges on so called convex liftings which emulate control lyapunov function by providing a constructive framework for optimization based control implementation it will be shown that this method can guarantee the recursive feasibility and robust stability finally a numerical example will be presented to illustrate this method