optimal two level regular fractional factorial block and split plot designs we propose a general and unified approach to the selection of regular fractional factorial designs which can be applied to experiments that are unblocked blocked or have a split plot structure our criterion is derived as a good surrogate for the model robustness criterion of information capacity in the case of random block effects it takes the ratio of intra and interblock variances into account in most of the cases we have examined there exist designs that are optimal for all values of that ratio examples of optimal designs that depend on the ratio are provided we also demonstrate that our criterion can further discriminate designs that cannot be distinguished by the existing minimum aberration criteria

nonlinear stochastic receding horizon control stability robustness and monte carlo methods for control approximation this work considers the stability of nonlinear stochastic receding horizon control when the optimal controller is only computed approximately a number of general classes of controller approximation error are analysed including deterministic and probabilistic errors and even controller sample and hold errors in each case it is shown that the controller approximation errors do not accumulate even over an infinite time frame and the process converges exponentially fast to a small neighbourhood of the origin in addition to this analysis an approximation method for receding horizon optimal control is proposed based on monte carlo simulation this method is derived via the feynman kac formula which gives a stochastic interpretation for the solution of a hamilton jacobi bellman equation associated with the true optimal controller it is shown and it is a prime motivation for this study that this particular controller approximation method practically stabilises the underlying nonlinear process

model predictive control of continuous time nonlinear systems with piecewise constant control a new model predictive control mpc algorithm for nonlinear systems is presented the plant under control the state and control constraints and the performance index to be minimized are described in continuous time while the manipulated variables are allowed to change at fixed and uniformly distributed sampling times in so doing the optimization is performed with respect to sequences as in discrete time nonlinear mpc but the continuous time evolution of the system is considered as in continuous time nonlinear mpc

d optimal split plot designs with given numbers and sizes of whole plots the design of split plot experiments has received considerable attention during the last few years the goal of this article is to provide an efficient algorithm to compute d optimal split plot designs with given numbers of whole plots and given whole plot sizes the algorithm is evaluated and applied to a protein extraction experiment in addition it is shown that two level factorial and fractional factorial designs are d optimal for estimating first order response surface models for specific numbers and sizes of whole plots

on the stability of receding horizon control with a general terminal cost we study the stability and region of attraction properties of a family of receding horizon schemes for nonlinear systems using dini s theorem on the uniform convergence of functions we show that there is always a finite horizon for which the corresponding receding horizon scheme is stabilizing without the use of a terminal cost or terminal constraints after showing that optimal infinite horizon trajectories possess a uniform convergence property we show that exponential stability may also be obtained with a sufficient horizon when an upper bound on the infinite horizon cost is used as terminal cost combining these important cases together with a sandwiching argument we are able to conclude that exponential stability is obtained for input constrained receding horizon schemes with a general nonnegative terminal cost for sufficiently long horizons region of attraction estimates are also included in each of the results

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

discrete time neural inverse optimal control for nonlinear systems via passivation this paper presents a discrete time inverse optimal neural controller which is constituted by combination of two techniques 1 inverse optimal control to avoid solving the hamilton jacobi bellman equation associated with nonlinear system optimal control and 2 on line neural identification using a recurrent neural network trained with an extended kalman filter in order to build a model of the assumed unknown nonlinear system the inverse optimal controller is based on passivity theory the applicability of the proposed approach is illustrated via simulations for an unstable nonlinear system and a planar robot

universality in quantum computation we show that in quantum computation almost every gate that operates on two or more bits is a universal gate we discuss various physical considerations bearing on the proper definition of universality for computational components such as logic gates

brief paper a predictive controller with artificial lyapunov function for linear systems with input state constraints this paper copes with the problem of satisfying input and or state hard constraints in set point tracking problems stability is guaranteed by synthesizing a lyapunov quadratic function for the system and by imposing that the terminal state lies within a level set of the function procedures to maximize the volume of such an ellipsoidal set are provided and interiorpoint methods to solve on line optimization are considered

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

robust stability analysis of nonlinear discrete time systems with application to mpc the regional input to state stability of nonlinear possibly discontinuous discrete time systems is studied under the assumption that the equilibrium of the corresponding nominal model is asymptotically stable the obtained results are used for the synthesis of a nominal model predictive control law ensuring inherent robustness a numerical example is reported that witnesses the effectiveness of the approach

a universal two bit gate for quantum computation we prove the existence of a class of two input two output gates any one of which is universal for quantum computation this is done by explicitly constructing the three bit gate introduced by deutsch proc r soc lond a 425 73 1989 as a network consisting of replicas of a single two bit gate

on robust tracking with non linear model predictive control in this paper a class of stabilizing model predictive control algorithms based on an optimization problem with two different horizons control and prediction is considered particular attention is devoted to the tracking problem for reference signals constant beyond a prescribed future horizon for such a problem it is pointed out the necessity of an output feedback scheme to guarantee robust steady state zero error regulation moreover an additional constraint is introduced in the optimization problem for the robust fulfilment of the constraints on the control variable the potentiality of this approach is shown through some simulation experiments on a highly non linear chemical reactor

stability of a truncated infinite constrained receding horizon scheme the general discrete nonlinear case some results concerning the constrained receding horizon formulation with infinite and truncated prediction horizon are presented in this formulation a distinction is made between prediction and control horizons the main result is a generalization of a known fact for linear systems namely that under certain technical requirements the asymptotic stability of the above formulation holds for a sufficiently large finite prediction horizon existence results are also provided under stabilizability assumptions

fractional resolution and minimum aberration in blocked 2 n k designs systematic sources of variation can be reduced in fractional factorial experiments by grouping the runs into blocks this is accomplished through the use of blocking factors the concepts of resolution and minimum aberration design optimization criteria ordinarily used to rank unblocked fractional factorial designs are extended to such blocked fractional factorial designs by treating the treatment and blocking factors differently in terms of their contribution to word length in the defining contrast subgroup some limited theoretical results are derived and tables of minimumaberration blocked two level fractional factorial designs are presented and considered the relationship between clear effects effects that are estimable when higher order effects are assumed negligible and minimum aberration in the presence of blocking is discussed

fake algebraic riccati techniques and stability conditions sufficient and necessary for monotonic behavior of the solutions of the riccati differential equation and riccati difference equation are derived for the optimal filtering respectively control equation these results are derived without the usual requirement of detectability respectively stabilizability the monotonic behavior allows proof of stabilizing properties of the solutions subject only to requirements on the initial conditions

choice of optimal blocking schemes in two level and three level designs blocking is commonly used in design of experiments to reduce systematic variation and increase precision of effect estimation for 2n k designs in 2p blocks others have studied the confounding pattern between blocking effects and treatment effects and proposed some criteria to choose optimal blocking schemes we propose alternative criteria that allow estimation of more lower order effects extensions to three level fractional factorial design are considered and tables of useful designs are given

changing supply rates for input output to state stable discrete time nonlinear systems with applications we present results on changing supply rates for input output to state stable discrete time nonlinear systems our results can be used to combine two lyapunov functions none of which can be used to verify that the system has a certain property into a new composite lyapunov function from which the property of interest can be concluded the results are stated for parameterized families of discrete time systems that naturally arise when an approximate discrete time model is used to design a controller for a sampled data system we present several applications of our results i a lasalle criterion for input to state stability iss of discrete time systems ii constructing iss lyapunov functions for time varying discrete time cascaded systems iii testing iss of discrete time systems using positive semidefinite lyapunov functions iv observer based input to state stabilization of discrete time systems our results are exploited in a case study of a two link manipulator and some simulation results that illustrate advantages of our approach are presented

robust model predictive control with integral sliding mode in continuous time sampled data nonlinear systems this paper proposes a control strategy for nonlinear constrained continuous time uncertain systems which combines robust model predictive control mpc with sliding mode control smc in particular the so called integral smc approach is used to produce a control action aimed to reduce the difference between the nominal predicted dynamics of the closed loop system and the actual one in this way the mpc strategy can be designed on a system with a reduced uncertainty in order to prove the stability of the overall control scheme some general regional input to state practical stability results for continuous time systems are proved

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

fractional factorial split plot designs for robust parameter experiments for robust parameter designs it has been noted that performing the experiment as a split plot often provides cost savings and increased efficiency thus experiments are often performed using fractional factorial split plot designs we consider how one should best choose such designs for robust parameter experiments and what is meant by maximum resolution and by minimum aberration in this context under various experimental settings

post fractionated strip block designs novel arrangements for strip block designs that reduce the experimental effort are presented theoretical properties of strip block designs using post fractionation are provided and appropriate data analysis is explained an experiment on an industrial process is used as an illustration as a tool to aid the selection of appropriate plans catalogs of post fractionated strip block designs with 16 and 32 trials are provided

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

a general framework to design stabilizing nonlinear model predictive controllers abstract we propose a new model predictive control mpc framework to generate feedback controls for time varying nonlinear systems with input constraints we provide a set of conditions on the design parameters that permits to verify a priori the stabilizing properties of the control strategies considered the supplied sufficient conditions for stability can also be used to analyse the stability of most previous mpc schemes the class of nonlinear systems addressed is significantly enlarged by removing the traditional assumptions on the continuity of the optimal controls and on the stabilizability of the linearized system some important classes of nonlinear systems including some nonholonomic systems can now be stabilized by mpc in addition we can exploit increased flexibility in the choice of design parameters to reduce the constraints of the optimal control problem and thereby reduce the computational effort in the optimization algorithms used to implement mpc

construction of two level split lot fractional factorial designs for multistage processes split lot designs also known as multiway split unit designs are useful in factorial experiments where there are multiple processing stages such experiments occur for example in the fabrication of integrated circuits in the semiconductor industry and in product assembly the designs have a split plot structure at each stage so that settings of the factors are applied to sublots of experimental runs rather than to individual runs this allows experimental runs to be processed at much less expense than if the runs were completely randomized in this article split lot designs are constructed for two three and four processing stages the designs have minimum aberration under the split lot structure and minimize in various senses the confounding of main effects and two factor interactions with the sublots at each stage

improved split plot and multistratum designs many industrial experiments involve some factors whose levels are harder to set than others the best way to deal with these is to plan the experiment carefully as a split plot or more generally a multistratum design several different approaches for constructing split plot type response surface designs have been proposed in the literature since 2001 which has allowed experimenters to make better use of their resources by using more efficient designs than the classical balanced ones one of these approaches the stratum by stratum strategy has been shown to produce designs that are less efficient than locally d optimal designs an improved stratum by stratum algorithm is given which though more computationally intensive than the old one makes better use of the advantages of this approach that is it can be used for any structure and does not depend on prior estimates of the variance components this is shown to be almost as good as the locally optimal designs in terms of their own criteria and more

existence and construction of randomization defining contrast subspaces for regular factorial designs regular factorial designs with randomization restrictions are widely used in practice this paper provides a unified approach to the construction of such designs using randomization defining contrast subspaces for the representation of randomization restrictions we use finite projective geometry to determine the existence of designs with the required structure and develop a systematic approach for their construction an attractive feature is that commonly used factorial designs with randomization restrictions are special cases of this general representation issues related to the use of these designs for particular factorial experiments are also addressed

brief paper on receding horizon feedback control receding horizon feedback control rhfc was originally introduced as an easy method for designing stable state feedback controllers for linear systems here those results are generalized to the control of nonlinear autonomous systems and we develop a performance index which is minimized by the rhfc inverse optimal control problem previous results for linear systems have shown that desirable nonlinear controllers can be developed by making the rhfc horizon distance a function of the state that functional dependence was implicit and difficult to implement on line here we develop similar controllers for which the horizon distance is an easily computed explicit function of the state

examples when nonlinear model predictive control is nonrobust we consider nominal robustness of model predictive control for discrete time nonlinear systems we show by examples that when the optimization problem involves state constraints or terminal constraints coupled with short optimization horizons the asymptotic stability of the closed loop may have absolutely no robustness that is to say it is possible for arbitrarily small disturbances to keep the closed loop strictly inside the interior of the feasibility region of the optimization problem and at the same time far from the desired set point this phenomenon does not occur when using model predictive control for linear systems with convex constraint sets we emphasize that a necessary condition for the absence of nominal robustness in nonlinear model predictive control is that the value function and feedback law are discontinuous at some point s in the interior of the feasibility region

minimum aberration two level fractional factorial split plot designs it is often impractical to perform the experimental runs of a fractional factorial in a completely random order in these cases restrictions on the randomization of the experimental trials are imposed and the design is said to have a split plot structure we rank these fractional factorial split plot designs similarly to fractional factorials using the aberration criterion to find the minimum aberration design we introduce an algorithm that constructs the set of all nonisomorphic two level fractional factorial split plot designs more efficiently than existing methods the algorithm can be easily modified to efficiently produce sets of all nonisomorphic fractional factorial designs fractional factorial designs in which the number of levels is a power of a prime and fractional factorial split plot designs in which the number of levels is a power of a prime

selecting defining contrasts and confounded effects in p n m factorial experiment fractional factorial designs presented in standard tables are not always suitable when some factors are more likely than others to interact if the fraction is small compared to the total number of treatments the selection of defining contrasts to generate a design meeting specified requirements is not straightforward a systematic procedure is given for selecting defining contrasts and confounded effects in p n m factorial designs where p 2 is prime

on the inherent robustness of optimal and suboptimal nonlinear mpc abstract suboptimal model predictive control mpc is a control algorithm that uses suboptimal solutions to optimal control problems to provide control actions quickly in mpc terminal control laws and terminal region constraints are frequently used to ensure recursive feasibility and stability suboptimal mpc was proven to be inherently robust for systems with soft terminal region constraints in pannocchia et al 2011 we extend that work to systems with hard terminal region constraints if these hard constraints are defined as sublevel sets of appropriate terminal cost functions a well chosen initial guess warm start for the optimization algorithm is robustly feasible as a result the system controlled by suboptimal mpc admits an iss lyapunov function and is therefore inherently robust the authors of yu et al 2014 noted that the result in pannocchia et al 2011 applied only to systems with continuous optimal cost functions however discontinuous optimal cost functions may be present in systems with hard terminal region constraints we include a simple example of a continuous dynamical system with a provably discontinuous optimal value function that as a consequence of the main result of this work is inherently robust this example is to our knowledge the first such system reported in the literature

heuristically enhanced feedback control of constrained discrete time linear systems recent advances in computer technology have spurred new interest in the use of feedback controllers based upon on line minimization for the control of constrained linear systems still the use of computers in the feedback loop has been hampered by the fact that the amount of time available for computation in most sampled data systems is not enough to achieve a complete solution using conventional algorithms several ad hoc techniques have been proposed but their applicability is restricted by the lack of supporting theory in this paper we present a theoretical framework to analyze the stability of the closed loop system resulting from the use of on line optimization in the feedback loop using these results we show that a suboptimal algorithm based upon the use of heuristic search techniques yields asymptotically stable systems provided that enough computation power is available to solve at each sampling interval an optimization problem considerably simpler than the original the controller presented in this paper is valuable for situations where the customary approaches of using pontryagin s minimum principle or storing a family of extremal curves are not applicable due to limitations in the computational resources available

model predictive control for want of a local control lyapunov function all is not lost we present stability results for unconstrained discrete time nonlinear systems controlled using finite horizon model predictive control mpc algorithms that do not require the terminal cost to be a local control lyapunov function the two key assumptions we make are that the value function is bounded by a k sub spl infin function of a state measure related to the distance of the state to the target set and that this measure is detectable from the stage cost we show that these assumptions are sufficient to guarantee closed loop asymptotic stability that is semiglobal and practical in the horizon length and robust to small perturbations if the assumptions hold with linear or locally linear k sub spl infin functions then the stability will be global or semiglobal for long enough horizon lengths in the global case we give an explicit formula for a sufficiently long horizon length we relate the upper bound assumption to exponential and asymptotic controllability using terminal and stage costs that are controllable to zero with respect to a state measure we can guarantee the required upper bound but we also require that the state measure be detectable from the stage cost to ensure stability while such costs and state measures may not be easy to construct in general we explore a class of systems called homogeneous systems for which it is straightforward to choose them in fact we show for homogeneous systems that the associated k sub spl infin functions are linear thereby guaranteeing global asymptotic stability we discuss two examples found elsewhere in the mpc literature including the discrete time nonholonomic integrator to demonstrate our methods for these systems we give a new result they can be globally asymptotically stabilized by a finite horizon mpc algorithm that has guaranteed robustness we also show that stable linear systems with control constraints can be globally exponentially stabilized using finite horizon mpc without requiring the terminal cost to be a global control lyapunov function

optimization search effort over the control landscapes for open quantum systems with kraus map evolution a quantum control landscape is defined as the expectation value of a target observable as a function of the control variables in this work control landscapes for open quantum systems governed by kraus map evolution are analyzed kraus maps are used as the controls transforming an initial density matrix i into a final density matrix to maximize the expectation value of the observable the absence of suboptimal local maxima for the relevant control landscapes is numerically illustrated the dependence of the optimization search effort is analyzed in terms of the dimension of the system n the initial state i and the target observable it is found that if the number of nonzero eigenvalues in i remains constant the search effort does not exhibit any significant dependence on n if i has no zero eigenvalues then the computational complexity and the required search effort rise with n the dimension of the top manifold i e the set of kraus operators that maximizes the objective is found to positively correlate with the optimization search efficiency under the assumption of full controllability incoherent control modeled by kraus maps is found to be more efficient in reaching the same value of the objective than coherent control modeled by unitary maps numerical simulations are also performed for control landscapes with linear constraints on the available kraus maps and suboptimal maxima are not revealed for these landscapes

minimum aberration two level split plot designs the treatment design portion of fractionated two level split plot designs is associated with a subset of the 2 n k fractional factorial designs the concept of aberration is then extended to these splitplot designs to compare designs two methods are presented for constructing two level minimumaberration split plot designs along with examples an extensive catalog of such designs is tabulated extensions to prime level designs and relations to inner outer arrays are also presented

designing experiments for causal networks causal networks are directed graphs representing cause effect relationships and are multiple response generalizations of ishikawa s cause effect diagrams emphasizing tolerance design applications this article describes an algorithm for designing suitable experiments when the factors and responses are organized as a causal network the causal network is transformed into a so called causal map which represents all factors and responses as points in a common d dimensional metric space the design approach is algorithmic optimizing the entropy criterion due to wynn this criterion is applied to maximize dispersion among the multiple responses using a distance in space coefficients model a key constraint is for the blocks to be self contained this implies that each block can be analyzed without reference to other blocks this is to be complemented by a unified all block analysis the resulting designs are evaluated for efficiency response dispersion and resolution v column rank particular attention

the design of blocked fractional factorial split plot experiments in industrial screening experiments if some factors are hard to vary and others are easy to vary randomization restrictions may lead to the use of fractional factorial split plot ffsp designs blocked ffsp bffsp designs arise when all runs cannot be performed under homogeneous conditions this article introduces three approaches for blocking ffsp designs a catalog of designs is presented in which bffsp designs are ranked according to the minimum aberration criterion in addition additional optimality criteria are used to assist in the ranking procedure the case study that motivated this research is also discussed in detail

regional input to state stability for nonlinear model predictive control in this note regional input to state stability iss is introduced and studied in order to analyze the domain of attraction of nonlinear constrained systems with disturbances iss is derived by means of a non smooth iss lyapunov function with an upper bound guaranteed only in a sub region of the domain of attraction these results are used to study the iss properties of nonlinear model predictive control mpc algorithms

a numerically robust state space approach to stable predictive control strategies recent work with predictive control strategies has shown that the stable gpc sgpc approach has significant computational and numerical advantages however sgpc is cast in the transfer function framework which limits its application here we develop a means of extending the results to state space models and show that improved numerical conditioning can be obtained for many stable predictive control strategies

unconstrained receding horizon control of nonlinear systems it is well known that unconstrained infinite horizon optimal control may be used to construct a stabilizing controller for a nonlinear system we show that similar stabilization results may be achieved using unconstrained finite horizon optimal control the key idea is to approximate the tail of the infinite horizon cost to go using as terminal cost an appropriate control lyapunov function roughly speaking the terminal control lyapunov function clf should provide an incremental upper bound on the cost in this fashion important stability characteristics may be retained without the use of terminal constraints such as those employed by a number of other researchers the absence of constraints allows a significant speedup in computation furthermore it is shown that in order to guarantee stability it suffices to satisfy an improvement property thereby relaxing the requirement that truly optimal trajectories be found we provide a complete analysis of the stability and region of attraction operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class it is shown that the guaranteed region of operation contains that of the clf controller and may be made as large as desired by increasing the optimization horizon restricted of course to the infinite horizon domain moreover it is easily seen that both clf and infinite horizon optimal control approaches are limiting cases of our receding horizon strategy the key results are illustrated using a familiar example the inverted pendulum where significant improvements in guaranteed region of operation and cost are noted

receding horizon control of nonlinear systems the receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems the method is especially useful for the control of slow nonlinear systems such as chemical batch processes where it is possible to solve sequentially open loop fixed horizon optimal control problems online the method has been shown to yield a stable closed loop system when applied to time invariant or time varying linear systems it is shown that the method also yields a stable closed loop system when applied to nonlinear systems

almost any quantum logic gate is universal it is shown that if one can apply some hamiltonian repeatedly to a few variables at a time one can in general effect any desired unitary time evolution on an arbitrarily large number of variables as a result almost any quantum logic gate with two or more inputs is computationally universal in that copies of the gate can be wired together to effect any desired logic circuit and to perform any desired unitary transformation on a set of quantum variables

stabilizing receding horizon control of nonlinear time varying systems a receding horizon control scheme for nonlinear time varying systems is proposed which is based on a finite horizon optimization problem with a terminal state penalty the penalty is equal to the cost that would be incurred over an infinite horizon by applying a locally stabilizing linear control law to the nonlinear system assuming only stabilizability of the linearized system around the desired equilibrium the new scheme ensures exponential stability of the equilibrium as the length of the optimization horizon goes from zero to infinity the domain of attraction moves from the basin of attraction of the linear controller toward the basin of attraction of the infinite horizon nonlinear controller stability robustness in the face of system perturbations is also established

worst case formulations of model predictive control for systems with bounded parameters two different predictive control formulations are developed based on minimization of the worst case quadratic cost for systems with bounded parameters the two formulations differ on the assumptions made about the future inputs in optimizing the current input one assumes open loop control while the other considers closed loop control their closed loop properties such as asymptotic stability are examined we then focus on a moving average model with an integrator and derive computationally simpler suboptimal algorithms

on optimality of nonlinear model predictive control in this note the optimality property of nonlinear model predictive control mpc is analyzed it is well known that the mpc approximates arbitrarily well the infinite horizon ih controller as the optimization horizon increases hence it makes sense to suppose that the performance of the mpc is a not decreasing function of the optimization horizon this work by means of a counterexample shows that the previous conjecture is fallacious even for simple linear systems

moving horizon control of nonlinear systems with input saturation disturbances and plant uncertainty we present a moving horizon feedback system based on constrained optimal control algorithms for nonlinear plants with input saturation disturbances and plant uncertainty the system is a non conventional sampled data system its sampling periods vary from sampling instant to sampling instant and the control during the sampling time is not constant but determined by the solution of an open loop optimal control problem we show that the proposed moving horizon control system is robustly stable and is capable of attenuating l bounded disturbances

robustness of nonlinear state feedback a survey a survey of robustness of nonlinear state feedback is given for series perturbations there are fairly complete results showing that under mild restrictions an optimal controller can tolerate an infinite increase in gain for gain reductions there are some results for systems linear in the control in particular there is a 50 reduction tolerance if the control penalty is quadratic usually the optimal controller cannot be computed exactly there are some results showing the effects of truncation on the robustness essentially robustness is maintained but in a reduced computable part of the state space

receding horizon control and discontinuous state feedback stabilization this paper addresses three aspects of receding horizon control in discrete time 1 feedback stabilization of general nonlinear systems with receding horizon control 2 the generation of stabili

path integral for quantum operations in this paper we consider a phase space path integral for general time dependent quantum operations not necessarily unitary we obtain the path integral for a completely positive quantum operation satisfied lindblad equation quantum markovian master equation we consider the path integral for quantum operation with a simple infinitesimal generator

a quasi infinite horizon nonlinear model predictive control scheme with guaranteed stability we present in this paper a novel nonlinear model predictive control scheme that guarantees asymptotic closed loop stability the scheme can be applied to both stable and unstable systems with input constraints the objective functional to be minimized consists of an integral square error ise part over a finite time horizon plus a quadratic terminal cost the terminal state penalty matrix of the terminal cost term has to be chosen as the solution of an appropriate lyapunov equation furthermore the setup includes a terminal inequality constraint that forces the states at the end of the finite prediction horizon to lie within a prescribed terminal region if the jacobian linearization of the nonlinear system to be controlled is stabilizable we prove that feasibility of the open loop optimal control problem at time t 0 implies asymptotic stability of the closed loop system the size of the region of attraction is only restricted by the requirement for feasibility of the optimization problem due to the input and terminal inequality constraints and is thus maximal in some sense

inherent robustness properties of quasi infinite horizon nonlinear model predictive control we consider inherent robustness properties of model predictive control mpc for continuous time nonlinear systems with input constraints and terminal constraints we show that mpc with a nominal prediction model and persistent but bounded disturbances has some degree of inherent robustness when the terminal control law and the terminal penalty matrix are chosen as the linear quadratic control law and the related lyapunov matrix respectively we emphasize that the input constraint sets can be any compact set rather than convex sets and our results do not depend on the continuity of the optimal cost function or of the control law in the interior of the feasible region

limit cycle generation for a class of non linear systems with jumps using a low dimensional predictive control in this paper it is shown that using a low dimensional non linear predictive control scheme provably stable limit cycles can be obtained for open loop non linear systems with unstable equilibrium point a particular case where the limit cycle may be reduced to a single point in the state space can be obtained which corresponds to asymptotic stabilization the system may present hybrid nature in the sense that discontinuities jump phenomena on the state evolution may be handled the proposed feedback scheme holds for classical jump free systems as a particular case the proposed strategy is illustrated through two examples a jump free system the ball and beam and a non linear hybrid dynamical system including state jumps the modified impulsive lorenz chaotic system

bayesian analysis of split plot experiments with nonnormal responses for evaluating nonstandard performance criteria nonnormal responses are common in industrial experiments and many experiments contain factors with levels that are difficult or costly to change resulting in a split plot randomization structure for valid statistical inferences it is important to account for the correlation induced by the restricted randomization we demonstrate the usefulness of bayesian methods for the analysis of split plot experiments with nonnormal responses specifically we illustrate the flexibility of bayesian methods when one is interested in various functions of the response distribution such as specific percentiles or exceedance probabilities these summaries beyond examining just the mean and variance are straightforward with the bayesian approach and do not require additional theoretical development the discussion uses a split plot film manufacturing example with gamma responses for illustration

robust model predictive control of stable linear systems a new robust model predictive control mpc algorithm is presented for stable constrained linear plants that is a direct generalization of the nominally stabilizing regulator presented by rawlings and muske model uncertainty is parametrized by a list of possible plants robust stability is achieved through the addition of constraints that prevent the sequence of optimal controller costs from increasing for the true plant asymptotic stability is demonstrated through a lyapunov argument simulation experiments demonstrate the performance of the algorithm for two example processes

representing continuous t norms in quantum computation with mixed states a model of quantum computation is discussed in aharanov et al 1997 proc 13th annual acm symp on theory of computation stoc pp 20 30 and tarasov 2002 j phys a math gen 35 5207 35 in which quantum gates are represented by quantum operations acting on mixed states it allows one to use a quantum computational model in which connectives of a four valued logic can be realized as quantum gates in this model we give a representation of certain functions known as t norms menger 1942 proc natl acad sci usa 37 57 60 that generalize the triangle inequality for the probability distribution valued metrics as a consequence an interpretation of the standard operations associated with the basic fuzzy logic hajek 1998 metamathematics of fuzzy logic trends in logic vol 4 dordrecht kluwer is provided in the frame of quantum computation

controllability of open quantum systems with kraus map dynamics this paper presents a constructive proof of complete kinematic state controllability of finite dimensional open quantum systems whose dynamics are represented by kraus maps for any pair of states pure or mixed on the hilbert space of the system we explicitly show how to construct a kraus map that transforms one state into another moreover we prove by construction the existence of a kraus map that transforms all initial states into a predefined target state such a process may be used for example in quantum information dilution thus in sharp contrast to unitary control kraus map dynamics allows for the design of controls which are robust to variations in the initial state of the system the capabilities of non unitary control for population transfer between pure states illustrated for an example of a two level system by constructing a family of non unitary kraus maps to transform one pure state into another the problem of dynamic state controllability of open quantum systems i e controllability of state to state transformations given a set of available dynamical resources such as coherent controls incoherent interactions with the environment and measurements is also discussed

receding horizon revisited an easy way to robustly stabilize an ltv system stabilization schemes are often based on infinite horizon optimization of a non singular cost functional for such schemes to make sense in a time varying context a fairly good knowledge of the system parameters at all times is a prerequisite that is a major disadvantage in adaptive implementations when applicable the receding horizon approach overcomes this difficulty as though it relies on general qualitative long term properties such as controllability it requires quantitative knowledge only of temporally local parameter values work done on receding horizon stabilization during the 1970 s focused on lq h2 optimization criteria looking for a stabilization method which carries also the robustness properties of infinite horizon h design we consider here local minimization of the l2 induced i o norm h optimization as the design objective both state and observation based feedback scheme are derived and relations to finite and infinite horizon optimization are discussed

constructing general orthogonal fractional factorial split plot designs while the orthogonal design of split plot fractional factorial experiments has received much attention already there are still major voids in the literature first designs with one or more factors acting at more than two levels have not yet been considered second published work on nonregular fractional factorial split plot designs was either based only on plackett burman designs or on small nonregular designs with limited numbers of factors in this article we present a novel approach to designing general orthogonal fractional factorial split plot designs one key feature of our approach is that it can be used to construct two level designs as well as designs involving one or more factors with more than two levels moreover the approach can be used to create two level designs that match or outperform alternative designs in the literature and to create two level designs that cannot be constructed using existing methodology our new approach involves the use of integer linear programming and mixed integer linear programming and for large design problems it combines integer linear programming with variable neighborhood search we demonstrate the usefulness of our approach by constructing two level split plot designs of 16 96 runs an 81 run three level split plot design and a 48 run mixed level split plot design supplementary materials for this article are available online 2015 american statistical association and the american society for quality

algorithmic construction of efficient fractional factorial designs with large run sizes fractional factorial ff designs are widely used in practice and typically are chosen according to the minimum aberration criterion a sequential algorithm is developed for constructing efficient ff designs a construction procedure is proposed that allows a design to be constructed only from its minimum aberration projection in the sequential buildup process to efficiently identify nonisomorphic designs designs are categorized according to moment projection pattern a fast isomorphism checking procedure is developed by matching the factors using their delete one factor projections this algorithm is used to completely enumerate all 128 run designs of resolution 4 all 256 run designs of resolution 4 up to 17 factors all 512 run designs of resolution 5 all 1024 run designs of resolution 6 and all 2048 and 4 096 run designs of resolution 7 a method is proposed for constructing minimum aberration ma designs using only a partial catalog of some good designs three approaches to constructing good de

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

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

brief a receding horizon approach to the nonlinear h control problem the receding horizon rh methodology is extended to the design of a robust controller of h type for nonlinear systems using the nonlinear analogue of the fake h algebraic riccati equation we derive an inverse optimality result for the rh schemes for which increasing the horizon causes a decrease of the optimal cost function this inverse optimality result shows that the input output map of the closed loop system obtained with the rh control law has a bounded l 2 gain robustness properties of the nonlinear h control law in face of dynamic input uncertainty are considered

fulfilling hard constraints in uncertain linear systems by reference managing a method based on conceptual tools of predictive control is described for tackling tracking problems of uncertain linear systems wherein pointwise in time input and or state inequality constraints are present the method consists of adding to a primal compensated system a nonlinear device called predictive reference filter which manipulates the desired reference in order to fulfill the prescribed constraints provided that an admissibility condition on the initial state is satisfied the control scheme is proved to fulfill the constraints as well as stability and set point tracking requirements for all systems whose impulse step responses lie within given uncertainty ranges

robust receding horizon control of constrained nonlinear systems we present a method for the construction of a robust dual mode receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error the controller is dual mode in a neighborhood of the origin the control action is generated by a linear feedback controller designed for the linearized system outside this neighborhood receding horizon control is employed existing receding horizon controllers for nonlinear continuous time systems which are guaranteed to stabilize the nonlinear system to which they are applied require the exact solution at every instant of an optimal control problem with terminal equality constraints these requirements are considerably relaxed in the dual mode receding horizon controller presented in this paper stability is achieved by imposing a terminal inequality rather than an equality constraint only approximate minimization is required a variable time horizon is permitted robustness is achieved by employing conservative state and stability constraint sets thereby permitting a margin of error the resultant dual mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear constrained systems

discrete time stability with perturbations application to model predictive control exponential stability and asymptotic perturbed stability results are derived for nonlinear discrete time systems some related results are available in the literature but proofs for the discrete time case are difficult to find our motivation for obtaining these results was to determine conditions under which discrete time nonlinear model predictive control is stabilizing in the face of perturbations this problem has particular relevance when output rather than state feedback is used a nonlinear state estimator is then required to reconstruct the state and it is necessary to identify the class of reconstruction errors for which the cascaded estimator controller assembly is stabilizing

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

conditions under which suboptimal nonlinear mpc is inherently robust abstract we address the inherent robustness properties of nonlinear systems controlled by suboptimal model predictive control mpc i e when a suboptimal solution of the generally nonconvex optimization problem rather than an element of the optimal solution set is used for the control the suboptimal control law is then a set valued map and consequently the closed loop system is described by a difference inclusion under mild assumptions on the system and cost functions we establish nominal exponential stability of the equilibrium and with a continuity assumption on the feasible input set we prove robust exponential stability with respect to small but otherwise arbitrary additive process disturbances and state measurement estimation errors these results are obtained by showing that the suboptimal cost is a continuous exponential lyapunov function for an appropriately augmented closed loop system written as a difference inclusion and that recursive feasibility is implied by such nominal exponential cost decay these novel robustness properties for suboptimal mpc are inherited also by optimal nonlinear mpc we conclude the paper by showing that in the absence of state constraints we can replace the terminal constraint with an appropriate terminal cost and the robustness properties are established on a set that approaches the nominal feasibility set for small disturbances the somewhat surprising and satisfying conclusion of this study is that suboptimal mpc has the same inherent robustness properties as optimal mpc

robust nonlinear model predictive control with variable block length robust model predictive controllers for discrete time nonlinear systems are proposed in this technical note the algorithms first search for an open loop controller with some block length and then try to improve it in a closed loop fashion by solving minimax problems on line it is proved that the controllers are capable of making a subsequence of the state converge into a target set in the presence of bounded disturbances

brief paper predictive control of hybrid systems input to state stability results for sub optimal solutions this article presents a novel model predictive control mpc scheme that achieves input to state stabilization of constrained discontinuous nonlinear and hybrid systems input to state stability iss is guaranteed when an optimal solution of the mpc optimization problem is attained special attention is paid to the effect that sub optimal solutions have on iss of the closed loop system this issue is of interest as firstly the infimum of mpc optimization problems does not have to be attained and secondly numerical solvers usually provide only sub optimal solutions an explicit relation is established between the deviation of the predictive control law from the optimum and the resulting deterioration of the iss property of the closed loop system by imposing stronger conditions on the sub optimal solutions iss can even be attained in this case

multistratum response surface designs response surface designs are usually described as if the treatments have been completely randomized to the experimental units however in practice there is often a structure to the units implying the need for blocking if in addition some factors are more difficult to vary between units than others a multistratum structure arises naturally we present a general strategy for constructing response surface designs in multistratum unit structures designs are constructed stratum by stratum starting in the highest stratum in each stratum a prespecified treatment set for the factors applied in that stratum is arranged to be nearly orthogonal to the units in the higher strata allowing for all the effects that have to be estimated three examples are given to show the applicability of the method and are also used to check the relationship of the final design to the choice of treatment set finally some practical considerations in randomization are discussed

quantum computer with mixed states and four valued logic in this paper we discuss a model of quantum computer in which a state is an operator of density matrix and gates are general quantum operations not necessarily unitary a mixed state operator of density matrix of n twolevel quantum systems is considered as an element of 4 n dimensional operator hilbert space liouville space it allows us to use a quantum computer model with four valued logic the gates of this model are general superoperators which act on n ququat state ququat is a quantum state in a four dimensional operator hilbert space unitary two valued logic gates and quantum operations for an n qubit open system are considered as four valued logic gates acting on n ququats we discuss properties of quantum four valued logic gates in the paper we study universality for quantum four valued logic gates

on the stabilizing property of siorhc it is shown that the stabilizing property of siorhc stabilizing i o receding horizon control holds for general stabilizable discrete time linear plants irrespective of the condition that the plant has no poles at the origin

stability margins of nonlinear receding horizon control via inverse optimality using the nonlinear analog of the fake riccati equation developed for linear systems we derive an inverse optimality result for several receding horizon control schemes this inverse optimality result unifies stability proofs and shows that receding horizon control possesses the stability margins of optimal control laws

nominally robust model predictive control with state constraints in this paper we present robust stability results for constrained discrete time nonlinear systems using a finite horizon model predictive control mpc algorithm for which we do not require the terminal cost to have any particular properties we introduce a definition that attempts to characterize the robustness properties of the mpc optimization problem we assume the systems under consideration satisfy this definition for which we give sufficient conditions and make two further assumptions these are that the value function is bounded by a kinfin function of a state measure related to the distance from the state to some target set and that this measure is detectable from the stage cost used in the mpc algorithm we show that these assumptions lead to stability that is robust to sufficiently small disturbances while in general the results are semiglobal and practical when the detectability and upper bound assumptions are satisfied with linear kinfin functions the stability and robustness are either semiglobal or global with respect to the feasible set we discuss algorithms employing terminal inequality constraints and also provide a specific example of an algorithm that employs a terminal equality constraint

on the robustness of receding horizon control with terminal constraints robustness properties of nonlinear receding horizon controllers with zero terminal state constraints are investigated with respect to gain and additive perturbations some robustness margins are derived by extending to the receding horizon case the analysis originally proposed by geromel and da cruz for infinite horizon controllers in the linear case it is shown that the zero terminal state receding horizon controller exhibits worse robustness margins compared to standard infinite horizon lq control

new path generation based receding horizon formulation for constrained stabilization of nonlinear systems in this paper a new formulation of constrained stabilizing receding horizon control is proposed this formulation is based on the use of open loop steering path generators the open loop optimization problem associated to the proposed receding horizon formulation is scalar in which the optimization variable is the prediction horizon length stability is proved in a sampling control scheme a simple example is given to illustrate the main concepts

toward infinite horizon optimality in nonlinear model predictive control a new model predictive control scheme with guaranteed stability is presented for constrained discrete time nonlinear systems the open loop optimization problem does not involve explicit terminal constraints and employs a nonstandard terminal cost function the closed loop system is shown to be infinite horizon optimal provided that the terminal cost exactly captures the infinite horizon optimal value in a neighborhood of the origin stability and optimality are proven for a set of initial states which is invariant and approaches the set of all controllable states as the prediction horizon increases