two conditions concerning common quadratic lyapunov functions for linear systems concerning a pair of linear systems some triangle conditions for the existence of a common quadratic lyapunov function are presented in this paper these conditions are derived from a criterion for judging the semipositiveness of a linear map defined on symmetric matrices

the sensitivity of the stable lyapunov equation we present an analysis of the sensitivity of the solution of the lyapunov equation a x xa w where a is stable this analysis leads to a spectral norm bound on the relative perturbation of the solution which is optimal for a certain class of estimates and which is essentially equivalent to the frobenius norm bound obtained from the associated kronecker product system the latter bound can be expressed in terms of operatorname sep a a and is known to accurately reflect the sensitivity of the lyapunov problem but it is hard to interpret in terms of the original matrix a in contrast the spectral norm bound which we derive is directly related to the minimal l 2 damping of the dynamical system dot z az moreover this dynamical link with the sensitivity problem leads to a new method of systematically investigating the norm behavior of e at as well as providing a wealth of information about control theoretic aspects of dot z az when a is the closed loop state matrix

quadratically saturated regulator for constrained linear systems the problem of stabilization and null controllability of open loop unstable discrete time multi input systems with constraints on the inputs and the controls is addressed in this paper first necessary and sufficient conditions for solvability of the problem are derived they guarantee the existence of a linear controller leaving the state constraint set for the closed loop system positively invariant an optimal control law is computed and the admissible set of initial conditions is given such that along trajectories of the closed loop system the state and input constraints are satisfied then the domain of feasible initial conditions is enlarged using a saturating control if such is feasible

on a common quadratic lyapunov function for widely distant systems a sufficient condition concerning the construction of a common quadratic lyapunov function for widely distant linear systems is presented the condition is set on a mutual relation matrix whose size is just equal to the number of the coefficient matrices

fuzzy r d portfolio selection of interdependent projects global competition of markets has forced firms to invest in targeted r d projects so that resources can be focused on successful outcomes a number of options are encountered to select the most appropriate projects in an r d project portfolio selection problem the selection is complicated by many factors such as uncertainty interdependences between projects risk and long lead time that are difficult to measure our main concern is how to deal with the uncertainty and interdependences in project portfolio selection when evaluating or estimating future cash flows this paper presents a fuzzy multi objective programming approach to facilitate decision making in the selection of r d projects here we present a fuzzy tri objective r d portfolio selection problem which maximizes the outcome and minimizes the cost and risk involved in the problem under the constraints on resources budget interdependences outcome projects occurring only once and discuss how our methodology can be used to make decision support tools for optimal r d project selection in a corporate environment a case study is provided to illustrate the proposed method where the solution is done by genetic algorithm ga as well as by multiple objective genetic algorithm moga

minimality and local state decompositions of a nonlinear state space realization using energy functions in this paper a set of sufficient conditions is developed in terms of controllability and observability functions under which a given state space realization of a formal power series is minimal specifically it is shown that positivity of these functions in addition to a stability requirement and a few technical conditions implies minimality using the nonlinear analogue of the kalman decomposition connections are then established between minimality singular value functions balanced realizations and various notions of reachability and observability for nonlinear systems

robust control strategies for multi inventory systems with average flow constraints in this paper we consider multi inventory systems in the presence of uncertain demand we assume that i demand is unknown but bounded in an assigned compact set and ii the control inputs controlled flows are subject to assigned constraints given a long term average demand we select a nominal flow that feeds such a demand in this context we are interested in a control strategy that meets at each time all possible current demands and achieves the nominal flow in the average we provide necessary and sufficient conditions for such a strategy to exist and we characterize the set of achievable flows such conditions are based on linear programming and thus they are constructive in the special case of a static flow i e a system with 0 capacity buffers we show that the strategy must be affine the dynamic problem can be solved by a linear saturated control strategy inspired by the previous one we provide numerical analysis and illustrative examples

a condition for the stability of switched nonlinear systems in this paper we present a sufficient condition for the global asymptotic stability of a switched nonlinear system composed of a finite family of subsystems we show that the global asymptotic stability of each subsystem and the pairwise commutation of the vector fields that define the subsystems i e the lie bracket of any pair of them is zero are sufficient for the global asymptotic stability of the switched system we also show that these conditions are sufficient for the existence of a common lyapunov function

stabilizing controllers for bilinear systems the problem of finding stabilizing feedback controllers for continuous bilinear systems where the controls act additively and multiplicatively simultaneously is treated the applicability of the quadratic control law of jacobson 5 and others is extended to the case when the a matrix has arbitary eigenvalues under certain conditions a class of bilinear systems common among biochemical flow systems is defined the dyadic bilinear systems a control scheme the so called division controller for dyadic bilinear systems is suggested the practicality of the control schemes is demonstrated on the problem of controlling the neutron level in a fission reactor

quadratic stability of a class of switched nonlinear systems quadratic stability of a class of switched nonlinear systems is studied in this note we first transform quadratic stability problem into an equivalent nonlinear programming problem then we derive a necessary and sufficient condition for quadratic stability of this class of switched systems by using karush kuhn tucker condition for nonlinear programming problems the necessary and sufficient condition is given in terms of the strict completeness of a certain set of functions on a subset of the state space which is much easier to check

min max control of uncertain multi inventory systems with multiplicative uncertainties in this note we consider production distribution systems with buffer and capacity constraints for such systems we assume that the model is not known exactly more precisely the entries of the matrix representing the system structure may be affine functions of some uncertain time varying parameters that take values within assigned bounds we give stabilizability conditions that can be checked in principle by solving a min max problem on the surface of the state space buffer level space unit ball then we consider a special case in which each uncertain parameter affects a single column of the system matrix and is independent of all the other ones in this case we propose a mixed integer linear programming algorithm to check the stabilizability conditions and we provide a stabilizing control in an explicit form

stability robustness for linear state space models a lyapunov mapping approach some pythagorean like conditions for the existence of a common lyapunov solution for two given matrices are presented these conditions are set on the lyapunov mappings associated with given matrices the key is the semipositiveness of linear mappings defined on symmetric matrices from the viewpoint of the existence of a common lyapunov solution some known stability robustness results are reviewed and refined

a stochastic programming model using an endogenously determined worst case risk measure for dynamic asset allocation we present a new approach to asset allocation with transaction costs a multiperiod stochastic linear programming model is developed where the risk is based on the worst case payoff that is endogenously determined by the model that balances expected return and risk utilizing portfolio protection and dynamic hedging an investment portfolio similar to an option like payoff structure on the initial investment portfolio is characterized the relative changes in the expected terminal wealth worst case payoff and risk aversion are studied theoretically and illustrated using a numerical example this model dominates a static mean variance model when the optimal portfolios are evaluated by the sharpe ratio

stability of a class of linear switching systems with applications to two consensus problems in this paper we first establish a stability result for a class of linear switched systems involving kronecker product the problem is interesting in that the system matrix does not have to be hurwitz at any time instant this class of linear switched systems arises in the control of multi agent systems under switching network topology as applications of this stability result we give the solvability conditions for both the leaderless consensus problem and the leader following consensus problem for general marginally stable linear multi agent systems under switching network topology in contrast with some existing results our results only assume that the dynamic graph is uniformly connected

constrained stochastic lqc a tractable approach despite the celebrated success of dynamic programming for optimizing quadratic cost functions over linear systems such an approach is limited by its inability to tractably deal with even simple constraints in this paper we present an alternative approach based on results from robust optimization to solve the stochastic linear quadratic control slqc problem in the unconstrained case the problem may be formulated as a semidefinite optimization problem sdp we show that we can reduce this sdp to optimization of a convex function over a scalar variable followed by matrix multiplication in the current state thus yielding an approach that is amenable to closed loop control and analogous to the riccati equation in our framework we also consider a tight second order cone socp approximation to the sdp that can be solved much more efficiently when the problem has additional constraints both the sdp and socp are tractable in the presence of control and state space constraints moreover compared to the riccati approach they provide much greater control over the stochastic behavior of the cost function when the noise in the system is distributed normally

two stage robust network flow and design under demand uncertainty we describe a two stage robust optimization approach for solving network flow and design problems with uncertain demand in two stage network optimization one defers a subset of the flow decisions until after the realization of the uncertain demand availability of such a recourse action allows one to come up with less conservative solutions compared to single stage optimization however this advantage often comes at a price two stage optimization is in general significantly harder than single stage optimization for network flow and design under demand uncertainty we give a characterization of the first stage robust decisions with an exponential number of constraints and prove that the corresponding separation problem is np hard even for a network flow problem on a bipartite graph we show however that if the second stage network topology is totally ordered or an arborescence then the separation problem is tractable unlike single stage robust optimization under demand uncertainty two stage robust optimization allows one to control conservatism of the solutions by means of an allowed budget for demand uncertainty using a budget of uncertainty we provide an upper bound on the probability of infeasibility of a robust solution for a random demand vector we generalize the approach to multicommodity network flow and design and give applications to lot sizing and location transportation problems by projecting out second stage flow variables we define an upper bounding problem for the two stage min max min optimization problem finally we present computational results comparing the proposed two stage robust optimization approach with single stage robust optimization as well as scenario based two stage stochastic optimization

stability criteria for switched and hybrid systems the study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems the objective of this paper is to outline some of these problems to review progress made in solving them in a number of diverse communities and to review some problems that remain open an important contribution of our work is to bring together material from several areas of research and to present results in a unified manner we begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions closely related to the concept of stability are the notions of exponential growth rates and converse lyapunov theorems both of which are discussed in detail in particular results on common quadratic lyapunov functions and piecewise linear lyapunov functions are presented as they represent constructive methods for proving stability and also represent problems in which significant progress has been made we also comment on the inherent difficulty in determining stability of switched systems in general which is exemplified by np hardness and undecidability results we then proceed by considering the stability of switched systems in which there are constraints on the switching rules through both dwell time requirements and state dependent switching laws also in this case the theory of lyapunov functions and the existence of converse theorems are reviewed we briefly comment on the classical lur e problem and on the theory of stability radii both of which contain many of the features of switched systems and are rich sources of practical results on the topic finally we present a list of questions and open problems which provide motivation for continued research in this area

on stability l2 gain and h control for switched systems this paper addresses the issues of stability l 2 gain analysis and h control for switched systems via multiple lyapunov function methods a concept of general lyapunov like functions is presented a necessary and sufficient condition for stability of switched systems is given in terms of multiple generalized lyapunov like functions which enables derivation of improved stability tests an l 2 gain characterization and a design method for stabilizing switching laws a solution to the h control problem for switched systems is also provided

adaptation coordination and local interactions via distributed approachability abstract this paper investigates the relation between cooperation competition and local interactions in large distributed multi agent systems the main contribution is the game theoretic problem formulation and solution approach based on the new framework of distributed approachability and the study of the convergence properties of the resulting game model approachability theory is the theory of two player repeated games with vector payoffs and distributed approachability is here presented for the first time as an extension to the case where we have a team of agents cooperating against a team of adversaries under local information and interaction structure the game model turns into a nonlinear differential inclusion which after a proper design of the control and disturbance policies presents a consensus term and an exogenous adversarial input local interactions enter into the model through a graph topology and the corresponding graph laplacian matrix given the above model we turn the original questions on cooperation competition and local interactions into convergence properties of the differential inclusion in particular we prove convergence and exponential convergence conditions around zero under general markovian strategies we illustrate our results in the case of decentralized organizations with multiple decision makers

a vague set based decision support approach for evaluating research funding programs abstract scientific research assessment sra is receiving increasing attention in both academic and industry more and more organizations are recognizing the importance of sra for the optimal use of scarce resources in this paper a vague set theory based decision support approach is proposed for sra specifically a family of parameterized s owa operator is developed for the aggregation of vague assessments the proposed approach is introduced to evaluate the research funding programs of the national natural science foundation of china nsfc it provides a soft and expansive way to help the decision maker in nsfc to make his decisions the proposed approach can also be used for some other agencies to make similar assessment

passivity and stability of switched systems a multiple storage function method this paper presents a concept of passivity for switched systems using multiple storage functions this passivity property is invariant under compatible feedback interconnection branicky s stability theorem of multiple lyapunov functions is generalized by relaxing the non increasing condition on values of lyapunov like functions using this result we show that a passive switched system is stable in the sense of lyapunov moreover asymptotic stability is reached if all subsystems are asymptotically detectable

linear matrix inequalities riccati equations and indefinite stochastic linear quadratic controls this paper deals with an optimal stochastic linear quadratic lq control problem in infinite time horizon where the diffusion term in dynamics depends on both the state and the control variables in contrast to the deterministic case we allow the control and state weighting matrices in the cost functional to be indefinite this leads to an indefinite lq problem which may still be well posed due to the deep nature of uncertainty involved the problem gives rise to a stochastic algebraic riccati equation sare which is however fundamentally different from the classical algebraic riccati equation as a result of the indefinite nature of the lq problem to analyze the sare we introduce linear matrix inequalities lmis whose feasibility is shown to be equivalent to the solvability of the sare moreover we develop a computational approach to the sare via a semi definite programming associated with the lmis finally numerical experiments are reported to illustrate the proposed approach

dissipativity theory for switched systems a framework of dissipativity theory for switched systems using multiple storage functions and multiple supply rates is set up each subsystem of a switched system is associated with a storage function to describe the energy stored in the subsystem and is associated with a supply rate that represents energy coming from outside the subsystem when the subsystem is active the exchange of energy between the active subsystem and an inactive subsystem is characterized by cross supply rates stability is reached when all supply rates can be made negative as long as the total exchanged energy between the active subsystem and any inactive subsystems is finite in some sense two special forms of dissipativity passivity and l 2 gain are addressed for both cases asymptotic stability is guaranteed under certain negative output feedback plus asymptotic zero state detectability switched passivity conditions and switched l 2 gain inequalities are respectively derived which are generalizations of classical ones feedback invariance of passivity and a small gain theorem are also given

a mixed r d projects and securities portfolio selection model the business environment is full of uncertainty allocating the wealth among various asset classes may lower the risk of overall portfolio and increase the potential for more benefit over the long term in this paper we propose a mixed single stage r d projects and multi stage securities portfolio selection model specifically we present a bi objective mixed integer stochastic programming model moreover we use semi absolute deviation risk functions to measure the risk of mixed asset portfolio based on the idea of moments approximation method via linear programming we propose a scenario generation approach for the mixed single stage r d projects and multi stage securities portfolio selection problem the bi objective mixed integer stochastic programming problem can be solved by transforming it into a single objective mixed integer stochastic programming problem a numerical example is given to illustrate the behavior of the proposed mixed single stage r d projects and multi stage securities portfolio selection model

an alternate numerical solution to the linear quadratic problem this note proposes a new method based on convex programming for solving the linear quadratic problem lqp directly on the parameter space generated by the feedback control gain all stabilizing controllers are mapped into a convex set the problem is then formulated as a minimization of a linear function over this convex set its optimal solution furnishes under certain conditions the same feedback control gain obtained from the classical riccati equation generalizations to decentralized control and output feedback control design are included the theory is illustrated by some numerical examples

decentralized robust control invariance for a network of storage devices robust control of networked storage devices is considered each storage device is modeled as a single state discrete time integrator with bounded control input and subject to additive disturbance the values of the disturbance are unknown but are assumed to belong to bounded sets nodes exchange stored resource through links of limited capacity characterization of the maximal robust control invariant rci set is provided and decentralization of the robust feasibility problem is considered a notion of decentralized rci set is introduced and a parametrization of a family of decentralized rci sets is proposed it is shown that the set of parameters for which the decentralized rci sets are non empty is a polyhedral set the result offers a possibility to use convex optimization for selection of bounds on the admissible flow through the network which ensure feasibility of the proposed decentralized design

attainability in repeated games with vector payoffs we introduce the concept of attainable sets of payoffs in two player repeated games with vector payoffs a set of payoff vectors is called attainable by a player if there is a positive integer such that the player can guarantee that in all finite game longer than that integer the distance between the set and the cumulative payoff is arbitrarily small regardless of the strategy player 2 is using we provide a necessary and sufficient condition for the attainability of a convex set using the concept of b sets we then particularize the condition to the case in which the set is a singleton and provide some equivalent conditions we finally characterize when all vectors are attainable

stabilization of uncertain systems with norm bounded uncertainty a control a robust stabilization problem in a state space setting is treated it is assumed that the states are available for feedback using a fixed lyapunov function approach quadratic stability it is shown that an open loop stabilizability condition is equivalent to the existence of a stabilizing memoryless linear state feedback controller as a consequence it is shown that the existence of a quadratically stabilizing nonlinear time varying dynamic state feedback controller implies the existence of a quadratically stabilizing memoryless linear time invariant state feedback compensator

model free plant tuning given a static plant described by a differentiable input output function which is completely unknown but whose jacobian takes values in a known polytope in the matrix space this paper considers the problem of tuning i e driving to a desired value the output by suitably choosing the input it is shown that if the polytope is robustly nonsingular or has full rank in the nonsquare case then a suitable tuning scheme drives the output to the desired point the proof exploits a lyapunov like function and applies a well known game theoretic result concerning the existence of a saddle point for a min max zero sum game when the plant output is represented in an implicit form it is shown that the same result can be obtained resorting to a different lyapunov like function the case in which proper input or output constraints must be enforced during the transient is considered as well some application examples are proposed to show the effectiveness of the approach

on time scale designs for networks we motivate the problem of designing a subset of the edge weights in a graph to shape the spectrum of an associated linear time invariant dynamics we address a canonical design problem of this form by applying time scale assignment methods and give graph theoretic characterisations of the designed dynamics

optimal feedback production planning in a stochastic n machine flowshop we consider a production planning problem in an n machine flowshop subject to breakdown and repair of machines and to non negativity constraints on work in process the machine capacities and demand processes are assumed to be finite state markov chains the problem is to choose the rates of production on the n machines over time to minimize the expected discounted cost of production and inventory backlog over an infinite horizon it is formulated as a stochastic dynamic programming problem we show that the value function of the problem is locally lipschitz and is a solution to a dynamic programming equation together with a certain boundary condition we provide an interpretation of the boundary condition we also prove a verification theorem and derive the optimal feedback control policy in terms of the directional derivatives of the value function finally we obtain a deterministic optimal control problem that is equivalent to the stochastic production planning problem under consideration

heuristic algorithms for the portfolio selection problem with minimum transaction lots the problem of selecting a portfolio has been largely faced in terms of minimizing the risk given the return while the complexity of the quadratic programming model due to markowitz has been overcome by the recent progress in algorithmic research the introduction of linear risk functions has given rise to the interest in solving portfolio selection problems with real constraints in this paper we deal with the portfolio problem with minimum transaction lots we show that in this case the problem of finding a feasible solution is independently of the risk function np complete moreover given the mixed integer linear model new heuristics are proposed which starting from the solution of the relaxed problem allow to find a solution close to the optimal one the algorithms are based on the construction of mixed integer subproblems using only a part of the securities available formulated using the information obtained from the solution of the relaxed problem the heuristics have been tested with respect to two disjoint time periods using real data from the milan stock exchange

mean absolute deviation portfolio optimization model and its applications to tokyo stock market the purpose of this paper is to demonstrate that a portfolio optimization model using the l1 risk mean absolute deviation risk function can remove most of the difficulties associated with the classical markowitz s model while maintaining its advantages over equilibrium models in particular the l1 risk model leads to a linear program instead of a quadratic program so that a large scale optimization problem consisting of more than 1 000 stocks may be solved on a real time basis numerical experiments using the historical data of nikkei 225 stocks show that the l1 risk model generates a portfolio quite similar to that of the markowitz s model within a fraction of time required to solve the latter

a linear programming approach to large scale linear optimal control problems this paper considers the solution of large scale linear optimal control problems subject to linear control and state constraints by application of a linear programming lp based methodology the proposed algorithm is based on a particular lp method that is suitably modified and adapted to the structure of the considered discrete time dynamic problem to keep the computation time low and efficiently store the arising large but sparse matrices the efficiency of the approach is demonstrated via a practical example arising in the field of traffic control in data communication networks the algorithm is shown to solve problems involving several thousands of variables in few seconds on a workstation thus enabling real time optimal control for a number of potential practical applications

stability of switched systems a lie algebraic condition we present a sucient condition for asymptotic stability of a switched linear system in terms of the lie algebra generated by the individual matrices namely if this lie algebra is solvable then the switched system is exponentially stable for arbitrary switching in fact we show that any family of linear systems satisfying this condition possesses a quadratic common lyapunov function we also discuss the implications of this result for switched nonlinear systems c 1999 elsevier science b v all rights reserved

tractable approximations to robust conic optimization problems in earlier proposals the robust counterpart of conic optimization problems exhibits a lateral increase in complexity i e robust linear programming problems lps become second order cone problems socps robust socps become semidefinite programming problems sdps and robust sdps become np hard we propose a relaxed robust counterpart for general conic optimization problems that a preserves the computational tractability of the nominal problem specifically the robust conic optimization problem retains its original structure i e robust lps remain lps robust socps remain socps and robust sdps remain sdps and b allows us to provide a guarantee on the probability that the robust solution is feasible when the uncertain coefficients obey independent and identically distributed normal distributions

piecewise linear quadratic optimal control the use of piecewise quadratic cost functions is extended from stability analysis of piecewise linear systems to performance analysis and optimal control lower bounds on the optimal control cost are obtained by semidefinite programming based on the bellman inequality this also gives an approximation to the optimal control law an upper bound to the optimal cost is obtained by another convex optimization problem using the given control law a compact matrix notation is introduced to support the calculations and it is proved that the framework of piecewise linear systems can be used to analyze smooth nonlinear dynamics with arbitrary accuracy

optimal control of production rate in a failure prone manufacturing system we address the problem of controlling the production rate of a failure prone manufacturing system so as to minimize the discounted inventory cost where certain cost rates are specified for both positive and negative inventories and there is a constant demand rate for the commodity produced the underlying theoretical problem is the optimal control of a continuous time system with jump markov disturbances with an infinite horizon discounted cost criterion we use two complementary approaches first proceeding informally and using a combination of stochastic coupling linear system arguments stable and unstable eigenspaces renewal theory parametric optimization etc we arrive at a conjecture for the optimal policy then we address the previously ignored mathematical difficulties associated with differential equations with discontinuous right hand sides singularity of the optimal control problem smoothness and validity of the dynamic programming equation etc to give a rigorous proof of optimality of the conjectured policy it is hoped that both approaches will find uses in other such problems also we obtain the complete solution and show that the optimal solution is simply characterized by a certain critical number which we call the optimal inventory level if the current inventory level exceeds the optimal one should not produce at all if less one should produce at the maximum rate while if exactly equal one should produce exactly enough to meet demand we also give a simple explicit formula for the optimal inventory level

stochastic linear quadratic control via semidefinite programming we study stochastic linear quadratic lq optimal control problems over an infinite time horizon allowing the cost matrices to be indefinite we develop a systematic approach based on semidefinite programming sdp a central issue is the stability of the feedback control and we show this can be effectively examined through the complementary duality of the sdp furthermore we establish several implication relations among the sdp complementary duality the generalized riccati equation and the optimality of the lq control problem based on these relations we propose a numerical procedure that provides a thorough treatment of the lq control problem via primal dual sdp it identifies a stabilizing feedback control that is optimal or determines that the problem possesses no optimal solution for the latter case we develop an epsilon approximation scheme that is asymptotically optimal

stability robustness bounds for linear state space models with structured uncertainty in this note we consider the robust stability analysis problem in linear state space models we consider systems with structured uncertainty some lower bounds on allowable perturbations which maintain the stability of a nominally stable system are derived these bounds are shown to be less conservative than the existing ones

brief paper insensitive h filter design for continuous time systems with respect to filter coefficient variations this paper is concerned with the problem of designing insensitive h filters for linear continuous time systems coefficient sensitivity functions of transfer functions with respect to filter additive multiplicative coefficient variations are defined and the h norms of the sensitivity functions are used to measure the sensitivity of the transfer functions with respect to additive filter coefficient variations in addition in order to deal with the filter design problem for the multiplicative filter coefficient variation case new measures based on the average of the sensitivity functions are also defined consequently the insensitive h filter design problem is reduced to a multi objective filter design problem which minimizes the coefficient s sensitivity and meets the prescribed h norm constraint simultaneously first a novel method for designing insensitive h filters subjected to additive filter coefficient variations is given in terms of the linear matrix inequality lmi optimization techniques furthermore based on the new sensitivity measures the obtained results are extended to the multiplicative coefficient variation case in addition an indirect method for solving the multiplicative variations is also proposed finally two numerical examples are provided to demonstrate the effectiveness of the proposed method

robust control of uncertain multi inventory systems via linear matrix inequality we consider a continuous time linear multi inventory system with unknown demands bounded within ellipsoids and controls bounded within ellipsoids or polytopes we address the problem of e stabilising the inventory since this implies some reduction of the inventory costs the main results are certain conditions under which e stabilisability is possible through a saturated linear state feedback control all the results are based on a linear matrix inequalities approach and on some recent techniques for the modelling and analysis of polytopic systems with saturations numerical simulations are provided

an optimal control approach to dynamic routing in networks this paper explores the application of optimal control theory to the problem of dynamic routing in networks the approach derives from a continuous state space model for dynamic routing and an associated linear optimal control problem with linear state and control variable inequality constraints the conceptual form of an algorithm is presented for finding a feedback solution to the optimal control problem when the inputs are assumed to be constant in time the algorithm employs a combination of necessary conditions dynamic programming and linear programming to construct a set of convex polyhedral cones which cover the admissible state space with optimal controls an implementable form of the algorithm along with a simple example is presented for a special class of single destination networks

on the optimality of myopic production controls for single server continuous flow manufacturing systems in this note we consider a broad class of dynamic scheduling problems associated with a single server multiclass continuous flow manufacturing system using a general framework we provide conditions under which the solution to these problems is the implementation of a class of production controls called myopic scheduling policies the proof of optimality which is intuitively appealing applies to more general production models than existing proofs in the literature which typically either use the maximum principle or solve the hamilton jacobi bellman hjb equation we also present several counter examples that explicitly illustrate the potential limitations of myopic scheduling policies

a minimax portfolio selection rule with linear programming solution a new principle for choosing portfolios based on historical returns data is introduced the optimal portfolio based on this principle is the solution to a simple linear programming problem this principle uses minimum return rather than variance as a measure of risk in particular the portfolio is chosen that minimizes the maximum loss over all past observation periods for a given level of return this objective function avoids the logical problems of a quadratic nonmonotone utility function implied by mean variance portfolio selection rules the resulting minimax portfolios are diversified for normal returns data the portfolios are nearly equivalent to those chosen by a mean variance rule framing the portfolio selection process as a linear optimization problem also makes it feasible to constrain certain decision variables to be integer or 0 1 valued this feature facilitates the use of more complex decision making models including models with fixed transaction charges and models with boolean type constraints on allocations

lie algebraic stability criteria for switched systems it was recently shown that a family of exponentially stable linear systems whose matrices generate a solvable lie algebra possesses a quadratic common lyapunov function which implies that the corresponding switched linear system is exponentially stable for arbitrary switching in this paper we prove that the same properties hold under the weaker condition that the lie algebra generated by given matrices can be decomposed into a sum of a solvable ideal and a subalgebra with a compact lie group the corresponding local stability result for nonlinear switched systems is also established moreover we demonstrate that if a lie algebra fails to satisfy the above condition then it can be generated by a family of stable matrices such that the corresponding switched linear system is not stable relevant facts from the theory of lie algebras are collected at the end of the paper for easy reference

the gain scheduling and the robust state feedback stabilization problems we consider dynamical uncertain systems of the form x spl dot a x w b x w u where w t spl isin w is an unknown but bounded time varying parameter we consider the robust state feedback stabilization problem in which we consider a control of the form u spl phi x and the gain scheduling stabilization problem in which a control of the form u spl phi x w full information control is admitted we show that for convex processes those systems in which for fixed x the set of all a x w b x w is convex the two problems are equivalent i e if there exists a locally lipschitz gain scheduling stabilizing control then there exists a robustly stabilizing control continuous everywhere except possibly at the origin thus for convex process stabilization knowledge of w t is not an advantage for the compensator then we consider the special class of polytopic lpv systems and show that there is no loss of regularity as in the general case if we pass from a gain scheduling controller to a state feedback controller in particular no discontinuity at the origin may occur we show that the existence of a dynamic controller always implies the existence of a static one finally we show that we can always find a linear gain scheduling controller for a stabilizable system this means that a possible advantage of the online measurement of the parameter w t is that this always allows for linear compensators whose implementation can be easier than that of nonlinear ones

the linear saturated decentralized strategy for constrained flow control is asymptotically optimal we present an algorithm for constrained network flow control in the presence of an unknown demand our algorithm is decentralized in the sense that it is implemented by a team of agents each controlling just the flow on a single arc of the network based only on the buffer levels at the nodes at the extremes of the arc while ignoring the actions of other agents and the network topology we prove that our algorithm is also stabilizing and steady state optimal specifically we show that it asymptotically produces the minimum norm flow we finally generalize our algorithm to networks with a linear dynamics and we prove that certain least square optimality properties still hold

generating scenario trees for multistage decision problems in models of decision making under uncertainty we often are faced with the problem of representing the uncertainties in a form suitable for quantitative models if the uncertainties are expressed in terms of multivariate continuous distributions or a discrete distribution with far too many outcomes we normally face two possibilities either creating a decision model with internal sampling or trying to find a simple discrete approximation of the given distribution that serves as input to the model this paper presents a method based on nonlinear programming that can be used to generate a limited number of discrete outcomes that satisfy specified statistical properties users are free to specify any statistical properties they find relevant and the method can handle inconsistencies in the specifications the basic idea is to minimize some measure of distance between the statistical properties of the generated outcomes and the specified properties we illustrate the method by single and multiple period problems the results are encouraging in that a limited number of generated outcomes indeed have statistical properties that are close to or equal to the specifications we discuss how to verify that the relevant statistical properties are captured in these specifications and argue that what are the relevant properties will be problem dependent

a primal dual interior point method for robust optimal control of linear discrete time systems this paper describes how to efficiently solve a robust optimal control problem using recently developed primal dual interior point methods one potential application is model predictive control the optimization problem considered consists of a worst case quadratic performance criterion over a finite set of linear discrete time models subject to inequality constraints on the states and control signals the scheme has been prototyped in matlab to give a rough idea of the efficiencies obtained it is possible to solve problems with more than 10 000 primal variables and 40 000 constraints on a workstation the key to the efficient implementation is an iterative solver in conjunction with a riccati recursion invertible pre conditioner for computing the search directions

network decentralized control strategies for stabilization we consider the problem of stabilizing a class of systems formed by a set of decoupled subsystems nodes interconnected through a set of controllers arcs controllers are network decentralized i e they use information exclusively from the nodes they interconnect this condition requires a block structured feedback matrix having the same structure as the transpose of the overall input matrix of the system if the subsystems do not have common unstable eigenvalues we demonstrate that the problem is solvable in the general case we provide sufficient conditions for solvability when subsystems are identical and each input agent controls a pair of subsystems with input matrices having opposite sign flow networks we prove that stabilization is possible if and only if the system is connected with the external environment our proofs are constructive and lead to structured linear matrix inequalities lmis

optimal h sub 2 l sub 1 control via duality theory in this paper we consider the problem of minimizing the h sub 2 norm of the closed loop map while maintaining its l sub 1 norm at a prescribed level the problem is analyzed in the case of discrete time siso closed loop maps utilizing duality theory it is shown that the optimal solution is unique and in the nontrivial case where the l sub 1 constraint is active the optimal solution has a finite impulse response a finite step procedure is given for the construction of the exact solution this procedure consists of solving a finite number of quadratic programming problems which can be performed using standard methods finally continuity properties of the optimal solution with respect to changes in the l sub 1 constraint are established

rate based flow controllers for communication networks in the presence of uncertain time varying multiple time delays an h based robust controller is designed for a rate feedback flow control problem in single bottleneck communication networks the controller guarantees stability robustness to uncertain time varying multiple time delays in different channels it also brings the queue length at the bottleneck node to the desired steady state value asymptotically and satisfies a weighted fairness condition lower bounds for stability margins for uncertainty in the time delays and for the rate of change of the time delays are derived a number of simulations are included to demonstrate the time domain performance of the controller trade offs between robustness and time domain performance are also discussed