controlled diffusions with constraints controlled diffusion problems with classical cost structures ergodic discounted etc are considered when finitely many additional cost functionals of the same type are required to lie in prescribed intervals existence of an optimal markov control is proved by convex analytic methods

pseudo integral and generalized choquet integral abstract due to many applications the choquet integral as a powerful tool for modeling non deterministic problems needs to be further extended therefore the paper is devoted to a generalization of the choquet integral as a basis the pseudo integral for bounded integrand is extended to the case for nonnegative integrands at first and then the generalized choquet integral is defined as special cases pseudo choquet stieltjes integrals pseudo fuzzy stieltjes integrals g choquet integrals pseudo n fuzzy integrals and pseudo s fuzzy integrals are obtained and various kinds of properties and convergence theorems are shown meanwhile markov jensen minkowski and holder inequalities are proved in the end the generalized discrete choquet integral is discussed the obtained results for the generalized choquet integral cover some previous results on different types of nonadditive integrals

several inequalities for the pan integral several inequalities for the pan integral are investigated it is shown that the chebyshev inequality holds for an arbitrary subadditive measure if and only if the integrands f g are comonotone thus we provide a new characterization for nonnegative comonotone functions it is also shown that the holder and minkowski inequalities for the pan integral hold if the monotone measure is subadditive since the pan integral coincides with the concave integral when is subadditive our results can also be applied to the concave integral

lebesgue theorems in non additive measure theory in this paper the sufficient and necessary conditions for different kinds of lebesgue theorem in non additive measure theory are presented respectively the equivalence among the lebesgue theorem the monotone convergence theorems of fuzzy and of choquet integral are shown as direct results of the lebesgue theorems the necessary conditions for egoroff s theorem are given

on the equality of integrals considering a finite space x several necessary conditions and one rather general sufficient condition describing when the choquet integral coincides with the pan integral with respect to the standard arithmetic operations are shown these conditions are characterized by using the minimal atoms of monotone measure under the introduced constraints the calculation of these coinciding two integrals is also given

a note on controlled diffusions on line with time averaged cost existence of stable optimal markov controls is established for a class of cost functions for controlled one dimensional diffusions with time averaged cost

a sufficient condition of equivalence of the choquet and the pan integral abstract in this note we continue to investigate the relationship between the choquet integral and the pan integral on infinite space we will show that the m property of monotone measures is a sufficient condition that the choquet integral coincides with the pan integral in this discussion the spaces are not restricted to be finite thus the previous results obtained in finite space are further generalized and developed a characteristic of the m property of monotone measures is also presented

controlled markov chains and stochastic networks controlled markov chains with average cost criterion and with special cost and transition structures are studied existence of optimal stationary strategies is established for the average cost criterion corresponding dynamic programming equations are derived a stochastic network problem that includes interconnected queues as a special case is described and studied within this framework

an algorithm to identify and compute average optimal policies in multichain markov decision processes this paper concerns discrete time finite state multichain mdps with compact action sets the optimality criterion is long run average cost simple examples illustrate that optimal stationary markov policies do not always exist we establish the existence of e optimal policies that are stationary markovian and develop an algorithm that computes these approximate optimal policies we establish a necessary and sufficient condition for the existence of an optimal policy that is stationary markovian and in case that such an optimal policy exists the algorithm computes it

sandwich games the extension of set functions or capacities in a concave fashion namely a concavification is an important issue in decision theory and combinatorics it turns out that some set functions cannot be properly extended if the domain is restricted to be bounded this paper examines the structure of those capacities that can be extended over a bounded domain in a concave manner we present a property termed the sandwich property that is necessary and sufficient for a capacity to be concavifiable over a bounded domain we show that when a capacity is interpreted as the product of any sub group of workers per a unit of time the sandwich property provides a linkage between optimality of time allocations and efficiency

the average cost of markov chains subject to total variation distance uncertainty abstract this paper addresses the problem of controlling a markov chain so as to minimize the long run expected average cost per unit time when the invariant distribution is unknown but we know it belongs to a given uncertain set the mathematical model used to describe this set is the total variation distance uncertainty we show that the equilibrium control policy which yields higher probability to the states with low cost and lower probability to the states with the high cost is an optimal control policy that minimizes the average cost recognition of such a policy may be of value in practical situations with constraints consistent to those studied here when the invariant distribution is uncertain and deriving online an optimal control policy is required

discrete time controlled markov processes with average cost criterion a survey this work is a survey of the average cost control problem for discrete time markov processes the authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades the exposition ranges from finite to borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies the authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography the authors have also identified several important questions that are still open to investigation

observer based adaptive neural network control for nonlinear systems in nonstrict feedback form this paper focuses on the problem of adaptive neural network nn control for a class of nonlinear nonstrict feedback systems via output feedback a novel adaptive nn backstepping output feedback control approach is first proposed for nonlinear nonstrict feedback systems the monotonicity of system bounding functions and the structure character of radial basis function rbf nns are used to overcome the difficulties that arise from nonstrict feedback structure a state observer is constructed to estimate the immeasurable state variables by combining adaptive backstepping technique with approximation capability of radial basis function nns an output feedback adaptive nn controller is designed through backstepping approach it is shown that the proposed controller guarantees semiglobal boundedness of all the signals in the closed loop systems two examples are used to illustrate the effectiveness of the proposed approach

on the continuity of the concave integral whenever a functional is concave it is natural to ask whether its sendograph is a closed convex set if so the hahn banach theory implies that the functional can be represented as the infimum of all continuous linear functionals greater than or equal to it we refer to such representation as a dual representation dominated convergence of the concave integral for capacities is characterized in terms of dual representation whenever sequences of functions converge pointwise outside a set of zero capacity

a note on the coincidence of decomposition integrals and superdecomposition integrals abstract it is known that the decomposition integral i h and the superdecomposition integral i h related to the system h of all finite chains from a where a is a algebra of the subsets of a nonvoid set x coincide with each other for each monotone measure and for each nonnegative measurable function and they are equal to the choquet integral in this note we show that the converse is also true that is for a complete system h of finite set systems from a if i h i h holds for each monotone measure and for each nonnegative measurable function then the system h and the system of all finite chains from a are equivalent in some sense and the integrals involved are the choquet integral

ergodic control of switching diffusions we study the ergodic control problem of switching diffusions representing a typical hybrid system that arises in numerous applications such as fault tolerant control systems flexible manufacturing systems etc under fairly general conditions we establish the existence of a stable nonrandomized markov policy which almost surely minimizes the pathwise long run average cost we then study the corresponding hamilton jacobi bellman hjb equation and establish the existence of a unique solution in a certain class using this we characterize the optimal policy as a minimizing selector of the hamiltonian associated with the hjb equations as an example we apply the results to a failure prone manufacturing system and obtain closed form solutions for the optimal policy

on the equivalence of the choquet pan and concave integrals on finite spaces abstract in this paper we introduce the concept of maximal cluster of minimal atoms on monotone measure spaces and by means of this new concept we continue to investigate the relation between the choquet integral and the pan integral on finite spaces it is proved that the m property of a monotone measure is a sufficient condition that the choquet integral coincides with the pan integral based on the usual addition and multiplication thus combining our recent results we provide a necessary and sufficient condition that the choquet integral is equivalent to the pan integral on finite spaces meanwhile we also use the characteristics of minimal atoms of monotone measure to present another necessary and sufficient condition that these two kinds of integrals are equivalent on finite spaces the relationships among the choquet integral the pan integral and the concave integral are summarized

robust partial state feedback prescribed performance control of cascade systems with unknown nonlinearities a universal controller is designed for cascade systems involving dynamic uncertainty unknown nonlinearities exogenous disturbances and or time varying parameters capable of guaranteeing prescribed performance for the output tracking error as well as uniformly bounded signals in the closed loop by prescribed performance we mean that the output tracking error should converge to a predefined arbitrarily small residual set with convergence rate no less than a certain prespecified value exhibiting maximum overshoot less than a sufficiently small preassigned constant the proposed control scheme is of low complexity utilizes partial state feedback and requires reduced levels of a priori system knowledge the results can be easily extended to systems affected by bounded state measurement errors as well as to mimo nonlinear systems in block triangular form simulations clarify and verify the approach

subjective probability and expected utility without additivity comonotic acts are defined and an axiom of comonotomic independence 19 introduced that weakens the von newmann morgenstern axiom of independence if a nondegenerate continuous and monotonic state independent weak order over acts satisfies comonotonic independence then it induces a unique non necessarily additive probability and a von neumann morgenstern utility an extension of theexpected utility theory covers situations as the ellsberg paradox which are inconsistent with additive expected utility the concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included

prescribed performance adaptive control for multi input multi output affine in the control nonlinear systems we consider the tracking problem of unknown robustly stabilizable multi input multi output mimo affine in the control nonlinear systems with guaranteed prescribed performance by prescribed performance we mean that the tracking error converges to a predefined arbitrarily small residual set with convergence rate no less than a prespecified value exhibiting maximum overshoot as well as undershoot less than some sufficiently small preassigned constants utilizing an output error transformation we obtain a transformed system whose robust stabilization is proven necessary and sufficient to achieve prescribed performance guarantees for the output tracking error of the original system provided that initially the transformed system is well defined consequently a switching robust control lyapunov function rclf based adaptive state feedback controller is designed to solve the stated problem the proposed controller is continuous and successfully overcomes the problem of computing the control law when the approximation model becomes uncontrollable simulations illustrate the approach

the lagrange and the vanishing discount techniques to controlled diffusions with cost constraints abstract in this paper we introduce two useful methods to compute optimal control policies for either the discounted or the average payoff criterion with cost constraints when the dynamic system evolves as a n dimensional diffusion processes as for the attribute cost constraints we mean the coexistence of a given cost function that in general is dominated above by another function in particular by a constant playing the role of an extra constraint in the control model to deduce optimality results for the discounted case we employ the lagrange multipliers technique along with dynamic programming arguments then the vanishing discount method is applied to easily obtain average optimal policies we support our theory by providing an example on pollution accumulation problem

tracking control for a class of unknown nonsquare mimo nonaffine systems a deep rooted information based robust adaptive approach the tracking control problem of multi input multi output mimo nonaffine dynamic systems is studied in this note a globally uniformly ultimately bounded guub stable tracking control solution for non square mimo nonaffine systems with unknown dynamics and disturbances is established different from most existing methods the proposed control design is based on the readily computable deep rooted information on the system and does not involve linearization or approximation and the resultant control algorithms are simple in structure inexpensive in computation user friendly in design and undemanding in implementation both theoretical analysis and numerical simulation verify the effectiveness and benefits of the proposed method

a universal construction of artstein s theorem on nonlinear stabilization abstract this note presents an explicit proof of the theorem due to artstein which states that the existence of a smooth control lyapunov function implies smooth stabilizability moreover the result is extended to the real analytic and rational cases as well the proof uses a universal formula given by an algebraic function of lie derivatives this formula originates in the solution of a simple riccati equation

the vitali convergence in measure theorem of nonlinear integrals abstract the vitali convergence in measure theorem for the abstract lebesgue integral is fundamental in lebesgue integration theory and yields the bounded convergence theorem and the dominated convergence theorem as its applications in this paper in a unified way using the perturbation method the vitali convergence in measure theorem is established for nonlinear integrals such as the choquet sipos sugeno and shilkret integrals and their symmetric and asymmetric extensions it is derived from the fatou and the reverse fatou type lemmas for perturbative nonlinear integral functionals

generalized convergence theorems for monotone measures abstract in this paper we propose three types of absolute continuity for monotone measures and present some of their basic properties by means of these three types of absolute continuity we establish generalized egoroff s theorem generalized riesz s theorem and generalized lebesgue s theorem in the framework involving the ordered pair of monotone measures the egoroff theorem the riesz theorem and the lebesgue theorem in the traditional sense concerning a unique monotone measure are extended to the general case these three generalized convergence theorems include as special cases several previous versions of egoroff like theorem riesz like theorem and lebesgue like theorem for monotone measures respectively

singular perturbations in ergodic control of diffusions ergodic control of a nondegenerate diffusion with two time scales is studied in the limiting case as the time scale separation increases to infinity it is shown that the limit problem is another ergodic control problem for the slow time scale component alone with its dynamics averaged over the controlled invariant probability measures for the fast component these measures in turn can be treated as the effective control variable

optimal policies for controlled markov chains with a constraint abstract the time average reward for a discrete time controlled markov process subject to a time average cost constraint is maximized over the class of al causal policies each epoch a reward depending on the state and action is earned and a similarly constituted cost is assessed the time average of the former is maximized subject to a hard limit on the time average of the latter it is assumed that the state space is finite and the action space compact metric an accessibility hypothesis makes it possible to utilize a lagrange multiplier formulation involving the dynamic programming equation thus reducing the optimization problem to an unconstrained optimization parametrized by the multiplier the parametrized dynamic programming equation possesses compactness and convergence properties that lead to the following if the constraint can be satisfied by any causal policy the supremum over time average rewards respective to all causal policies is attained by either a simple or a mixed policy the latter is equivalent to choosing independently at each epoch between two specified simple policies by the throw of a biased coin

a probabilistic representation of exact games on σ algebras the purpose of this paper is to establish the intrinsic relations between the cores of exact games on s algebras and the extensions of exact games to function spaces given a probability space exact functionals are defined on l as an extension of exact games to derive a probabilistic representation for exact functionals we endow them with two probabilistic conditions law invariance and the fatou property the representation theorem for exact functionals lays a probabilistic foundation for nonatomic scalar measure games based on the notion of p convexity we also investigate the equivalent conditions for the representation of anonymous convex games

robust switching adaptive control of multi input nonlinear systems during the last decade a considerable progress has been made in the design of stabilizing controllers for nonlinear systems with known and unknown constant parameters new design tools such as adaptive feedback linearization adaptive back stepping control lyapunov functions clfs and robust control lyapunov functions rclfs nonlinear damping and switching adaptive control have been introduced most of the results developed are applicable to single input feedback linearizable systems and parametric strict feedback systems these results however cannot be applied to multi input feedback linearizable systems parametric pure feedback systems and systems that admit a linear in the parameters clf in this paper we develop a general procedure for designing robust adaptive controllers for a large class of multi input nonlinear systems this class of nonlinear systems includes as a special case multi input feedback linearizable systems parametric pure feedback systems and systems that admit a linear in the parameters clf the proposed approach uses tools from the theory of rclf and the switching adaptive controllers proposed by the authors for overcoming the problem of computing the feedback control law when the estimation model becomes uncontrollable the proposed control approach has also been shown to be robust with respect to exogenous bounded input disturbances

asymptotic evolution of a stochastic control problem here we study the minimization problem of an integral discounted functional on a set of nonexplosive and nonconstrained diffusions the integrand is weakly coercive which leads us using the dynamic programming method to characterize the optimal cost among the solutions of the solving equation with radiative conditions expressing the centripetal aspect of the optimal control the evolution of the problem when the discount vanishes is then considered the integrand being strongly coercive i e its gradient being outward a limit problem is defined and similarly solved an inward optimal control exists which is the limit of the ones of the initial problems the existence properties are obtained by means of a priori estimates concerning suitable solutions of the solving equations in the whole space

an abelian limit approach to a singular ergodic control problem we consider an ergodic stochastic control problem for a class of one dimensional ito processes where the available control is an added bounded variation process the corresponding infinite horizon discounted control problem was solved in a weerasinghe siam j control optim 44 2005 pp 389 417 here we show that as the discount factor approaches zero the optimal strategies derived in a weerasinghe siam j control optim 44 2005 pp 389 417 converge to an optimal strategy for the ergodic control problem under different assumptions two types of optimal strategies were derived also the abelian limit relationships among the ergodic control problem the infinite horizon discounted control problem and the finite time horizon control problem are established here a solution to a constrained optimization problem is obtained as an application

an ergodic control problem for constrained diffusion processes existence of optimal markov control an ergodic control problem for a class of constrained diffusion processes is considered the goal is the almost sure minimization of long term cost per unit time the main result of the paper is that there exists an optimal markov control for the considered problem it is shown that under the assumption of regularity of the skorohod map and the assumption that the drift vector field takes values in a certain cone of stability the class of controlled diffusion processes considered have strong uniform in control stability properties the role of the boundary is critical in obtaining the stability and ergodic control results for the class of controlled constrained diffusion processes considered in this work since the domains are unbounded and the corresponding unconstrained diffusions are typically transient these stability properties are key in obtaining appropriate tightness estimates once these estimates are available the remaining work lies in identifying weak limits of a certain family of occupation measures in this regard an extension to the echeverria weiss kurtz characterization of invariant measures of markov processes to the case of constrained controlled processes considered in this paper is proved this characterization result is also crucially used in proving the compactness of the family of invariant measures of markov processes corresponding to all possible markov controls

long term optimal investment strategies in the presence of adjustment costs we consider the problem of determining in a dynamical way the optimal capacity level of an investment project that operates within a random economic environment in particular we consider an investment project that yields payoff at a rate that depends on its installed capacity level and on a random economic indicator such as the price of the project s output commodity we model this economic indicator by means of a general one dimensional ergodic diffusion at any time the project s capacity level can be increased or decreased at given proportional costs the aim is to maximize an ergodic performance criterion that reflects the long term average payoff resulting from the project s management we solve this genuinely two dimensional stochastic control problem by constructing an explicit solution to an appropriate hamilton jacobi bellman equation and by fully characterizing an optimal investment strategy

relationship between two types of superdecomposition integrals on finite spaces abstract this paper investigates the relationship between two types of superdecomposition integrals namely the convex integral and the pan integral from above on finite spaces to this end we introduce two new concepts related to monotone measures superadditivity with respect to singletons and minimal strictly subadditive set and discuss some of their properties in the case that the monotone measure is superadditive with respect to singletons we show that these two types of integrals are equivalent in other cases by means of the characteristics of minimal strictly subadditive sets we provide a set of necessary and sufficient conditions for which these two types of integrals coincide with each other

some new results on sample path optimality in ergodic control of diffusions we present some new results on sample path optimality for the ergodic control problem of a class of nondegenerate diffusions controlled through the drift the hypothesis most often used in the literature to ensure the existence of an almost sure sample path optimal stationary markov control requires finite second moments of the first hitting times tau of bounded domains over all admissible controls we show that this can be considerably weakened mathbb e tau 2 may be replaced with mathbb e tau ln tau thus reducing the required rate of convergence of averages from polynomial to logarithmic a foster lyapunov condition that guarantees this is also exhibited moreover we study a large class of models that are neither uniformly stable nor have a near monotone running cost and we exhibit sufficient conditions for the existence of a sample path optimal stationary markov control

ergodic control of multidimensional diffusions 1 the existence results the existence of optimal stable markov relaxed controls for the ergodic control of multidimensional diffusions is established by direct probabilistic methods based on a characterization of a s limit sets of empirical measures the optimality of the above is established in the strong i e almost sure sense among all admissible controls under very general conditions

smooth neuroadaptive pi tracking control of nonlinear systems with unknown and nonsmooth actuation characteristics this paper considers the tracking control problem for a class of multi input multi output nonlinear systems subject to unknown actuation characteristics and external disturbances neuroadaptive proportional integral pi control with self tuning gains is proposed which is structurally simple and computationally inexpensive different from traditional pi control the proposed one is able to online adjust its pi gains using stability guaranteed analytic algorithms without involving manual tuning or trial and error process it is shown that the proposed neuroadaptive pi control is continuous and smooth everywhere and ensures the uniformly ultimately boundedness of all the signals of the closed loop system furthermore the crucial compact set precondition for a neural network nn to function properly is guaranteed with the barrier lyapunov function allowing the nn unit to play its learning approximating role during the entire system operation the salient feature also lies in its low complexity in computation and effectiveness in dealing with modeling uncertainties and nonlinearities both square and nonsquare nonlinear systems are addressed the benefits and the feasibility of the developed control are also confirmed by simulations

survey paper a partial history of the early development of continuous time nonlinear stochastic systems theory this article is a survey of the early development of selected areas in nonlinear continuous time stochastic control key developments in optimal control and the dynamic programming principle existence of optimal controls under complete and partial observations nonlinear filtering stochastic stability the stochastic maximum principle and ergodic control are discussed issues concerning wide bandwidth noise for stability modeling filtering and ergodic control are dealt with the focus is on the earlier work but many important topics are omitted for lack of space

pseudo optimal measures based on a pseudo addition on 0 pseudo optimal measures related to non negative set functions vanishing at the empty set non negative games are introduced for a fixed pseudo addition an equivalence on non negative set functions is studied a special stress is given to pure pseudo optimal measures admitting no other equivalent set function

superdecomposition integrals this study introduces and discusses a new class of integrals based on superdecompositions of integrated functions including an analysis of their relationship with decomposition integrals which were introduced recently by even and lehrer the proposed superdecomposition integrals have several properties that are similar or dual with respect to decomposition integrals but they also have some significant differences the convex integral is obtained by considering all possible superdecompositions with no constraints on the applied sets which can be treated as the greatest convex homogeneous functional that is bounded from above by the measure we consider the relationship with the universal integral of klement et al is also discussed finally some possible generalizations are outlined

sandwich theorems for set functions an application of the lehrer teper integral abstract we show that a new integral recently introduced by lehrer and teper 2008 11 provides all the tools to determine the necessary and sufficient conditions for the existence of an additive set function m sandwiched between two arbitrary set functions and m

randomized and past dependent policies for markov decision processes with multiple constraints the markov decision problem of locating a policy to maximize the long run average reward subject to k long run average cost constraints is considered it is assumed that the state and action spaces are finite and the law of motion is unichain that is every pure policy gives rise to a markov chain with one recurrent class it is first proved that there exists an optimal stationary policy with a degree of randomization no greater than k consequently it is never necessary to randomize in more than k states a linear program produces the optimal policy with limited randomization for the special case of a single constraint we also address the problem of finding optimal nonrandomized but nonstationary policies we show that a round robin type policy is optimal and conjecture the same for a steering policy that depends on the entire past history of the process but whose implementation requires essentially no more storage than that of a pure policy

control of markov chains with long run average cost criterion the dynamic programming equations the long run average cost control problem for discrete time markov chains on a countable state space is studied in a very general framework necessary and sufficient conditions for optimality in terms of the dynamic programming equations are given when an optimal stable stationary strategy is known to exist e g for the situations studied in stochastic differential systems stochastic control theory and applications ima vol math app 10 springer verlag new york berlin 1988 pp 57 77 a characterization of the desired solution of the dynamic programming equations is given in a special case also included is a novel convex analytic argument for deducing the existence of an optimal stable stationary strategy when that of a randomized one is known

adaptive control for semilinear stochastic systems an adaptive ergodic cost stochastic control problem for a partially known semilinear stochastic system in an infinite dimensional space is formulated and solved the solutions of the hamilton jacobi bellman equations for the discounted cost and the ergodic cost stochastic control problems require some special interpretations because they do not typically exist in the usual sense the solutions of the parameter dependent ergodic hamilton jacobi bellman equations are obtained from some corresponding discounted cost control problems as the discount rate tends to zero the solutions of the ergodic hamilton jacobi bellman equations are shown to depend continuously on the parameter a certainty equivalence adaptive control is given that is based on the optimal controls from the solutions of the ergodic hamilton jacobi bellman equations and a strongly consistent family of estimates of the unknown parameter this adaptive control is shown to achieve the optimal ergodic cost for the known system

integrals based on monotone set functions an overview of various integrals is given which can be defined on arbitrary monotone set functions vanishing in the empty set called here monotone measures our survey includes not only the choquet integral 1954 10 the shilkret integral 1971 66 and the sugeno integral 1974 71 and some of their properties but also some more general and more recent concepts as universal integrals klement et al 2010 27 and decomposition integrals even 2014 13 together with some of their properties such as integral inequalities and convergence theorems

on minimum cost per unit time control of markov chains the minimum cost per unit time control problem is studied for a class of markov chains that though important in applications does not fit the conventional framework for this problem existence of optimal stationary strategies and necessary and sufficient conditions for optimality are established

adaptive output feedback control design with prescribed performance for switched nonlinear systems abstract in this paper an output feedback control method with prescribed performance is proposed for single input and single output siso switched non strict feedback nonlinear systems it is assumed that nonlinear functions of the concerned systems are unknown switching signals are unknown and arbitrary and the states are unmeasured a linear state observer is designed to estimate the unmeasured states and an observer based output feedback control scheme is developed the key advantages of the proposed control strategy are that virtual control gains of the concerned non strict feedback nonlinear systems are not required to be known and only one tuning parameter is needed based on lyapunov stability theory it is shown that all the signals in the resulting closed loop system are semi globally uniformly ultimately bounded and the tracking error converges to a small residual set with the prescribed performance bound the effectiveness of the proposed control approach is verified by a numerical example

average optimality in dynamic programming on borel spaces unbounded costs and controls abstract we show the existence of average cost optimal stationary policies in a class of discrete time markov control processes with borel state space unbounded costs and non compact control sets

an optimal stochastic multivariable pid controller a direct output tracking approach abstractthis paper deals with the design of an optimal stochastic controller possessing tracking capability of any reference output trajectory in the presence of measurement noise we consider multi input multi output linear time invariant systems and a proportional integral derivative pid controller the system under consideration needs not be stable a recursive algorithm providing optimal time varying pid gains is proposed for the case where the number of inputs is larger than or equal to the number of outputs the development of the proposed algorithm aims for per time sample minimisation of the mean square output error in the presence of erroneous initial conditions measurement noise and process noise necessary and sufficient conditions are provided for the convergence of the output error covariance in addition convergence results are presented for discretised continuous time plants simulation results are included to illustrate the performance capabilities of the proposed algorithm performan

an extended direct scheme for robust adaptive nonlinear control abstract the proposed adaptive scheme achieves regulation for a class of nonlinear systems with unknown constant parameters and unmodeled dynamics the scheme does not employ overparametrization and does not restrict the class of nonlinearities by any growth conditions instead the dependence on the unknown parameters is restricted by an extended matching condition which however is satisfied in many systems of practical importance such as most types of electric motors

ergodic control of semilinear stochastic equations and the hamilton jacobi equation abstract in this paper we consider optimal control of stochastic semilinear equations with lipschitz continuous drift and cylindrical noise we show existence and uniqueness up to an additive constant of solutions to the stationary hamilton jacobi equation associated with the cost functional given by the asymptotic average per unit time cost as a consequence we find the optimizing controls given in the feedback form to obtain these results we prove also some new results on the transition semigroups of semilinear diffusion acting in the spaces of continuous function with the weighted sup norms and on the optimal control of semilinear diffusions for the discounted cost functional

relationship between the concave integrals and the pan integrals on finite spaces a r t i c l e i n f o a b s t r a c t this study discusses the relationship between the concave integrals and the pan integrals on finite spaces the minimal atom of a monotone measure is introduced and some properties are investigated by means of two important structure characteristics related to minimal atoms minimal atoms disjointness property and subadditivity for minimal atoms a necessary and sufficient condition is given that the concave integral coincides with the pan integral with respect to the standard arithmetic operations a nd on finite spaces following this result we have shown that these two integrals coincide if the underlying monotone measure is sub additive

a discrete choquet integral for ordered systems a model for a choquet integral for arbitrary finite set systems is presented the model includes in particular the classical model on the system of all subsets of a finite set the general model associates canonical non negative and positively homogeneous superadditive functionals with generalized belief functions relative to an ordered system which are then extended to arbitrary valuations on the set system it is shown that the general choquet integral can be computed by a simple monge type algorithm for so called intersection systems which include as a special case weakly union closed families generalizing lovasz classical characterization we give a characterization of the superadditivity of the choquet integral relative to a capacity on a union closed system in terms of an appropriate model of supermodularity of such capacities

ergodic control problem for one dimensional diffusions with near monotone cost the existence and uniqueness of the solution to the bellman equation for ergodic control of one dimensional diffusions is established under a near monotonicity condition on the cost necessary and sufficient conditions for the optimality of a stable markov control are given in terms of the same

time continuity and nonadditive expected utility information consisting of probabilities of some but possibly not all events induces an integral with respect to a probability specified on a subalgebra a decision maker evaluates the alternatives using only the available information and completely ignoring unavailable information assume now that the decision maker assesses the worth of a different lottery at each point in a discrete time assume also that each such lottery is preferred to some fixed alternative lottery now consider the situation where the sequence of lotteries converges in some sense if the limiting lottery is preferred to the fixed alternative then the preference order is referred to as time continuous this paper studies time continuity for two preference functionals the choquet integral and the integral with respect to a probability specified on a subalgebra the integral with respect to probability specified on a subalgebra is determined by the structure of the available information by relating it to the choquet integral we characterize the structure of available information that would yield time continuity

the concave integral over large spaces this paper investigates the concave integral for capacities defined over large spaces we characterize when the integral with respect to capacity v can be represented as the infimum over all integrals with respect to additive measures that are greater than or equal to v we introduce the notion of loose extendability and study its relation to the concave integral a non additive version for the levi theorem and the fatou lemma are proven finally we provide several convergence theorems for capacities with large cores

optimal control of switching diffusions with application to flexible manufacturing systems a controlled switching diffusion model is developed to study the hierarchical control of flexible manufacturing systems the existence of a homogeneous markov nonrandomized optimal policy is established by a convex analytic method using the existence of such a policy the existence of a unique solution in a certain class to the associated hamilton jacobi bellman equations is established and the optimal policy is characterized as a minimizing selector of an appropriate hamiltonian

on the equivalence of the choquet integral and the pan integrals from above abstract a monotone measure is said to have dual m property if for any a b there exists c with a c b such that c a and b c b c by using this concept we study the relationship of the choquet integral and the pan integral from above we prove that the choquet integral coincides with the pan integral from above if has dual m property when the underlying space is finite we prove that the dual m property is also necessary for the coincidence of these two integrals thus we provide a necessary and sufficient condition for the equivalence of the choquet integral and the pan integral from above on a finite space

low complexity prescribed performance control of uncertain mimo feedback linearizable systems a continuous state feedback controller guaranteeing zero overshoot preselected bounds on the minimum admissible convergence rate and maximum allowable steady state values of the output tracking error is proposed for a class of uncertain multi input multi output nonlinear systems contrary to the current state of the art a decisive step towards minimizing controller implementation complexity is taken by designing a static approximation free control scheme defined by simple analytical expressions that scale well even for high relative degree systems simulations on a 2 dof robotic manipulator clarify and verify the approach

on the m property of monotone measures and integrals on atoms abstract we further investigate m property an important structure characteristic of monotone measures some necessary and or sufficient conditions of m property are shown and some characteristics of m property are described it is shown that the restriction of a monotone measure to an atom of its own possesses m property on this atom by means of the m property we characterize the equivalence among the choquet integral the pan integral the concave integral and the shilkret integral on atoms of monotone measures and obtain some special results we also show a necessary and sufficient condition for the concave integral and the pan integral to coincide on atoms of monotone measures

a simplified adaptive neural network prescribed performance controller for uncertain mimo feedback linearizable systems in this paper the problem of deriving a continuous state feedback controller for a class of multiinput multioutput feedback linearizable systems is considered with special emphasis on controller simplification and reduction of the overall design complexity with respect to the current state of the art the proposed scheme achieves prescribed bounds on the transient and steady state performance of the output tracking errors despite the uncertainty in system nonlinearities contrary to the current state of the art however only a single neural network is utilized to approximate a scalar function that partly incorporates the system nonlinearities furthermore the loss of model controllability problem typically introduced owing to approximation model singularities is avoided without attaching additional complexity to the control or adaptive law simulations are performed to verify and clarify the theoretical findings