design of state detectors for nonlinear systems using symmetries and semi invariants two techniques are proposed for the design of asymptotic state detectors for nonlinear systems both in the continuous time and discrete time cases the first technique allows one to design linear state detectors for nonlinear systems belonging to a given class which is studied and characterized in the paper the second technique extends the ideas of the first by using semi invariants to compute invariant sets and study their stability

observer design for nonlinear control systems abstract this paper deals with the observer design problem of a wide class of nonlinear systems subjected to bounded nonlinearities a sufficient liapunovlike condition is provided and the proposed dynamic observer is a direct extension of the one in linear case

hybrid dead beat observers for a class of nonlinear systems this paper studies both the full order and the reduced order dead beat observer problem for a class of nonlinear systems linear in the unmeasured states a novel hybrid observer design strategy is proposed with the help of the notion of strong observability in finite time the proposed methodology is applied for the estimation of the frequency of a sinusoidal signal the results show that accurate estimation can be provided even if the signal is corrupted by high frequency noise a brief discussion of the robustness properties of the proposed observer with respect to measurement errors is also provided

finite dimensional approximation in infinite dimensional mathematical programming we consider the problem of approximating an optimal solution to a separable doubly infinite mathematical program p with lower staircase structure by solutions to the programs p n obtained by truncating after the first n variables and n constraints of p viewing the surplus vector variable associated with the nth constraint as a state and assuming that all feasible states are eventually reachable from any feasible state we show that the efficient set of all solutions optimal to all possible feasible surplus states for p n converges to the set of optimal solutions to p a tie breaking algorithm which selects a nearest point efficient solution for p n is shown for convex programs to converge to an optimal solution to p a stopping rule is provided for discovering a value of n sufficiently large to guarantee any prespecified level of accuracy the theory is illustrated by an application to production planning

infinite horizon optimization we consider the general problem of choosing a discounted cost minimizing infinite sequence of decisions from a closed subset of the product space formed by a sequence of arbitrary compact metric spaces examples include equipment replacement production planning and more generally infinite stage mathematical programs it is shown that the optimal costs for finite horizon approximating problems converge to the optimal infinite horizon cost as the horizons diverge to infinity moreover the existence of a unique algorithmically optimal i e accumulation point solution is shown to be a necessary and sufficient condition for convergence in the product topology i e policy convergence of all finite horizon optima under the weaker condition of hausdorff convergence of the sets of finite horizon optima to the set of infinite horizon optima we show how to force policy convergence through a natural tie breaking rule finally a forward algorithm is presented which in the presence of a unique infinite horizon optimum is guaranteed to converge

complex structures on banach spaces with a subsymmetric basis we prove that a real banach space e with a subsymmetric basis and isomorphic to the sequence space e e has a unique complex structure we also show that if a real banach space x has the property p then all its complex structures also satisfies p when p is any of the following properties bounded approximation property g l l u st being injective and being complemented in a dual space

complex structures on real vector lattices the main result of this paper states that a universally complete real vector lattice admits a band preserving complex structure if and only if it contains no locally one dimensional bands a description of order bounded disjointness preserving complex structures on archimedean semiprime f algebras is also given

an exotic quasidiagonal operator let h be a separable infinite dimensional hilbert space we construct a block diagonal hence quasidiagonal operator t on h i e t tn for some tn s called blocks acting on finite dimensional mutually orthogonal subspaces of h which is not a norm limit of a sequence of algebraically m normal operators or equivalently block diagonal operators each of which has uniformly bounded sizes of blocks the construction is based on random techniques

observer design for nonlinear systems with discrete time measurements this paper focuses on the development of asymptotic observers for nonlinear discrete time systems it is argued that instead of trying to imitate the linear observer theory the problem of constructing a nonlinear observer can be more fruitfully studied in the context of solving simultaneous nonlinear equations in particular it is shown that the discrete newton method properly interpreted yields an asymptotic observer for a large class of discrete time systems while the continuous newton method may be employed to obtain a global observer furthermore it is analyzed how the use of broyden s method in the observer structure affects the observer s performance and its computational complexity an example illustrates some aspects of the proposed methods moreover it serves to show that these methods apply equally well to discrete time systems and to continuous time systems with sampled outputs

global exponential observers for two classes of nonlinear systems abstract this paper develops sufficient conditions for the existence of global exponential observers for two classes of nonlinear systems i the class of systems with a globally asymptotically stable compact set and ii the class of systems that evolve on an open set in the first class the derived continuous time observer also leads to the construction of a robust global sampled data exponential observer under additional conditions two illustrative examples of applications of the general results are presented one is a system with monotone nonlinearities and the other is a chemostat system

stabilization with relaxed controls cannot in general be stabilized using a continuous closed loop control u x even if each state separately can be driven asymptotically to the origin an example is analyzed in section 2 in this paper we examine the possibility of stabilizing such systems with a continuous closed loop relaxed control we find indeed that the family of systems stabilizable with relaxed controls is larger than the family of those stabilizable with ordinary controls an even larger class is obtained if the continuity of the closed loop at the origin is not required the latter class includes all one dimensional systems for which states can be driven asymptotically to the origin this result does not hold in two dimensional systems and we provide a counter example it should be pointed that relaxed control type stabilization is used both in theory and in practice the method is known as dither we shall comment on the similarities lyapunov functions for the system 1 help us in the construction of the continuous closed loop stabilizers in fact we find that the existence of a smooth lyapunov function is equivalent to the existence of a stabilizing closed loop which is continuous except possibly at the origin an additional condition on the lyapunov function implies the continuity at the origin as well we present these results in section 4 after a brief introduction of closed loop relaxed controls notations and terminology in section 3 prior to that in section 2 we discuss an example illustrating the power of relaxed controls in the particular case of systems linear in the controls relaxed controls can be replaced by ordinary controls this is discussed in section 5 the role of lyapunov functions in the stability and stabilization theories is of course well known examples of systems with lyapunov functions are available in the literature we display some in section 6 along with general comments on the construction applications and counterexamples including one which cannot be continuously stabilized yet possesses a nonsmooth lyapunov function closed loop stabilization with ordinary controls is analyzed extensively in the literature see sontag 8 sussmann ll and references therein lyapunov functions techniques in stabil

infinite horizon nonstationary stochastic optimal control problem a planning horizon result we show the existence of a planning horizon for the infinite horizon nonstationary stochastic optimal control problem hence the original problem generally untractable reduces to solve a sequence of finite horizon problems which is computationally attractive

a banach space without a basis which has the bounded approximation property can be approximated by finite rank operators uniformly on compact sets it is clear that xhasabasis xhasbap xhasap the fact that the converse implication to the second one does not hold in general was discovered by figiel and johnson 8 soon after enflo s example 7 of a space without ap the main purpose of this paper is to show that also the implication bap basis does not hold in general this answers problems asked by a number of authors e g 14 18 27 before stating the result we recall more notation for a given basis x n of x one denotes by bc x n the basis constant of ix the smallest k such that

nonlinear observer design for a general class of discrete time nonlinear systems with real parametric uncertainty this paper is a geometric study of the local observer design for a general class of discrete time nonlinear systems with real parametric uncertainty explicitly we study the observer design problem for a general class of discrete time nonlinear systems with real parametric uncertainty and with an input generator exosystem in this paper we show that for the classical case when the state equilibrium does not change with the parametric uncertainty and when the plant output is purely a function of the state there is no local asymptotic observer for the plant next we show that in sharp contrast to this case for the general case of problems where we allow the state equilibrium to change with the parametric uncertainty there typically exist local exponential observers even when the plant output is purely a function of the state we also present a characterization and construction procedure for local exponential observers for the general class of discrete time nonlinear systems with real parametric uncertainty under some stability assumptions we also show that for the general class of discrete time nonlinear systems considered under some stability assumptions the existence of local exponential observers in the presence of inputs implies and is implied by the existence of local exponential observers in the absence of inputs finally we generalize our results to a general class of discrete time nonlinear systems with input generator and with exogenous disturbance

solution and forecast horizons for infinite horizon nonhomogeneous markov decision processes we consider a nonhomogeneous infinite horizon markov decision process mdp problem with multiple optimal first period policies we seek an algorithm that given finite data delivers an optimal first period policy such an algorithm can thus recursively generate within a rolling horizon procedure an infinite horizon optimal solution to the original problem however it can happen that no such algorithm exists i e the mdp is not well posed equivalently it is impossible to solve the problem with a finite amount of data assuming increasing marginal returns in actions with respect to states and stochastically increasing state transitions with respect to actions we provide an algorithm that is guaranteed to solve the given mdp whenever it is well posed this algorithm determines in finite time a forecast horizon for which an optimal solution delivers an optimal first period policy as an application we solve all well posed instances of the time varying version of the classic asset selling problem

solution approximation in infinite horizon linear quadratic control we consider the problem of choosing a discounted cost minimizing infinite stage control sequence under nonstationary positive semidefinite quadratic costs and linear constraints specific cases include the nonstationary lq tracker and regulator problems we show that the optimal costs for finite stage approximating problems converge to the optimal infinite stage cost as the number of stages grows to infinity under a state reachability condition we show that the set unions of all controls optimal to all feasible states for the finite stage approximating problems converge to the set of infinite stage optimal controls a tie breaking rule is provided that selects finite stage optimal controls so as to force convergence to an infinite horizon optimal control

an existence theorem for observers of bilinear systems under suitable uniformity assumptions the existence of nonlinear state observers with exponentially decaying error for bilinear systems is proved to be equivalent to that of observers whose corresponding error dynamics is linear with respect to the error

on the existence and uniqueness of complex structure and spaces with few operators we construct a 2 n dimensional real normed space whose banach mazur distance to the set of spaces admitting complex structure is of order nl 2 and two complex n dimensional normed spaces which are isometric as real spaces but whose complex banach masur distance is of order n both orders of magnitude are the largest possible we also construct finite dimensional spaces with the property that all well bounded operators on them are rather small in the sense of some ideal norm perturbations of multiples of identity we also state some metatheorem which can be used to produce spaces with various pathological properties 1 introduction and the main results the main purpose of this paper is to prove the following results theorem 1 1 given n there exists a 2n dimensional real normed space x such that whenever y is an n dimensional complex normed space and yr is y treated as a real space then the banach mazur distance d x yr c4 where c is a numerical constant given a complex normed space y denote by y the space obtained from y by replacing the multiplication by scalar x y xy by k y a y xy and preserving the rest of the structure addition norm we then have theorem 1 2 given n there ejcists an n dimensional space y over c such that d y y cn where c is a numerical constant here d denotes distance of complex spaces the orders of magnitude o 4 and o n in theorems 1 1 and 1 2 are of course the largest possible in the first case the n dimensional complex hilbert space always gives the upper estimate in the second d yl y2 n if dimyl dim y2 n in both the real and complex case a weaker version of theorem 1 1 with estimate o 5 n log n was shown recently by p mankiewicz 8 a version of theorem 1 2 with estimate o n log n was shown independently of this paper and approximately at the same time by j bourgain 1 who also settled the infinite dimensional problem constructing a complex banach space y such that y and y are not isomorphic with all the consequences see corollary 1 3 below similar problems were considered recently by n j kalton 5 who constructed an analogous example received by the editors november 1 1984 and in revised form march 4 1985 1980 mathematics subject classification primary 46b20 51a99 secondary 46l99 47b10 47d15 52a22 52a40 60e15 supported in part by nsf dms 8401906 c 1986 american mathematical society 0002 9947 86 1 00 25 per page

a stopping rule for forecast horizons in nonhomogeneous markov decision processes we formulate a mixed integer program to determine whether a finite time horizon is a forecast horizon in a nonhomogeneous markov decision process we give a bender s decomposition approach to solving this problem that evaluates the stopping rule eliminates some suboptimal combinations of actions and yields bounds on the maximum error that could result from the selection of a candidate action in the initial stage the integer program arising from the decomposition has special properties that allow efficient solution we illustrate the approach with numerical examples

locally convergent nonlinear observers we introduce a new method for the design of observers for nonlinear systems using backstepping the method is applicable to a class of nonlinear systems slighter larger than those treated by gauthier hammouri and othman ieee trans automat control 27 1992 pp 875 880 they presented an observer design method that is globally convergent using high gain in contrast to theirs our observer is not high gain but it is only locally convergent if the initial estimation error is not too large then the estimation error goes to zero exponentially a design algorithm is presented

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

error bounds for finite step approximations for solving infinite horizon controlled markov set chains this note considers finite step approximations for solving an infinite horizon controlled markov set chain problem with finite state and action spaces we develop a value iteration type algorithm based on the optimality equation developed by kurano et al and analyze an error bound relative to the optimal value that satisfies the optimality equation from the successive approximation we further analyze an error bound of the approximate control policy defined from a finite step approximate value by applying the value iteration type algorithm

uniqueness of complex structure and real hereditarily indecomposable banach spaces there exists a real hereditarily indecomposable banach space x x c respectively x x h such that the algebra l x s x is isomorphic to c respectively to the quaternionic division algebra h up to isomorphism x c has exactly two complex structures which are conjugate totally incomparable and both hereditarily indecomposable so there exist two banach spaces which are isometric as real spaces but totally incomparable as complex spaces this extends results of j bourgain and s szarek j bourgain real isomorphic complex banach spaces need not be complex isomorphic proc amer math soc 96 2 1986 221 226 s szarek on the existence and uniqueness of complex structure and spaces with few operators trans amer math soc 293 1 1986 339 353 s szarek a superreflexive banach space which does not admit complex structure proc amer math soc 97 3 1986 437 444 and proves that a theorem of g godefroy and n j kalton g godefroy n j kalton lipschitz free banach spaces studia math 159 1 2003 121 141 about isometric embeddings of separable real banach spaces does not extend to the complex case the quaternionic example x h on the other hand has unique complex structure up to isomorphism other examples with a unique complex structure are produced including a space with an unconditional basis and non isomorphic to l2 this answers a question of s szarek in s szarek a superreflexive banach space which does not admit complex structure proc amer math soc 97 3 1986 437 444

nonlinear observer design for a general class of nonlinear systems with real parametric uncertainty this paper is a geometric study of the local observer design for a general class of nonlinear systems with real parametric uncertainty explicitly we study the observer design problem for a general class of nonlinear systems with real parametric uncertainty and with an input generator exosystem in this paper we show that for the classical case when the state equilibrium does not change with the parametric uncertainty and when the plant output is purely a function of the state there is no local asymptotic observer for the plant next we show that in sharp contrast to this case for the general case of problems where we allow the state equilibrium to change with the parametric uncertainty there typically exist local exponential observers even when the plant output is purely a function of the state we also present a characterization and construction procedure for local exponential observers for the general class of nonlinear systems with real parametric uncertainty under some stability assumptions we also show that for the general class of nonlinear systems considered under some stability assumptions the existence of local exponential observers in the presence of inputs implies and is implied by the existence of local exponential observers in the absence of inputs finally we generalize our results to a general class of nonlinear systems with input generator and with exogenous disturbance

nonuniform in time state estimation of dynamic systems in this paper it is shown that if a time varying uncertain system is robustly completely detectable then there exists an estimator for this system i e the state vector of the system can be estimated asymptotically if the time varying uncertain system is robustly completely observable it is shown that there exists an estimator for this system with assignable rate of convergence of the error moreover specialized constructions are developed for the special class of triangular systems

nonlinear observers with linearizable error dynamics we present a new method for designing asymptotic observers for a class of nonlinear systems the error between the state of the system and the state of the observer in appropriate coordinates evolves linearly and can be made to decay arbitrarily exponentially fast

a stochastic programming approach for planning horizons of infinite horizon capacity planning problems planning horizon is a key issue in production planning different from previous approaches based on markov decision processes we study the planning horizon of capacity planning problems within the framework of stochastic programming we first consider an infinite horizon stochastic capacity planning model involving a single resource linear cost structure and discrete distributions for general stochastic cost and demand data non markovian and non stationary we give sufficient conditions for the existence of an optimal solution furthermore we study the monotonicity property of the finite horizon approximation of the original problem we show that the optimal objective value and solution of the finite horizon approximation problem will converge to the optimal objective value and solution of the infinite horizon problem when the time horizon goes to infinity these convergence results together with the integrality of decision variables imply the existence of a planning horizon we also develop a useful formula to calculate an upper bound on the planning horizon then by decomposition we show the existence of a planning horizon for a class of very general stochastic capacity planning problems which have complicated decision structure

hyperreflexivity and operator ideals abstract suppose b is an operator ideal and a is a linear space of operators between banach spaces x and y modifying the classical notion of hyperreflexivity we say that a is called b hyperreflexive if there exists a constant c such that for any t b x y with sup q t i the supremum runs over all isometric embeddings i into x and all quotient maps of y satisfying q a i 0 there exists a a for which t a c in this paper we give examples of b hyperreflexive spaces as well as of spaces failing this property in the last section we apply s e hyperreflexivity of operator algebras s e is a regular symmetrically normed operator ideal to constructing operator spaces with prescribed families of completely bounded maps

existence and discovery of average optimal solutions in deterministic infinite horizon optimization we consider the problem of making a sequence of decisions each chosen from a finite action set over an infinite horizon so as to minimize its associated average cost both the feasibility and cost of a decision are allowed to depend upon all of the decisions made prior to that decision moreover time varying costs and constraints are allowed a feasible solution is said to be efficient if it reaches each of the states through which it passes at minimum cost we show that efficient solutions exist and that under a state reachability condition efficient solutions are also average optimal exploiting the characterization of efficiency via a solution s short run as opposed to long run behavior a forward algorithm is constructed which recursively discovers the first second and subsequent decisions of an efficient and hence average optimal infinite horizon solution

solving nonstationary infinite horizon dynamic optimization problems monotonicity of optimal solutions to finite horizon dynamic optimization problems is used to prove the existence of a forecast horizon i e a long enough planning horizon that ensures that a first period optimal action for the infinite horizon and the finite horizon problem agree regardless of problem parameter changes in the tail the existence of extremal monotone optimal solutions motivates a stopping rule that is ensured to detect the minimal forecast horizon to be used in a rolling horizon procedure to exactly solve the problem

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

an existence theorem for discrete time infinite horizon optimal control problems an existence theorem is given for a general class of deterministic infinite horizon discrete time optimal control problems the hypotheses of the theorem are weak and can be easily verified the objective function may be either a summation or supremum over time

approximating extreme points of infinite dimensional convex sets the property that an optimal solution to the problem of minimizing a continuous concave function over a compact convex set in rn is attained at an extreme point is generalized by the bauer minimum principle to the infinite dimensional context the problem of approximating and characterizing infinite dimensional extreme points thus becomes an important problem consider now an infinite dimensional compact convex set in the nonnegative orthant of the product space rinfinity we show that the sets of extreme points en of its corresponding finite dimensional projections onto rn converge in the product topology to the closure of the set of extreme points e of the infinite dimensional set as an application we extend the concept of total unimodularity to infinite systems of linear equalities in nonnegative variables where we show when extreme points inherit integrality from approximating finite systems an application to infinite horizon production planning is considered

a state observer for nonlinear dynamical systems the problem of state observation for nonlinear systems is of main importance in automatic control in recent years many contributions have been presented in literature that solve the design problem for classes of nonlinear systems most works can be roughly classi ed into two categories in one the geometrical properties of vector elds de ning the system are exploited and therefore mathematical tools of the di erential geometry are extensively employed in the other one the functional properties of the input state and state output maps which de ne the system are mainly used while the geometrical methods often provide a general solution of the problem for systems that belong to restricted classes characterized by geometrical properties 1 2 3 4 5 6 7 13 14 17 18 19 the second approach gives solutions for classes of nonlinear systems whose geometrical nature is not investigated and only macroscopic parameters norms gains lipschitz constants and so on are involved in the design procedure 8 9 11 12 21 one main problem in state observation for nonlinear systems is that the property of driftobservability does not imply observability for any input function as shown in 16 19 thus it is interesting to investigate when the drift observability property allows the solution of the state observation problem nding conditions that restricts the class of input functions due to the mathematical tools employed this work may be considered as belonging to both the categories above mentioned in this paper nonlinear systems of the form

forecast horizons for a class of dynamic lot size problems under discrete future demand we present structural and computational investigations of a new class of weak forecast horizons minimal forecast horizons under the assumption that future demands are integer multiples of a given positive real number for a specific class of dynamic lot size dls problems apart from being appropriate in most practical instances the discreteness assumption offers a significant reduction in the length of a minimal forecast horizon over the one using the classical notion of continuous future demands we provide several conditions under which a discrete demand forecast horizon is also a continuous demand forecast horizon we also show that the increase in the cost resulting from using a discrete minimal forecast horizon instead of the classical minimal forecast horizon is modest the discreteness assumption allows us to characterize forecast horizons as feasibility optimality questions in 0 1 mixed integer programs on an extensive test bed we demonstrate the computational tractability of the integer programming approach owing to its prevalence in practice our computational experiments emphasize the special case of integer future demands

nonlinear observers for lipschitz continuous systems with inputs this paper considers the state observation problem for nonlinear dynamical systems the proposed framework is a direct generalization of a method introduced in a recent paper for autonomous system its characteristic feature is that the dynamic part of the observer is linear and as a consequence that convergence takes place globally in the observer coordinates the observer is completed by a static nonlinearity which maps the observer state in the original state space an associated observation mapping is introduced and is interpreted in terms of an orthonormal expansion of the input and the output with respect to a certain basis in a suitable hilbert space it is shown that by choosing the observer dimension properly an observer with arbitrary small asymptotic observation error is obtained provided that some compactness properties for the subset to be observed and the set of input signals hold under a stronger condition the finite complexity property an exact observer is achieved finally an integral formula representation for the observer nonlinearity is given

bilinearization up to output injection abstract this paper deals with nonlinear systems that can be steered to bilinear systems by output injection and nonlinear change of coordinates we give an abstract non constructive theorem and an algorithm which allows us to recognize such systems

conditions for the discovery of solution horizons we present necessary and sufficient conditions for discrete infinite horizon optimization problems with unique solutions to be solvable these problems can be equivalently viewed as the task of finding a shortest path in an infinite directed network we provide general forward algorithms with stopping rules for their solution the key condition required is that of weak reachability which roughly requires that for any sequence of nodes or states it must be possible from optimal states to reach states close in cost to states along this sequence moreover the costs to reach these states must converge to zero applications are considered in optimal search undiscounted markov decision processes and deterministic infinite horizon optimization

observer design for nonlinear triangular systems with unobservable linearisation the article deals with the observer design problem for a wide class of triangular time varying nonlinear systems with unobservable linearisation sufficient conditions are derived for the existence of a luenberger type observer when it is a priori known that the initial state of the system belongs to a given nonempty bounded subset of the state space for the general case the state estimation is exhibited by means of a switching sequence of time varying dynamics

degeneracy in infinite horizon optimization we consider sequential decision problems over an infinite horizon the forecast or solution horizon approach to solving such problems requires that the optimal initial decision be unique we show that multiple optimal initial decisions can exist in general and refer to their existence as degeneracy we then present a conceptual cost perturbation algorithm for resolving degeneracy and identifying a forecast horizon we also present a general near optimal forecast horizon

convergence of nonlinear observers on bbr n with a riemannian metric part i we study how convergence of an observer whose state lives in a copy of the given system s space can be established using a riemannian metric we show that the existence of an observer guaranteeing the property that a riemannian distance between system and observer solutions is nonincreasing implies that the lie derivative of the riemannian metric along the system vector field is conditionally negative moreover we establish that the existence of this metric is related to the observability of the system s linearization along its solutions moreover if the observer has an infinite gain margin then the level sets of the output function are geodesically convex conversely we establish that if a complete riemannian metric has a lie derivative along the system vector field that is conditionally negative and is such that the output function has a monotonicity property then there exists an observer with an infinite gain margin

on the classification of positions and complex structures in banach spaces abstract a topological setting is defined to study the complexities of the relation of equivalence of embeddings or position of a banach space into another and of the relation of isomorphism of complex structures on a real banach space the following results are obtained a if x is not uniformly finitely extensible then there exists a space y for which the relation of position of y inside x reduces the relation e 0 and therefore is not smooth b the relation of position of l p inside l p or inside l p p 2 reduces the relation e 1 and therefore is not reducible to an orbit relation induced by the action of a polish group c the relation of position of a space inside another can attain the maximum complexity e max d there exists a subspace of l p 1 p 2 on which isomorphism between complex structures reduces e 1 and therefore is not reducible to an orbit relation induced by the action of a polish group

dual based methods for solving infinite horizon nonstationary deterministic dynamic programs we develop novel dual ascent and primal dual methods to solve infinite horizon nonstationary deterministic dynamic programs these methods are finitely implementable and converge in value to optimality moreover the dual ascent method produces a sequence of improving dual solutions that pointwise converge to an optimal dual solution while the primal dual algorithm provides a sequence of primal basic feasible solutions with value error bounds from optimality that converge to zero our dual based methods work on a more general class of infinite network flow problems that include the shortest path formulation of dynamic programs as a special case to our knowledge these are the first dual based methods proposed in the literature to solve infinite horizon nonstationary deterministic dynamic programs

state observation of nonlinear uncertain dynamical systems this note proposes new types of observers for nonlinear dynamical systems subjected to bounded nonlinearities or uncertainties the design of these observers utilizes techniques related to variable structure systems theory a measure for the rate at which the estimates converge to the actual states is derived

output feedback stabilization the stabilization of control systems using output feedback is addressed necessary and sufficient lyapunov conditions are established generalizing the artstein s stabilization theorem for linear control systems a necessary and sufficient lyapunov condition is provided for stabilization by means of a linear output feedback law

canonical form observer design for non linear time variable systems an observer of canonical phase variable form for non linear time variable systems is introduced the development of this non linear time variable form requires regularity of the non linear time variable observability matrix of the system from the relationships derived during the development it follows that a non linear time variable observer can be dimensioned by an eigenvalue assignment with respect to the canonical state coordinates if a linearization of system non linearities about the reconstructed state trajectories is permissible this is an assumption similar to that of the extended kalman filter based on a linearization about the current estimate

recursive nonlinear observer design beyond the uniform observability we propose a recursive design scheme of a state observer for multiple input multiple output partly lower triangular nonlinear systems the design begins from the subdynamics far from the output and propagates to the subdynamics close to the output recalling the backstepping scheme for nonlinear control the proposed class of systems is fairly general since it includes nonuniformly observable and or detectable multioutput systems error convergence to zero is proved assuming boundedness of inputs a posteriori i e after the design which is preferable whereas most results in the literature assume the boundedness a priori i e before the design a global observer is proposed with the global lipschitz condition of the system but without any restriction on the size of lipschitz coefficient the lipschitz condition can be removed when a semiglobal observer is of interest

a generalization of vidyasagar s theorem on stability using state detection in this paper we generalize the vidyasagar s well known theorem on the local stabilizability problem of nonlinear systems using state detection 11 our purpose is to prove that if a system is weakly detectable and stabilizable by means of a continuous state feedback u x for which no differentiability assumption is imposed then the system is also stabilized by the law u z where z is the output of a weak detector for the state x the result above is applicable to several cases not covered by other works

semiclassical non concentration near hyperbolic orbits for a large class of semiclassical pseudodifferential operators including schrodinger operators p h h2 g v x on compact riemannian manifolds we give logarithmic lower bounds on the mass of eigenfunctions outside neighbourhoods of generic closed hyperbolic orbits more precisely we show that if a is a pseudodifferential operator which is microlocally equal to the identity near the hyperbolic orbit and microlocally zero away from the orbit then u c log 1 h h p h u clog 1 h i a u this generalizes earlier estimates of colin de verdiere and parisse y colin de verdiere b parisse equilibre instable en regime semi classique i concentration microlocale comm partial differential equations 19 1994 1535 1563 equilibre instable en regime semi classique ii conditions de bohr sommerfeld ann inst h poincare phys theor 61 1994 347 367 obtained for a special case and of burq and zworski n burq m zworski geometric control in the presence of a black box j amer math soc 17 2004 443 471 for real hyperbolic orbits

feedback control of nonlinear systems by extended linearization for single input multiple output nonlinear systems we consider a design method based on the family of linearizations of the system parameterized by constant operating points nonlinear state feedback control laws and observer state feedback control laws are designed such that the eigenvalues of the family of linearized closed loop systems are placed at specified values that are locally invariant with respect to the closed loop operating point the method is illustrated by application to the problem of automatically balancing an inverted pendulum

a luenberger like observer for nonlinear systems a state observer is proposed for nonlinear continuous time systems which extends the well known luenberger observer in particular on the basis of simple assumptions on the regularity of the system equations observability and the global holder condition for suitable functions which are generally satisfied for physically meaningful dynamic systems the global asymptotic convergence of the estimated state towards the true state is shown finally some examples of applications are also reported showing the effectiveness of the proposed observer

conditions for the existence of planning horizons we consider the general class of discounted problems involving sequential decision making over an unbounded horizon under the assumptions of a finite set of policy alternatives at each decision time and costs that are eventually uniformly bounded by some exponential existence of an optimal infinite horizon strategy is established moreover it is shown that there is a finite horizon version whose first policy decision agrees with an infinite horizon optimal policy under the additional assumption that the infinite horizon optimal strategy is eventually cyclic the stronger result follows that the infinite horizon optimal solution is unique for almost all interest rates and that therefore a planning horizon exists algorithmic implications are explored for a restricted subclass of these problems

discrete time nonlinear observer design using functional equations abstract the present research work proposes a new approach to the discrete time nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer the proposed approach develops a nonlinear analogue the formulation of the discrete time nonlinear observer design problem is realized via a system of first order linear nonhomogeneous functional equations and a rather general set of necessary and sufficient conditions for solvability is derived using results from functional equations theory the solution to the above system of functional equations can be proven to be locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

nonlinear system immersion observers and finite dimensional filters abstract nonlinear deterministic and stochastic systems which can be immersed into linear observable ones are identified by necessary and sufficient conditions those systems are shown to admit observers in the deterministic case and exact finite dimensional filters in the stochastic case the sufficient conditions obtained generalize earlier results in both cases

optimization based non linear observers revisited optimization based non linear observers are those where the integrated output prediction error is used to define the dynamic of the observer s state their main advantage is genericity and the natural assumptions that are needed for the related convergence results to hold here we present some new theoretical results concerning these observers despite the title we use our observer is not based on the search for a global minimum of a cost function it is based on a descent like approach without the use of the hessian matrix a nice feature is that the resulting observer takes a classical form of in the sense that it is defined by a set of ordinary differential equations besides the theoretical results some implementation issues are discussed in particular we propose to use the post stabilization approach well known when dealing with differential systems with invariant submanifolds this enables to increase the sampling period while keeping very good precision two illustrative examples are presente

existence of bilinear state observers for bilinear systems a recent result by kudva et al 1 is applied to find necessary and sufficient conditions for the existence of bilinear state observers for bilinear systems

design of state observers from a drift observability property in this paper the problem of state observation with exponential error decay for nonlinear systems affine in the input is considered and an observer is proposed for such an observer the drift observability property of the system i e observability for zero input together with an assumption on the input amplitude or on the observation relative degree are sufficient conditions for exponential convergence of the observation error the existence of an exponential observer is correlated to the existence of a solution for an h sub spl infin riccati like inequality global and semiglobal convergence results are presented

duality in infinite dimensional linear programming we consider the class of linear programs with infinitely many variables and constraints having the property that every constraint contains at most finitely many variables while every variable appears in at most finitely many constraints examples include production planning and equipment replacement over an infinite horizon we form the natural dual linear programming problem and prove strong duality under a transversality condition that dual prices are asymptotically zero that is we show under this transversality condition that optimal solutions are attained in both primal and dual problems and their optimal values are equal the transversality condition and hence strong duality is established for an infinite horizon production planning problem

a linear programming approach to nonstationary infinite horizon markov decision processes nonstationary infinite horizon markov decision processes mdps generalize the most well studied class of sequential decision models in operations research namely that of stationary mdps by relaxing the restrictive assumption that problem data do not change over time linear programming lp has been very successful in obtaining structural insights and devising solution methods for stationary mdps however an lp approach for nonstationary mdps is currently missing this is because the lp formulation of a nonstationary infinite horizon mdp includes countably infinite variables and constraints and research on such infinite dimensional lps has traditionally faced several hurdles for instance duality results may not hold an extreme point may not be a basic feasible solution and in the context of a simplex algorithm a pivot operation may require infinite data and computations and a sequence of improving extreme points need not converge in value to optimal in this paper we tackle these challenges a

brief an observer for systems with nonlinear output map a nonlinear observer with the feedback gain weighted by the sensitivity of the output with respect to the state is developed for systems with nonlinear output map the observer can be obtained from the extended kalman filter by a special choice of time varying weighting matrices it is shown that the estimation error dynamics are asymptotically stable and a region of attraction is derived the observer is applied to the top blown converter process for estimating the content of impurities in the liquid metal using plant data from the converter at ssab oxelosund ab the observer is shown to provide accurate estimates of the carbon content

on exponential observers for nonlinear systems abstract the aim of the paper is to identify the class of nonlinear systems that have exponential observers a concept introduced by previous authors it is shown that a necessary condition for the existence of an exponential observer for a nonlinear system is that the corresponding linearized system is detectable and for local exponential stabilization problems the condition is also sufficient this paper gives also a theorem on the separation property for the exponential design problem and it enables us to tell exactly to what extent the classical local linearization approach is applicable

a tie breaking rule for discrete infinite horizon optimization we study discrete infinite horizon optimization problems without the common assumption of a unique optimum a method based on solution set convergence is employed for finding optimal initial decisions by solving finite horizon problems this method is applicable to general discrete decision models that satisfy a weak reachability condition the algorithm together with a stopping rule is applied to production planning and capacity expansion and computational results are reported

nonlinear observer design using lyapunov s auxiliary theorem abstract the present work proposes a new approach to the nonlinear observer design problem based on the early ideas that influenced the development of the linear luenberger observer theory the proposed approach develops a nonlinear analogue the formulation of the observer design problem is realized via a system of singular first order linear pdes and a rather general set of necessary and sufficient conditions for solvability is derived by using lyapunov s auxiliary theorem the solution to the above system of pdes is locally analytic and this enables the development of a series solution method that is easily programmable with the aid of a symbolic software package

observability through delayed measurements a new approach to state observers design an original approach for the construction of state observers for dynamic systems is presented in this article new notions of observability delay observability and delay drift observability useful for the development of the observer equations and for the convergence proof are introduced and compared with other standard observability concepts in particular it is shown that delay drift observability is an extension of the well known drift observability property the construction of the proposed observer is straightforward and does not require any coordinate transformation of the system into a canonical form which is a common feature of many other approaches a numerical example is reported where a system that is not drift observable is considered in this case the proposed observer is easily constructed and performs well

on nonlinear observers in this note we make some remarks about the general observer problem for nonlinear systems we show how the existence of a partial observer without stability requirements is locally equivalent to the existence of a conditioned invariant distribution we argue that by considering not only identity observers we can put the stability issue in a broader perspective

nonlinear observer design in the presence of delayed output measurements the present work proposes a new approach to the nonlinear observer design problem in the presence of delayed output measurements the proposed nonlinear observer possesses a state dependent gain which is computed from the solution of a system of first order singular partial differential equations and in particular consists of a chain of state observation algorithms that reconstruct the unmeasurable state vector at different delayed time instants within the time delay window introduced by the available output measurements therefore the proposed nonlinear observer exhibits a chain like structure that explicitly reflects and takes into account the magnitude of the output delay furthermore a set of conditions is derived under which convergence of the estimation error to zero is established finally the performance of the proposed observer and its convergence properties are evaluated in an illustrative biological reactor example

concepts of forecast and decision horizons applications to dynamic stochastic optimization problems in this paper we develop a rigorous new framework for the concepts of forecast and decision horizons these concepts are conditional in nature and in turn enable us to unify the existing concepts of strong and weak horizons moreover we are able to precisely state the questions of existence of forecast decision horizons finally we are able to further develop the theory of existence of forecast decision horizons in the discounted case and procedures to compute these horizons

sontag s input to state stability condition and global stabilization using state detection this paper deals with the global stabilization problem for nonlinear system using state detection sufficient algebraic conditions for stabilization and detectability concerning particular classes of systems are included these conditions are based to a version of a lyapunov like condition proposed by sontag which guarantees input to state stability