robust control of cascaded and individually feedback linearizable nonlinear systems abstract feedback linearization technique is applied to design robust controllers for a class of nonlinear uncertain systems every system in the class is a series connection of finite number of nonlinear subsystems which are individually feedback linearizable and have significant but matched nonlinear functional uncertainties the key difference between this work and existing robust results is that the matching conditions and the existence of feedback linearization transformation are only required individually for each subsystem a constructive robust control design procedure is proposed for the unique control in the overall system the procedure is conceptually simple and contains three steps first perform input output feedback linearization for all individual subsystems second design fictitious robust controllers for inputs of each subsystem as if the subsystem had an independent control finally a mapping is developed which maps the individual fictitious controls recursively into the unique control of the overall system since neither the matching conditions nor feedback linearization are required for the overall system this becomes the broadest class of nonlinear uncertain or known systems for which a robust regular tracking control can be constructed using feedback linearization method global stability of the overall system is always guaranteed

self dual instantons and holomorphic curves a gradient flow of a morse function on a compact riemannian manifold is said to be of morse smale type if the stable and unstable manifolds of any two critical points intersect transversally for such a morse smale gradient flow there is a chain complex generated by the critical points and graded by the morse index the boundary operator has as its x y entry the number of gradient flow lines running from x to y counted with appropriate signs whenever the difference of the morse indices is 1 the homology of this chain complex agrees with the homology of the underlying manifold m and this can be used to prove the morse inequalities cf 33 26 around 1986 floer generalized this idea to infinite dimensional variational problems in which every critical point has infinite morse index but the moduli spaces of connecting orbits form finite dimensional manifolds for every pair of critical points the dimensions of these spaces give rise to a relative morse index and the boundary operator is defined by counting connecting

control effort considerations in the stabilization of uncertain dynamical systems abstract this paper investigates the problem of designing a state feedback control to stabilize an uncertain nonlinear system we focus attention on the amplitude norm of the controller which is used to achieve this end the uncertain system is described by a state equation which contains uncertain parameters which are unknown but bounded a lyapunov function is used to establish the stability of the closed loop system the paper gives necessary and sufficient concitions for the uncertain system to be stabilizable with a given lyapunov function furthermore a procedure is indicated for the construction of the desired feedback control law

convergence of anti self dual connections on su n bundles over product of two riemann surfaces we obtain a convergence result on anti self dual connections over a product of two riemann surfaces in the adiabetic limit

an effective dynamic programming algorithm for the minimum cost maximal knapsack packing problem abstract given a set of items with profits and weights and a knapsack capacity we study the problem of finding a maximal knapsack packing that minimizes the profit of the selected items we propose an effective dynamic programming dp algorithm which has a pseudo polynomial time complexity we demonstrate the equivalence between this problem and the problem of finding a minimal knapsack cover that maximizes the profit of the selected items in an extensive computational study on a large and diverse set of benchmark instances we demonstrate that the new dp algorithm outperforms a state of the art commercial mixed integer programming mip solver applied to the two best performing mip models from the literature

global stabilization with almost disturbance decoupling of a class of uncertain non linear systems in this paper we study the global stabilization of a class of non linear uncertain systems while decoupling the output from external disturbances to any specified degree of accuracy the class of non linear systems considered could be viewed as a generalization of uniform rank multivariable linear systems which have the property that all their infinite zeros are of the same order although the plants considered are non linear the compensator developed here is linear our compensator which achieves global exponential stability and almost disturbance decoupling of the output requires only output feedback rather than full state feedback model uncertainty is dealt with either by restricting the uncertain elements to particular subspaces satisfying the so called matching conditions and or by treating a family of plants for which a single controller simultaneously globally exponentially stabilizes all the plants in while achieving almost disturbance decoupling of the output

disturbance observer based robust mixed h2 h fuzzy tracking control for hypersonic vehicles this paper introduces a disturbance observer do based mixed h2 h robust fuzzy tracking control design for the longitudinal dynamics of a generic hypersonic vehicle hv with modeled and unmodeled disturbances a takagisugeno ts fuzzy model is firstly employed to approximate the nonlinear dynamics of hv subsequently based on the fuzzy model a do is constructed to estimate the modeled disturbance next by integrating the hv dynamics the tracking error integral and the disturbance estimation error dynamics an augmented system is established for the control design then a do based mixed h2 h robust fuzzy control design is developed to ensure the asymptotic stability as well as the mixed h2 h control performance of the augmented system the proposed control scheme includes a fuzzy tracking controller with state feedback plus the tracking error integral a robust nonlinear compensator for eliminating the matched part of the compound disturbance consisting of the unmodeled disturbance and fuzzy modeling error and a do based compensator for the modeled disturbance cancellation the outcome of the do based mixed h2 h robust fuzzy control problem is formulated in terms of linear matrix inequalities lmis furthermore by utilizing the existing lmi optimization technique a suboptimal controller is obtained in the sense of minimizing an upper bound of h2 performance finally simulation results on an hv demonstrate the effectiveness of the proposed design method

surrogate constraint normalization for the set covering problem the set covering problem scp is central in a wide variety of practical applications for which finding good feasible solutions quickly often in real time is crucial surrogate constraint normalization is a classical technique used to derive appropriate weights for surrogate constraint relaxations in mathematical programming this framework remains the core of the most effective constructive heuristics for the solution of the scp chiefly represented by the widely used chvatal method this paper introduces a number of normalization rules and demonstrates their superiority to the classical chvatal rule especially when solving large scale and real world instances directions for new advances on the creation of more elaborate normalization rules for surrogate heuristics are also provided

notions of stabilizability and controllability for a class of uncertain linear systems abstract this paper investigates the relationship between stabilizability and certain notions of controllability for a class of uncertain linear systems containing time varying unknown but bounded uncertain parameters the paper introduces a notion of controllability invariance roughly speaking an uncertain system is controllability invariant if it is controllable in the usual sense for each fixed value of the uncertain parameters the paper describes a class of uncertain systems for which controllability invariance implies stabilizability

new matching conditions for output regulation of a class of uncertain nonlinear systems some sufficient conditions for the structure of modelling uncertainties for output regulation of uncertain systems are presented it turns out that these conditions include as special cases the ordinary matching conditions for state regulation of uncertain systems and the disturbance decoupling condition the previous restrictions on the structure of modelling uncertainties can be considerably relaxed in the case of output regulation the significance of the result is shown by a simple example

an improved version of a core based algorithm for the multi objective multi dimensional knapsack problem in this paper we propose an improved version of a core based algorithm for the multi objective extension of one of the most well known combinatorial optimization problems the multi dimensional knapsack problem the original algorithm was designed only for bi objective problems combining an extension of the core concept and a branch and bound algorithm it is a deterministic algorithm and the core concept exploits the divide and conquer solution strategy which proves very effective in such problems the new version is not limited to bi objective problems it can effectively handle problems with more than two objective functions and it has features that greatly accelerate the solution process namely these features are the use of a heuristic based on the dantzig bound in the fathoming process and the better housekeeping of the incumbent list through filtering of solutions the key parameters of the new algorithm are a the size of the core and b the number of provided cores varying these parameters the user can easily tune the size of the obtained pareto set a comparison with evolutionary algorithms like nsga ii spea2 and moea d has been made according to run time and the most widely used metrics set coverage set convergence etc our new version performs better than the most popular evolutionary algorithms and it is comparable to very recent state of the art metaheuristics like multi objective memetic algorithm based on decomposition momad for multi objective programming

practical stabilization of a class of uncertain nonlinear systems abstract in this paper the problem of robust control of a class of nonlinear systems with internal and input channel uncertainties is addressed the proposed control algorithm reflects the two level structure of the plant and guarantees the system uniform asymptotic stability with respect to an arbitrary neighbourhood of the nominal system stability point

variable structure robust control of uncertain time delay systems abstract this paper introduces a variable structure output feedback robust control for uncertain time delay systems new types of switching manifolds with integral terms are implemented to consider larger class of linear systems by overcoming both the observability constraints of the reduced order system and the kimura davison condition two types of control laws are introduced by which an estimate of a region of asymptotic stability to the origin and a region of attraction to the switching manifold are defined

advanced greedy algorithms and surrogate constraint methods for linear and quadratic knapsack and covering problems new variants of greedy algorithms called advanced greedy algorithms are identified for knapsack and covering problems with linear and quadratic objective functions beginning with single constraint problems we provide extensions for multiple knapsack and covering problems in which objects must be allocated to different knapsacks and covers and also for multi constraint multi dimensional knapsack and covering problems in which the constraints are exploited by means of surrogate constraint strategies in addition we provide a new graduated probe strategy for improving the selection of variables to be assigned values going beyond the greedy and advanced greedy frameworks we describe ways to utilize these algorithms with multi start and strategic oscillation metaheuristics finally we identify how surrogate constraints can be utilized to produce inequalities that dominate those previously proposed and tested utilizing linear programming methods for solving multi constraint knapsack problems which are responsible for the current best methods for these problems while we focus on 0 1 problems our approaches can readily be adapted to handle variables with general upper bounds

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

exploiting nested inequalities and surrogate constraints abstract the exploitation of nested inequalities and surrogate constraints as originally proposed in glover glover f 1965 a multiphase dual algorithm for the zero one integer programming problem operations research 13 879 919 glover f 1971 flows in arborescences management science 17 568 586 has been specialized to multidimensional knapsack problems in osorio et al osorio m a glover f hammer p 2002 cutting and surrogate constraint analysis for improved multidimensional knapsack solutions annals of operations research 117 71 93 we show how this specialized exploitation can be strengthened to give better results this outcome results by a series of observations based on surrogate constraint duality and properties of nested inequalities the consequences of these observations are illustrated by numerical examples to provide insights into uses of surrogate constraints and nested inequalities that can be useful in a variety of problem settings

tabu enhanced iterated greedy algorithm a case study in the quadratic multiple knapsack problem abstract iterated greedy search is a simple and effective metaheuristic for combinatorial problems its flexibility enables the incorporation of components from other metaheuristics with the aim of obtaining effective and powerful hybrid approaches we propose a tabu enhanced destruction mechanism for iterated greedy search that records the last removed objects and avoids removing them again in subsequent iterations the aim is to provide a more diversified and successful search process with regards to the standard destruction mechanism which selects the solution components for removal completely at random we have considered the quadratic multiple knapsack problem as the application domain for which we also propose a novel local search procedure and have developed experiments in order to assess the benefits of the proposal the results show that the tabu enhanced iterated greedy approach in conjunction with the new local search operator effectively exploits the problem knowledge associated with the requirements of the problem considered attaining competitive results with regard to the corresponding state of the art algorithms

bounded amplitude performance of switched lpv systems with applications to hybrid systems this paper discusses recent results on multiple linear agent control for systems satisfying a bounded amplitude performance constraint the plant is assumed to be a linear parameter varying lpv system scheduled along a nominal parameter trajectory in this respect the control problem represents a plant operating between a prespecified set of operating conditions linear controllers are designed at setpoints along this scheduling trajectory to satisfy bounded amplitude performance constraints this paper discusses an approach to analyze the switched system behavior under practical assumptions on the structure of the switching rule the approach combines the scheduling parameter with lpv system properties to derive bounds on the switching behavior of the system these estimates are then used to construct a logical model of the switched system behavior in the form of a timed automaton in this respect this paper presents a way of extracting logical models of continuous time system behavior

robust state feedback stabilization of discrete time uncertain dynamical systems the problem of stabilization of a class of discrete time dynamic systems containing uncertain elements using the direct method of lyapunov is considered state feedback controllers that guarantee uniform boundedness and uniform ultimate boundedness of the closed loop system are proposed

a new class of lyapunov functions for the constrained stabilization of linear systems the constrained stabilization of linear uncertain systems is investigated via the set theoretic framework of control lyapunov r functions a novel composition rule allows the design of a composite control lyapunov function with external level set that exactly shapes the maximal controlled invariant set and inner sublevel sets arbitrarily close to any choice of smooth ones generalizing both polyhedral and truncated ellipsoidal control lyapunov functions the feasibility test of the proposed smooth control lyapunov functions can be cast into matrix inequalities conditions the constrained linear quadratic control is addressed as an application

design of robust state feedback laws existence criteria and computational methods are presented for finding stabilizing state feedback laws for systems with uncertain state or control matrices the uncertainties are modelled as sector bounded non linearities and feedback laws ensuring global asymptotic closed loop stability are obtained using lyapunov e direct method the algorithms essentially amount to repeatedly solving a parameter dependent riccati equation until the maximal solution becomes positive definite

continuous robust control design for nonlinear uncertain systems without a priori knowledge of control direction in this paper a robust control scheme is proposed for a class of nonlinear systems that have not only additive nonlinear uncertainties but also unknown multiplicative signs these signs are called control directions since they represent effectively the direction of motion under any given control except for the unknown control directions the class of systems satisfy the generalized matching conditions nonlinear robust control is designed to identify on line unknown control directions and to guarantee global stability of uniform ultimate boundedness without the knowledge of nonlinear dynamics except their size bounding functions it is also shown that the proposed robust control can be made continuous through utilizing the so called shifting laws that change smoothly and accordingly the signs of robust controls and that no matter what time constants and gains of the shifting laws are global stability is always ensured the analysis and design is done using lyapunov s direct method

robust stabilization of the angular velocity of a rigid body the problem of robust control for the angular velocity of a rigid body subject to external disturbances is addressed it is shown that if the disturbances are matched there exists a control law attenuating the effect of the disturbances whereas in the case of non matched disturbances no such a feedback law generically exists hence a new concept of disturbance attenuation is introduced and it is proved that the aforementioned problem is solvable in this weaker sense explicit expressions of the control laws solving the proposed robust stabilization problems are given

linear and nonlinear stabilizing continuous controllers of uncertain dynamical systems including state delay the problem of robust stabilization of a class of time varying dynamical systems with disturbance uncertain parameters and a bounded time varying state delay is considered two classes of stabilizing continuous controllers are proposed the proposed controllers can guarantee the existence of the solution to the dynamical system in the usual sense and can also be directly implemented in the practical control problems moreover since the proposed controllers are completely independent of the time delay which is only assumed to be any nonnegative bounded and continuous function the results developed in this note are applicable to a class of dynamical systems with uncertain time delays finally a numerical example is given to demonstrate the validity of the results

further results on the observer design problem abstract in this paper the observer design problem for nonlinear systems is considered sufficient lyapunov like conditions are presented for the existence of a nonlinear observer the theory we develop considerably improves and extends the results of our recent work 14

decentralized variable structure control for tracking in non linear systems the problem of tracking time varying trajectories in non linear systems is considered these trajectories could be generated on line by a reference model the problem is tackled by considering the overall system as a set of decentralized linear sub systems which can be modelled as a set of double integrators and treating the non linearities as uncertainties with known bounds on their magnitudes a variable structure controller is designed based on the theory of uncertain dynamical systems the system is shown to track a class of trajectories generated by the reference mode a set of double integrators to within a specified tolerance some analysis is presented to explain the dynamic behaviour of the closed loop system and bounds are derived linking the rate of convergence and the tracking ability to system parameters such as available control and magnitude of the uncertainty simulation results are presented to validate the conclusions

stabilizing controllers for uncertain linear systems with additive disturbances this paper is concerned with the problem of designing stabilizing controllers for linear systems containing uncertainty the uncertainty is time varying with values lying in a specified set and enters through the system matrix through the input connection matrix and additively a method is presented for obtaining a linear state feedback controller which guarantees that the system response ultimately lies in a prespecified neighbourhood of the origin in some situations this neighbourhood can be made arbitrarily small and practical stability is achieved the solution of an algebraic riccati equation is used to generate the feedback gains for the linear controller several examples are included to illustrate the application of the method

bounded feedback stabilization and global separation principle of distributed parameter systems we show that the infinite dimensional system spl sigma x spl dot t ax t bu t x sub 0 spl epsiv h is globally strongly asymptotically stabilizable by an arbitrarily small smooth feedback here the operator a is the infinitesimal generator of a c sub 0 semigroup of contractions e sup ta on real hilbert space h and b is a bounded linear operator mapping a hilbert space of controls u into h an explicit smooth feedback control law is given further we identify the class of perturbations for which the system is still stabilizable by the same feedback law as for the nominal system based on these results and some differential lyapunov operator equations we then establish a global separation principle for the system spl sigma with a kalman like observer finally these results are illustrated via an example dealing with the wave equation

on the lyapunov stability of discrete time processes modeled by difference inclusions abstract the subject of this note is the stability in the sense of lyapunov of difference inclusions connection with the convergence of algorithms is also discussed

logical composition of lyapunov functions this article introduces the use of r functions to compose single lyapunov functions lfs via classic boolean operators with the aim to obtain a rich family of non conventional generally non convex functions the main benefit of the proposed composition is the nice geometric interpretation since it corresponds to intersection and union operations in the phase space region the composition of lfs is parameterised through a variable and classic compositions of lfs through min and max operations are recovered as a special case for a particular value of the proposed logical composition is applied to region of asymptotic stability ras estimation problems where the union of several lfs corresponds to the union of the ras estimates obtained from the separate use of each lf likewise the intersection of several lfs defined on independent subsets of the state space variables provides a single lf for the overall dynamical system sufficient conditions for the composition function to be an lf are provide

dynamic surface control for a class of nonlinear systems a method is proposed for designing controllers with arbitrarily small tracking error for uncertain mismatched nonlinear systems in the strict feedback form this method is another synthetic input technique similar to backstepping and multiple surface control methods but with an important addition spl tau 1 low pass filters are included in the design where spl tau is the relative degree of the output to be controlled it is shown that these low pass filters allow a design where the model is not differentiated thus ending the complexity arising due to the explosion of terms that has made other methods difficult to implement in practice the backstepping approach while suffering from the problem of explosion of terms guarantees boundedness of tracking errors globally however the proposed approach while being simpler to implement can only guarantee boundedness of tracking error semiglobally when the nonlinearities in the system are non lipschitz

quadratic stabilizability of linear systems with structural independent time varying uncertainties the author investigates the problem of designing a linear state feedback control to stabilize a class of single input uncertain linear dynamical systems the systems under consideration contain time varying uncertain parameters whose values are unknown but bounded in given compact sets the method used to establish asymptotical stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the author first shows that to ensure a stabilizable system some entries of the system matrices must be sign invariant he then derives necessary and sufficient conditions under which a system can be quadratically stabilized by a linear control for all admissible variations of uncertainties the conditions show that all uncertainties can only enter the system matrices in such a way as to form a particular geometrical pattern called an antisymmetric stepwise configuration for the systems satisfying the stabilizability conditions a computational control design procedure is also provided and illustrated via an example

bubbling of the heat flows for harmonic maps from surfaces in this article we prove that any palais smale sequence of the energy functional on surfaces with uniformly l2 bounded tension fields converges pointwise by taking a subsequence if necessary to a map from connected possibly singular surfaces which consist of the original surfaces and finitely many bubble trees we therefore get the corresponding results about how the solutions of heat flow for harmonic maps from surfaces form singularities at infinite time 1997 john wiley sons inc

convergence of adiabatic family of anti self dual connections on products of riemann surfaces we prove a convergence theorem for a sequence of anti self dual connections on a family of products of two riemann surfaces where the metric of one factor shrinks establishing the conjecture of bershadsky et al topological reduction of 4d sym to 2d sigma models nucl phys b 448 166 1995

quadratic controllability strong controllability and a related output feedback property quadratic controllability and strong controllability are the two system properties to be discussed for a special class of norm bounded uncertain linear systems the main contribution of this paper is twofold first we show that it is possible to reduce the problem of checking quadratic controllability or strong controllability of a given uncertain system to the same problem for a reduced order subsystem which we call the essential subsystem then we use this result to examine a related output feedback property specifically for a given uncertain system we will answer the following question what condition is necessary and sufficient for the existence of a dynamic output feedback controller such that the states of the closed loop system converge to the origin with an arbitrarily fast rate our aim is to provide an insight and better understanding of uncertain systems through these results

removable singularities in yang mills fields we show that a field satisfying the yang mills equations in dimension 4 with a point singularity is gauge equivalent to a smooth field if the functional is finite we obtain the result that every yang mills field overr4 with bounded functional l2 norm may be obtained from a field ons4 r4 hodge or coulomb gauges are constructed for general small fields in arbitrary dimensions including 4

letter to the editor on the exponential stability of a class of nonlinear systems including delayed perturbations in this letter the problem of robust stabilization of a class of nonlinear dynamical systems with delayed perturbations is considered based on the stability of the nominal systems a new stabilizing control law for exponential stability of the system is designed using lyapunov stability theory

robust semi global output tracking for nonlinear singularly perturbed systems in this work a robust controller design methodology for a broad class of singularly perturbed nonlinear systems with time varying uncertainties is developed when the fast subsystem is stabilizable and the slow subsystem is input output linearizable with input to state stable iss inverse dynamics the developed state feedback controller guarantees boundedness of the trajectories of the closed loop system and robust output tracking with arbitrary degree of asymptotic attenuation of the effect of uncertainty on the output for initial conditions and uncertainties in an arbitrarily large compact set so long as the singular perturbation parameter is sufficiently small the controller is a continuous function of the state of the system and its construction requires the knowledge of bounding functions on the size of uncertainty the developed method is applied to a non isothermal continuous stirred tank reactor with fast jacket dynamics

rapidly exponentially stabilizing control lyapunov functions and hybrid zero dynamics this paper addresses the problem of exponentially stabilizing periodic orbits in a special class of hybrid models systems with impulse effects through control lyapunov functions the periodic orbit is assumed to lie in a c1 submanifold z that is contained in the zero set of an output function and is invariant under both the continuous and discrete dynamics the associated restriction dynamics are termed the hybrid zero dynamics the orbit is furthermore assumed to be exponentially stable within the hybrid zero dynamics prior results on the stabilization of such periodic orbits with respect to the full order dynamics of the system with impulse effects have relied on input output linearization of the dynamics transverse to the zero dynamics manifold the principal result of this paper demonstrates that a variant of control lyapunov functions that enforce rapid exponential convergence to the zero dynamics surface z can be used to achieve exponential stability of the periodic orbit in the full order dynamics thereby significantly extending the class of stabilizing controllers the main result is illustrated on a hybrid model of a bipedal walking robot through simulations and is utilized to experimentally achieve bipedal locomotion via control lyapunov functions

output feedback decentralized control of large scale systems using weighted sensitivity functions minimization this paper considers the problem of achieving stability and desired dynamical transient behavior for linear large scale systems by decentralized control it can be done by making the effects of the interconnections between the subsystems arbitrarily small sufficient conditions for stability and diagonal dominance of the closed loop system are introduced these conditions are in terms of decentralized subsystems and directly make a constructive h control design possible a mixed h pole region placement is suggested such that by assigning the closed loop eigenvalues of the isolated subsystems appropriately the eigenvalues of the overall closed loop system are assigned in desirable range the designs are illustrated by an example

stabilization of some distributed parameter systems the question of stabilization of perturbed or uncertain infinite dimensional systems is considered one class of perturbations for which the system remains stabilizable by the same feedback law as for the nominal system is identified sufficient conditions are presented that generate strong stabilizability of the perturbed system given that the unperturbed system has similar properties it is also shown that for deterministic as well as stochastic systems exponential stability can be achieved by choice of a suitable feedback controller the theoretical results are illustrated by some numerical examples

output feedback variable structure control design this paper describes a procedure for variable structure output feedback control vsofc for a class of multivariable linear time invariant systems the equivalent control method of utkin in the output feedback mode yields a reduced order system exhibiting output feedback equivalent dynamics using the kimura davison sufficient conditions for pole placement using output feedback a sufficient condition is derived to assign the eigenvalues of the reduced order system the observability and controllability of the reduced system is discussed two switching surface design algorithms are introduced based on both a static output feedback and on an eigenstructure assignment techniques a control design is discussed as well

output feedback decentralized stabilization ilmi approach in this paper the static output feedback decentralized stabilization problem is addressed using a linear matrix inequality approach a necessary and sufficient condition for static output feedback decentralized stabilizability is derived for linear time invariant large scale systems it is proven that the existence of a stabilizing decentralized gain is equivalent to that of the solution of a quadratic matrix inequality the extension of the result to h control is studied an iterative lmi algorithm based on the linear matrix inequality technique is proposed to obtain the decentralized feedback gain examples show the effectiveness of the algorithm

stabilization of lpv systems state feedback state estimation and duality in this paper we consider the problem of stabilizing linear parameter varying lpv systems by means of gain scheduling control this technique amounts to designing a controller which is able to update its parameters on line according to the variations of the plant parameters we first consider the state feedback case and show a design procedure based on the construction of a lyapunov function for discrete time lpv systems in which the parameter variations are affine and occur in the state matrix only this procedure produces a nonlinear static controller we show that different from the robust stabilization case we can always derive a linear controller that is nonlinear controllers cannot outperform linear ones for the gain scheduling problem then we show that this procedure has a dual version which leads to the construction of a linear gain scheduling observer the two procedures may be combined to derive an observer based linear gain scheduling compensator

a new class of universal lyapunov functions for the control of uncertain linear systems the authors analyze the problem of synthesizing a state feedback control for the class of uncertain continuous time linear systems affected by time varying memoryless parametric uncertainties they consider as candidate lyapunov functions the elements of the class spl sigma sub p sup z which is formed by special homogeneous positive definite functions they show that this class is universal in the sense that a lyapunov function exists if and only if there exists a lyapunov function in spl sigma sub p sup z they prove this result in a constructive way showing that such a lyapunov function can always be obtained by smoothing a polyhedral function for which construction algorithms are available the authors show that unlike the polyhedral lyapunov functions these functions allow us to derive explicit formulas for the stabilizing controller

nonquadratic lyapunov functions for robust control abstract this paper deals with the problem of controlling a linear continuous time system with structured time varying parameter uncertainties and input disturbances with a lyapunov function approach in contrast with most of the previous results in the literature we do not confine our attention to the class of quadratic lyapunov functions conversely the basic motivation of this paper is to determine whether there exist other functions that can be conveniently used as candidate lyapunov functions this question has a positive answer the proposed class is that of polyhedral norms or more generally of polyhedral minkowski functionals we show that the class of these functions is universal in the sense that if the problem of ultimately bounding the state in an assigned convex set via state feedback control can be solved via a lyapunov function and a continuous state feedback compensator then it can be solved via a polyhedral lyapunov function and a possibly different continuous control moreover we show that the control can be piecewise linear a numerical technique for constructing the controller is presented for the case in which the uncertainty constraint sets are polyhedral

on the equivalence between global recurrence and the existence of a smooth lyapunov function for hybrid systems abstract we study a weak stability property called recurrence for a class of hybrid systems an open set is recurrent if there are no finite escape times and every complete trajectory eventually reaches the set under sufficient regularity properties for the hybrid system we establish that the existence of a smooth radially unbounded lyapunov function that decreases along solutions outside an open bounded set is a necessary and sufficient condition for recurrence of that set recurrence of open bounded sets is robust to sufficiently small state dependent perturbations and this robustness property is crucial for establishing the existence of a lyapunov function that is smooth we also highlight some connections between recurrence and other well studied properties like asymptotic stability and ultimate boundedness

fuzzy dynamical system approach for a dual parameter hybrid order robust control design abstract robust control for uncertain dynamical systems is considered the uncertainty is assumed to be bounded and the fuzzy set theory is adopted to describe the bound a new dual parameter hybrid order robust control design is then proposed in two steps first a class of robust controls is designed taking the advantage of the flexibility in choosing the order and a design parameter the controls are deterministic and are not if then fuzzy rules based deterministic performance including uniform boundedness and uniform ultimate boundedness for the controlled systems is guaranteed second a fuzzy set theoretic based performance index consisting of average and steady state system performance and control cost is proposed a constrained optimization problem is formulated with the intension of minimizing the performance index the objective of the optimization problem is to search for the optimal choice of dual parameters that minimizes the performance index we show that the solution to the optimization problem always exists as a result the resulting control design achieves two concurrent goals guaranteeing deterministic performance as well as minimizing the performance index the theory is illustrated by an unmanned aerial vehicle uav system control design

discrete time robust control via state feedback for single input systems a nonlinear robust state feedback controller for discrete time uncertain systems is proposed the uncertainties in the system must satisfy the matching condition but only their bounds need to be known the controller is designed via the second method of lyapunov the detailed derivation of the controller for single input systems is given the system response remains in the neighborhood of the zero state if uncertainties are small the uncertainty bound for the stability condition is derived

stabilization of linear time invariant interval systems via constant state feedback control this paper investigates the stabilization problem of linear uncertain systems via constant state feedback control the systems under consideration contain time invariant uncertain parameters whose values are unknown but bounded in given compact sets and are thus called interval systems the criterion for the asymptotic stability of the closed loop system obtained when a state feedback control is applied is that all the eigenvalues of the resulting system matrix are in the strict left half of the complex plane first the author shows that to insure an interval system stabilizable some entries of the system matrices must be sign invariant more precisely the number of the least required sign invariant entries in system matrices is equal to the system order then the author studies the stabilizability of a set of interval systems called standard systems which contain sufficient numbers of sign invariant entries in proper locations after dividing all standard systems into some subsets by the uncertainty locations the author then derives necessary and sufficient conditions under which every system in a subset is stabilizable regardless of its parameter varying bounds the conditions show that all uncertain entries in system matrices should form a particular geometrical pattern called a generalized antisymmetric stepwise configuration for an interval system satisfying the stabilizability conditions a computational control design procedure is also provided and illustrated via an example the result is further generalized for nonstandard systems via linear transformation

practical stabilization of nonlinear uncertain dynamic systems with bounded controllers we address the problem of practically stabilizing nonlinear and or uncertain continuous time dynamic systems when the norm of the control input is subject to a given fixed bound we consider a class of systems whose nominal part is linear and whose nonlinear uncertain part does not satisfy the matching condition in this treatment no statistical information regarding the uncertainties is needed only a norm bound on each nonlinear uncertain quantity is assumed we propose a bounded state feedback controller whose design incorporates elements from both variable structure control theory and the deterministic control methodology using the second method of lyapunov we obtain sliding domains regions of uniform ultimate boundedness and estimates of the domain of attraction for systems employing this controller the closed loop stability analysis as well as the design of the controller is facilitated by introducing a special coordinate transformation the approach is illustrated by a numerical example

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

design of softer robust nonlinear control laws abstract we show that the lyapunov function used in backstepping feedback designs for uncertain nonlinear systems leads to unnecessarily hard control laws having undesirable high gain properties we present a new lyapunov function and use it to design softer control laws which exhibit the high gain properties to a much lesser extent we show that the soft designs eliminate the chattering exhibited by the hard designs and achieve the same or better performance with less control effort

gromov s compactness theorem for pseudo holomorphic curves we give a complete proof for gromov s compactness theorem for pseudo holomorphic curves both in the case of closed curves and curves with boundary

robust tracking control of robots by a linear feedback law for the trajectory following problem of a robot manipulator a simple linear robust fedback control law with constant gain matrix is proposed that makes the resulting error system uniformly ultimately bounded this control law is very easy to implement by simply choosing a feedback gain according to the coefficients of a polynomial function of the tracking errors which is a bounding function for the terms in the lagrange euler formulation in the limit as the gain approaches infinity the error system becomes globally asymptotically stable

a new class of stabilizing controllers for uncertain dynamical systems this paper is concerned with the problem of designing a stabilizing controller for a class of uncertain dynamical systems the vector of uncertain parameters q cdot is time varying and its values q t lie within a prespecified bounding set q in r p furthermore no statistical description of q cdot is assumed and the controller is shown to render the closed loop system practically stable in a so called guaranteed sense that is the desired stability properties are assured no matter what admissible uncertainty q cdot is realized within the perspective of previous research in this area this paper contains one salient feature the class of stabilizing controllers which we characterize is shown to include linear controllers when the nominal system happens to be linear and time invariant in contrast in much of the previous literature see for example 1 2 7 and 9 a linear system is stabilized via nonlinear control another feature of this paper is the fact that the

on the state observation and output feedback problems for nonlinear uncertain dynamic systems abstract in this paper we examine the problems of state observation and state trajectory control by output feedback for the class of non linear systems in 3 11 we begin by modifying a known discontinuous variable structure type observer into a continuous type observer that guarantees the observation error is globally exponentially stable ges we then modify a known discontinuous variable structure type output feedback controller into continuous type output feedback controller that forces the state to the origin in the ges sense specific time varying bounds on the observation error and the state trajectory are also developed revealing how the corresponding observer or control parameters can be adjusted to improve the system performance

universal construction of feedback laws achieving iss and integral iss disturbance attenuation we study nonlinear systems with both control and disturbance inputs the main problem addressed in the paper is design of state feedback control laws that render the closed loop system integral input to state stable iiss with respect to the disturbances we introduce an appropriate concept of control lyapunov function iiss clf whose existence leads to an explicit construction of such a control law the same method applies to the problem of input to state stabilization converse results and techniques for generating iiss clfs are also discussed

brief robust control of nonlinear systems with parametric uncertainty probabilistic robustness analysis and synthesis for nonlinear systems with uncertain parameters are presented monte carlo simulation is used to estimate the likelihood of system instability and violation of performance requirements subject to variations of the probabilistic system parameters stochastic robust control synthesis searches the controller design parameter space to minimize a cost that is a function of the probabilities that design criteria will not be satisfied the robust control design approach is illustrated by a simple nonlinear example a modified feedback linearization control is chosen as controller structure and the design parameters are searched by a genetic algorithm to achieve the tradeoff between stability and performance robustness

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

connections with l p bounds on curvature we show by means of the implicit function theorem that coulomb gauges exist for fields over a ball inr n when the integrall n 2 field norm is sufficiently small we then are able to prove a weak compactness theorem for fields on compact manifolds withl p integral norms bounded p n 2

bound invariant lyapunov functions a means for enlarging the class of stabilizable uncertain systems inaccuracies between a physical system and its mathematical model are often accounted for via the introduction of uncertain parameters this paper addresses the problem of stabilizing systems described by linear state equations whose matrices contain uncertain time varying parameters whose values are unknown but are required to live in a prescribed compact bounding set one approach to this stabilizability problem which has received attention in the literature is to construct a quadratic lyapunov function however it has been shown that necessary and sufficient conditions for the existence of such a quadratic lyapunov function may require the execution of a non linear feasible point search hence recent work has focused on developing sufficient conditions for stabilizability which avoid a nonlinear programming problem to this same end this paper introduces the notion of stabilizability via a bound invariant quadratic lyapunov function bilf which requires that the lyapunov function be independent o

a riccati equation approach to the stabilization of uncertain linear systems this paper presents a method for designing a feedback control law to stabilize a class of uncertain linear systems the systems under consideration contain uncertain parameters whose values are known only to within a given compact bounding set furthermore these uncertain parameters may be time varying the method used to establish asymptotic stability of the closed loop system obtained when the feedback control is applied involves the use of a quadratic lyapunov function the main contribution of this paper involves the development of a computationally feasible algorithm for the construction of a suitable quadratic lyapunov function once the lyapunov function has been obtained it is used to construct the stabilizing feedback control law the fundamental idea behind the algorithm presented involves constructing an upper bound for the lyapunov derivative corresponding to the closed loop system this upper bound is a quadratic form by using this upper bounding procedure a suitable lyapunov function can be found by solving a certain matrix riccati equation another major contribution of this paper is the identification of classes of systems for which the success of the algorithm is both necessary and sufficient for the existence of a suitable quadratic lyapunov function

stabilization of uncertain discrete time linear system with limited communication this technical note proposes a procedure to control an uncertain discrete time networked system using an aperiodic stabilizing input information the system is primarily affected by the time varying norm bounded mismatched parametric uncertainty aperiodic exchange of information is done due to bandwidth constraint of the communication network an event triggered based robust control strategy is adopted to reduce the effects of system uncertainty in such bandwidth constrained networks in event triggered control the control input is computed and actuated at the system end only when a pre specified event condition is violated the robust control input is derived to stabilize the uncertain system by solving an optimal control problem based on a virtual nominal dynamics and a modified cost functional it is shown that the robust control law with aperiodic information ensures input to state stability iss of the original system in the presence of mismatched uncertainty deriving the event triggering condition for a discrete time uncertain system and ensuring the stability of such system analytically are the key contributions of this technical note a numerical example is given to prove the efficacy of the proposed event based control algorithm over the conventional periodic one

structural stabilization of uncertain systems necessity of the matching condition this paper investigates one aspect of the problem of stabilizing an uncertain linear system that is the systems under consideration contain uncertain parameters which are unknown but bounded the question arises as to whether such a system can be stabilized via feedback control in some of the previous papers in this area the system is assumed to satisfy a so called matching condition this type of assumption is used to assure that the uncertain system can be stabilized it is known however that the matching condition is not a necessary condition for stabilizability this paper introduces a strengthened notion of stabilizability referred to as structural stabilizability via a nominally determined quadratic lyapunov function it is then shown that if a system is to have this stronger property the matching condition must necessarily be satisfied

improved results on the 0 1 multidimensional knapsack problem abstract geometric constraint and cutting planes have been successfully used to solve the 0 1 multidimensional knapsack problem our algorithm combines linear programming with an efficient tabu search it gives best results when compared with other algorithms on benchmarks issued from the or l ibrary embedding this algorithm in a variables fixing heuristic still improves our previous results furthermore difficult sub problems with about 100 variables issued from the 500 original ones could be generated these small sub problems are always very hard to solve

bubble tree convergence for harmonic maps let be a compact riemann surface any sequence fn m of harmonic maps with bounded energy has a bubble tree limit consisting of a harmonic map o m and a tree of bubbles fk s2 m we give a precise construction of this bubble tree and show that the limit preserves energy and homotopy class and that the images of the fn converge pointwise we then give explicit counterexamples showing that bubble tree convergence fails i for harmonic maps fn when the conformal structure of varies with n and ii when the conformal structure is fixed and n is a palais smale sequence for the harmonic map energy

robust static and dynamic output feedback stabilization deterministic and stochastic perspectives three parallel gaps in robust feedback control theory are examined sufficiency versus necessity deterministic versus stochastic uncertainty modeling and stability versus performance deterministic and stochastic output feedback control problems are considered with both static and dynamic controllers the static and dynamic robust stabilization problems involve deterministically modeled bounded but unknown measurable time varying parameter variations while the static and dynamic stochastic optimal control problems feature state control and measurement dependent white noise general sufficiency conditions for the deterministic problems are obtained using lyapunov s direct method while necessary conditions for the stochastic problems are derived as a consequence of minimizing a quadratic performance criterion the sufficiency tests are then applied to the necessary conditions to determine when solutions of the stochastic optimization problems also solve the deterministic robust stability problems as an additional application of the deterministic result the modified riccati equation approach of petersen and hollot is generalized in the static case and extended to dynamic compensation

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions