constrained receding horizon predictive control for systems with disturbances a receding horizon predictive control method for systems with input constraints and disturbances is proposed a polyhedral feasible set of states which is invariant with respect to a given state feedback control law is derived in the presence of bounded disturbances the proposed predicted control algorithm deploys a strategy in which the current state is steered into the polyhedral invariant feasible set within a finite number n of feasible control moves despite the presence of disturbances the future control moves over the horizon n are represented as the sum of the state feedback control and a perturbation the perturbation term provides the degrees of freedom with which to enlarge the stabilizable set of initial states the control algorithm is formulated in linear matrix inequalities so that it can be solved using semidefinite programming

brief paper convergence properties of constrained linear system under mpc control law using affine disturbance feedback this paper shows new convergence properties of constrained linear discrete time system with bounded disturbances under model predictive control mpc law the mpc control law is obtained using an affine disturbance feedback parametrization with an additional linear state feedback term this parametrization has the same representative ability as some recent disturbance feedback parametrization but its choice together with an appropriate cost function results in a different closed loop convergence property more exactly the state of the closed loop system converges to a minimal invariant set with probability one deterministic convergence to the same minimal invariant set is also possible if a less intuitive cost function is used numerical experiments are provided that validate the results

robust model predictive control of constrained linear systems with bounded disturbances this paper provides a novel solution to the problem of robust model predictive control of constrained linear discrete time systems in the presence of bounded disturbances the optimal control problem that is solved online includes uniquely the initial state of the model employed in the problem as a decision variable the associated value function is zero in a disturbance invariant set that serves as the origin when bounded disturbances are present and permits a strong stability result namely robust exponential stability of the disturbance invariant set for the controlled system with bounded disturbances to be obtained the resultant online algorithm is a quadratic program of similar complexity to that required in conventional model predictive control

the natural element method in solid mechanics the application of the natural element method nem 1 2 to boundary value problems in two dimensional small displacement elastostatics is presented the discrete model of the domain consists of a set of distinct nodes n and a polygonal description of the boundary in the natural element method the trial and test functions are constructed using natural neighbour interpolants these interpolants are based on the voronoi tessellation of the set of nodes n the interpolants are smooth c 1 everywhere except at the nodes where they are c 0 in one dimension nem is identical to linear nite elements the nem interpolant is strictly linear between adjacent nodes on the boundary of the convex hull which facilitates imposition of essential boundary conditions a methodology to model material discontinuities and non convex bodies cracks using nem is also described a standard displacement based galerkin procedure is used to obtain the discrete system of linear equations application of nem to various problems in solid mechanics which include the patch test gradient problems bimaterial interface and a static crack problem are presented excellent agreement with exact analytical solutions is obtained which exemplies the accuracy and robustness of nem and suggests its potential application in the context of other classes of problems crack growth plates and large deformations to name a few 1998 john wiley sons ltd

distributed bounded error state estimation based on practical robust positive invariance we propose a state estimator for linear discrete time systems composed by coupled subsystems affected by bounded disturbances the architecture is distributed in the sense that each subsystem is equipped with a local state estimator that exploits suitable pieces of information from parent subsystems furthermore each local estimator reconstructs the state of the corresponding subsystem only different from methods based on moving horizon estimation our approach does not require the online solution to optimisation problems our state estimation scheme which is based on the notion of practical robust positive invariance also guarantees satisfaction of constraints on local estimation errors and it can be updated with a limited computational effort when subsystems are added or removed

a reproducing kernel method with nodal interpolation property a general formulation for developing reproducing kernel rk interpolation is presented this is based on the coupling of a primitive function and an enrichment function the primitive function introduces discrete kronecker delta properties while the enrichment function constitutes reproducing conditions a necessary condition for obtaining a rk interpolation function is an orthogonality condition between the vector of enrichment functions and the vector of shifted monomial functions at the discrete points a normalized kernel function with relative small support is employed as the primitive function this approach does not employ a finite element shape function and therefore the interpolation function can be arbitrarily smooth to maintain the convergence properties of the original rk approximation a mixed interpolation is introduced a rigorous error analysis is provided for the proposed method optimal order error estimates are shown for the meshfree interpolation in any sobolev norms optimal order convergence is maintained when the proposed method is employed to solve one dimensional boundary value problems numerical experiments are done demonstrating the theoretical error estimates the performance of the method is illustrated in several sample problems copyright 2003 john wiley sons ltd

robust output feedback model predictive control of constrained linear systems this paper provides a solution to the problem of robust output feedback model predictive control of constrained linear discrete time systems in the presence of bounded state and output disturbances the proposed output feedback controller consists of a simple stable luenberger state estimator and a recently developed robustly stabilizing tube based model predictive controller the state estimation error is bounded by an invariant set the tube based controller ensures that all possible realizations of the state trajectory lie in a simple uncertainty tube the center of which is the solution of a nominal disturbance free system and the cross section of which is also invariant satisfaction of the state and input constraints for the original system is guaranteed by employing tighter constraint sets for the nominal system the complexity of the resultant controller is similar to that required for nominal model predictive control

on input to state stability of min max nonlinear model predictive control in this paper we consider discrete time nonlinear systems that are affected possibly simultaneously by parametric uncertainties and other disturbance inputs the min max model predictive control mpc methodology is employed to obtain a controller that robustly steers the state of the system towards a desired equilibrium the aim is to provide a priori sufficient conditions for robust stability of the resulting closed loop system using the input to state stability iss framework first we show that only input to state practical stability can be ensured in general for closed loop min max mpc systems and we provide explicit bounds on the evolution of the closed loop system state then we derive new conditions for guaranteeing iss of min max mpc closed loop systems using a dual mode approach an example illustrates the presented theory

on generalized horn formulas and k resolution abstract a hierarchy of classes h k of propositional formulas has been introduced by yamasaki and doshita 1983 and gallo and scutella 1988 the classes h k have polynomially solvable satisfiability problem and the basic class is the set of horn formulas we show that the k resolution is complete and sound for h k where k resolution is a restriction of ordinary resolution in that at least one of the parent clauses has at most k literals furthermore we discuss to what extent the class of unsatisfiable formulas in h k and the class of unsatisfiable formulas for which a k resolution refutation exists coincide

reproducing kernel particle methods for large deformation analysis of non linear structures abstract large deformation analysis of non linear elastic and inelastic structures based on reproducing kernel particle methods rkpm is presented the method requires no explicit mesh in computation and therefore avoids mesh distortion difficulties in large deformation analysis the current formulation considers hyperelastic and elasto plastic materials since they represent path independent and path dependent material behaviors respectively in this paper a material kernel function and an rkpm material shape function are introduced for large deformation analysis the support of the rkpm material shape function covers the same set of particles during material deformation and hence no tension instability is encountered in the large deformation computation the essential boundary conditions are introduced by the use of a transformation method the transformation matrix is formed only once at the initial stage if the rkpm material shape functions are employed the appropriate integration procedures for the moment matrix and its derivative are studied from the standpoint of reproducing conditions in transient problems with an explicit time integration method the lumped mass matrices are constructed at nodal coordinate so that masses are lumped at the particles several hyperelasticity and elasto plasticity problems are studied to demonstrate the effectiveness of the method the numerical results indicated that rkpm handles large material distortion more effectively than finite elements due to its smoother shape functions and consequently provides a higher solution accuracy under large deformation unlike the conventional finite element approach the nodal spacing irregularity in rkpm does not lead to irregular mesh shape that significantly deteriorates solution accuracy no volumetric locking is observed when applying non linear rkpm to nearly incompressible hyperelasticity and perfect plasticity problems further model adaptivity in rkpm can be accomplished simply by adding more points in the highly deformed areas without remeshing

local control lyapunov functions for constrained linear discrete time systems the minkowski algebra approach this technical note utilizes minkowski algebra of convex sets to characterize a family of local control lyapunov functions for constrained linear discrete time systems local control lyapunov functions are induced by parametrized contractive invariant sets underlying contractive invariant sets belong to a family of minkowski decomposable convex sets and are in fact parametrized by a basic shape set and linear transformations of system matrices and a set of design matrices corresponding local control lyapunov functions can be detected by solving a single tractable convex optimization problem which in case of polyhedral constraints reduces to a single linear program the a priori complexity estimate of the characterized local control lyapunov function is provided for some practically relevant cases an illustrative example and relevant numerical experience are also reported

brief paper adaptive model predictive control for a class of constrained linear systems based on the comparison model this paper proposes an adaptive model predictive control mpc algorithm for a class of constrained linear systems which estimates system parameters on line and produces the control input satisfying input state constraints for possible parameter estimation errors the key idea is to combine the robust mpc method based on the comparison model with an adaptive parameter estimation method suitable for mpc to this end first a new parameter update method based on the moving horizon estimation is proposed which allows to predict an estimation error bound over the prediction horizon second an adaptive mpc algorithm is developed by combining the on line parameter estimation with an mpc method based on the comparison model suitably modified to cope with the time varying case this method guarantees feasibility and stability of the closed loop system in the presence of state input constraints a numerical example is given to demonstrate its effectiveness

brief constrained receding horizon predictive control for nonlinear systems the paper concerns the receding horizon predictive control of constrained nonlinear systems and presents an algorithm which relies on the online solution of a simple linear program lp use is made of a finite control horizon in conjunction with a terminal inequality constraint and a predicted cost that includes a terminal penalty term the optimization procedure is based on predictions made by linearized incremental models at points of a given seed trajectory and the effects of linearization error are taken into account to give a bound on the predicted tracking error the algorithm is posed in the form of an lp and the proper selection of the terminal penalty term of the predicted cost guarantees the asymptotic stability the results of the paper are illustrated by means of a simple example

robust model predictive control via scenario optimization this paper discusses a novel probabilistic approach for the design of robust model predictive control mpc laws for discrete time linear systems affected by parametric uncertainty and additive disturbances the proposed technique is based on the iterated solution at each step of a finite horizon optimal control problem fhocp that takes into account a suitable number of randomly extracted scenarios of uncertainty and disturbances followed by a specific command selection rule implemented in a receding horizon fashion the scenario fhocp is always convex also when the uncertain parameters and disturbance belong to nonconvex sets and irrespective of how the model uncertainty influences the system s matrices moreover the computational complexity of the proposed approach does not depend on the uncertainty disturbance dimensions and scales quadratically with the control horizon the main result in this work is related to the analysis of the closed loop system under receding horizon implementation of the scenario fhocp and essentially states that the devised control law guarantees constraint satisfaction at each step with some a priori assigned probability p while the system s state reaches the target set either asymptotically or in finite time with probability at least p the proposed method may be a valid alternative when other existing techniques either deterministic or stochastic are not directly usable due to excessive conservatism or to numerical intractability caused by lack of convexity of the robust or chance constrained optimization problem

efficient robust optimization for robust control with constraints this paper proposes an efficient computational technique for the optimal control of linear discrete time systems subject to bounded disturbances with mixed linear constraints on the states and inputs the problem of computing an optimal state feedback control policy given the current state is non convex a recent breakthrough has been the application of robust optimization techniques to reparameterize this problem as a convex program while the reparameterized problem is theoretically tractable the number of variables is quadratic in the number of stages or horizon length n and has no apparent exploitable structure leading to computational time of mathcal o n 6 per iteration of an interior point method we focus on the case when the disturbance set is norm bounded or the linear map of a hypercube and the cost function involves the minimization of a quadratic cost here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem that is the policy optimization problem may be decomposed into a set of coupled finite horizon control problems this decomposition can then be formulated as a highly structured quadratic program solvable by primal dual interior point methods in which each iteration requires mathcal o n 3 time this cubic iteration time can be guaranteed using a riccati based block factorization technique which is standard in discrete time optimal control numerical results are presented using a standard sparse primal dual interior point solver that illustrate the efficiency of this approach

causal state feedback parameterizations in robust model predictive control in this paper we investigate the problem of nonlinearity and non convexity typically associated with linear state feedback parameterizations in the robust model predictive control rmpc for uncertain systems in particular we propose two tractable approaches to compute an rmpc controller consisting of both a causal state feedback gain and a control perturbation component for linear discrete time systems involving bounded disturbances and norm bounded structured model uncertainties along with hard constraints on the input and state both the state feedback gain and the control perturbation are explicitly considered as decision variables in the online optimization while avoiding nonlinearity and non convexity in the formulation the proposed rmpc controller computed through lmi optimizations is responsible for steering the uncertain system state to a terminal invariant set numerical examples from the literature demonstrate the advantages of the proposed scheme

robust constrained predictive control using comparison model this paper proposes a quadratic programming qp approach to robust model predictive control mpc for constrained linear systems having both model uncertainties and bounded disturbances to this end we construct an additional comparison model for worst case analysis based on a robust control lyapunov function rclf for the unconstrained system not necessarily an rclf in the presence of constraints this comparison model enables us to transform the given robust mpc problem into a nominal one without uncertain terms based on a terminal constraint obtained from the comparison model we derive a condition for initial states under which the ultimate boundedness of the closed loop is guaranteed without violating state and control constraints since this terminal condition is described by linear constraints the control optimization can be reduced to a qp problem

element free galerkin approach based on the reproducing kernel particle method for solving 2d fractional tricomi type equation with robin boundary condition the traditional element free galerkin efg approach is constructed on variational weak form that the test and trial functions are shape functions of moving least squares mls approximation in the current paper we propose a new version of the efg method based on the shape functions of reproducing kernel particle method rkpm in other words based on the developed approach in han and meng 2001 the fractional tricomi type equation will be solved using the new technique the fractional derivative has been introduced in the caputos sense and is approximated by a finite difference plan of order o 3 1 2 we use the efg rkpm to discrete the spatial direction we illustrate some numerical results on non rectangular domains the unconditional stability and convergence of the new technique have been proved numerical examples display the theoretical results and the efficiency of the proposed approach also the numerical results are compared with the finite element method fem and efg mls procedure

parameterized tube model predictive control this paper develops a parameterized tube model predictive control mpc synthesis method the most relevant novel feature of our proposal is the online use of a single tractable linear program that optimizes parameterized minkowski decomposable state and control tubes and an associated fully separable nonlinear control policy the induced control policy enjoys a higher degree of nonlinearity than existing tube mpc and robust mpc using disturbance affine control policy our proposal offers greater generality than the state of the art robust mpc methods it is conjectured and also established in three cases that our proposal is equivalent feasibility wise to dynamic programming dp it is also shown that under natural assumptions our method is computationally efficient while it possesses rather strong system theoretic properties

input to state stability of robust receding horizon control with an expected value cost this paper is concerned with the stability of a class of receding horizon control rhc laws for constrained linear discrete time systems subject to bounded state disturbances and convex state and input constraints the paper considers the class of finite horizon feedback control policies parameterized as affine functions of the system state calculation of which can be shown to be tractable via a convex reparameterization when minimizing the expected value of a finite horizon quadratic cost we show that the value function is convex when solving this optimal control problem at each time step and implementing the result in a receding horizon fashion we provide sufficient conditions under which the closed loop system is input to state stable iss

model predictive control using segregated disturbance feedback this paper proposes a new control parametrization under the model predictive control mpc framework for constrained linear discrete time systems with bounded disturbances the proposed parametrization takes the form of a special piecewise affine disturbance feedback in an effort to reduce conservatism it is a generalization of linear disturbance feedback parametrization introduced in the recent literature numerical computations and stability properties of the resulting mpc problem using the proposed parametrization are discussed when the disturbance set and the problem data satisfy mild assumptions the associated finite horizon optimization can be computed efficiently and exactly the advantage of the proposed parametrization over linear disturbance feedback is illustrated via numerical examples

stable generalized predictive control with constraints and bounded disturbances disturbances in the presence of constraints can drive predictive control into infeasibility and instability this problem has attracted little research effort despite its significant practical importance earlier work has given stability conditions but these are restricted to systems with at most one unstable pole and do not lead to suitable algorithms because they apply to infinite horizons only here we modify the constraint limits and derive an algorithm with guaranteed stability and asymptotic tracking available degrees of freedom are given up in order to optimize performance the results of the paper are illustrated by means of numerical examples

brief robust receding horizon predictive control for systems with uncertain dynamics and input saturation a receding horizon predictive control method which assures stability for systems with model uncertainty and input saturation is derived by extending earlier work in two important respects i ellipsoidal invariant sets are replaced by polyhedral invariant sets and ii the constraint that the state lie in an invariant set is invoked n steps ahead the new algorithm allows for a considerable enlargement of the stabilizable set and provides extra degrees of freedom with which to improve performance

brief paper feedback and invariance under uncertainty via set iterates we examine discrete time control systems under non parametric disturbances sets which a given control feedback makes invariant under the disturbance are analyzed via lifting the feedback operation to the space of sets properties of being an attractor of the disturbed dynamics and being a minimal invariant set are derived from the corresponding notions of the set dynamics yielding in turn useful characterizations and error estimates for numerical algorithms which detect the minimal invariant sets concrete numerics for some examples of practical feedback rules are offered

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

optimized robust control invariance for linear discrete time systems theoretical foundations this paper introduces the concept of optimized robust control invariance for discrete time linear time invariant systems subject to additive and bounded state disturbances a novel characterization of two families of robust control invariant sets is given the existence of a constraint admissible member of these families can be checked by solving a single and tractable convex programming problem in the generic linear convex case and a standard linear quadratic program when the constraints are polyhedral or polytopic the solution of the same optimization problem yields the corresponding feedback control law that is in general set valued a procedure for selection of a point valued nonlinear control law is provided

ultimate boundedness control for uncertain discrete time systems via set induced lyapunov functions in this note linear discrete time systems affected by both parameter and input uncertainties are considered the problem of the synthesis of a feedback control assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence is investigated it is shown that the problem has a solution if and only if there exists a certain lyapunov function which does not belong to a preassigned class of functions e g the quadratic ones but it is determined by the target set in which ultimate boundedness is desired one of the advantages of this approach is that we may handle systems with control constraints no matching assumptions are made for systems with linearly constrained uncertainties it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets the resulting compensator may be implemented as a linear variable structure control

receding horizon output feedback control for constrained uncertain systems using periodic invariance in this article we consider a receding horizon output feedback control rhoc method for linear discrete time systems with polytopic model uncertainties and input constraints first we derive a set of estimator gains and then we obtain on the basis of the periodic invariance a series of state feedback gains stabilising the augmented output feedback system with these estimator gains these procedures are formulated as linear matrix inequalities an rhoc strategy is proposed based on these state feedback and state estimator gains in conjunction with their corresponding periodically invariant sets the proposed rhoc strategy enhances the performance in comparison with the case in which static periodic gains are used and increases the size of the stabilisable region by introducing a degree of freedom to steer the augmented state into periodically invariant sets

linear threshold discrete time recurrent neural networks stability and globally attractive sets the stability of linear threshold dynamic neural networks is studied and a series of methods to obtain globally attractive sets is proposed a sufficient condition to judge whether an invariant set is a globally attractive set is also proposed this method requires only the solution to a class of linear matrix inequalities also two direct methods to obtain globally attractive sets are given the stability criteria presented are based on the proposed globally attractive sets some numerical examples are given to illustrate the effectiveness of the obtained results

on functional dependencies in q horn theories this paper studies functional dependencies in q horn theories and discusses their use in knowledge condensation we introduce compact model based representations of q horn theories analyze the structure of functional dependencies in q horn theories and show that every minimal functional dependency in a q horn theory can be expressed either by a single term or by a single clause we also prove that the set of all minimal functional dependencies in is quasi acyclic we then develop polynomial time algorithms for recognizing whether a given functional dependency holds in a q horn theory which is represented either by a q horn cnf or as the q horn envelope of a set of models finally we show that every q horn theory has a unique condensation and can be condensed in polynomial time

convex computation of the maximum controlled invariant set for polynomial control systems we characterize the maximum controlled invariant mci set for discrete as well as continuous time nonlinear dynamical systems as the solution of an infinite dimensional linear programming problem for systems with polynomial dynamics and compact semialgebraic state and control constraints we describe a hierarchy of finite dimensional linear matrix inequality lmi relaxations whose optimal values converge to the volume of the mci set dual to these lmi relaxations are sum of squares sos problems providing a converging sequence of outer approximations to the mci set the approach is simple and readily applicable in the sense that the approximations are the outcome of a single semidefinite program with no additional input apart from the problem description a number of numerical examples illustrate the approach

a linear programming approach to constrained robust predictive control a receding horizon predictive control algorithm for systems with model uncertainty and input constraints is developed the proposed algorithm adopts the receding horizon dual mode i e free control moves and invariant set paradigm the approach is novel in that it provides a convenient way of combining predictions of control moves which are optimal in the sense of worst case performance with large target invariant sets thus the proposed algorithm has a large stabilizable set of states corresponding to a cautious state feedback law while enjoying the good performance of a tightly tuned but robust control law unlike earlier approaches which are based on qp or semidefinite programming here computational complexity is reduced through the use of lp

infinite horizon performance bounds for uncertain constrained systems we present a new method to bound the performance of controllers for uncertain linear systems with mixed state and input constraints and bounded disturbances we take as a performance metric either an expected value or minimax discounted cost over an infinite horizon and provide a method for computing a lower bound on the achievable performance of any causal control policy in either case our lower bound is compared to an upper performance bound provided by restricting the choice of controller to one that is affine in the observed disturbances and we show that the two bounds are closely related in particular the lower bounds have a natural interpretation in terms of affine control policies that are optimal for a problem with a restricted disturbance set we show that our performance bounds can be computed via solution of a finite dimensional convex optimization problem and provide numerical examples to illustrate the efficacy of our method

striped parameterized tube model predictive control a modification of the parameterized tube model predictive control ptmpc strategy for linear systems with additive disturbances is proposed which reduces the dependence of the number of optimization variables on horizon length from quadratic to linear by using a triangular striped prediction structure unlike ptmpc which assumes a fixed linear terminal feedback law for predictions the proposed prediction scheme allows disturbance compensation to extend beyond the initial n step prediction horizon the resulting scheme can potentially outperform ptmpc in terms of the size of the domain of attraction and allows for a longer horizon n for the same computational demand

output feedback receding horizon control of constrained systems this paper considers output feedback control of linear discrete time systems with convex state and input constraints which are subject to bounded state disturbances and output measurement errors we show that the non convex problem of finding a constraint admissible affine output feedback policy over a finite horizon to be used in conjunction with a fixed linear state observer can be converted to an equivalent convex problem when used in the design of a time varying robust receding horizon control law we derive conditions under which the resulting closed loop system is guaranteed to satisfy the system constraints for all time given an initial state estimate and bound on the state estimation error when the state estimation error bound matches the minimal robust positively invariant mrpi set for the system error dynamics we show that this control law is time invariant but its calculation generally requires solution of an infinite dimensional optimization problem finally using an invariant outer

optimization over state feedback policies for robust control with constraints this paper is concerned with the optimal control of linear discrete time systems subject to unknown but bounded state disturbances and mixed polytopic constraints on the state and input it is shown that the class of admissible affine state feedback control policies with knowledge of prior states is equivalent to the class of admissible feedback policies that are affine functions of the past disturbance sequence this implies that a broad class of constrained finite horizon robust and optimal control problems where the optimization is over affine state feedback policies can be solved in a computationally efficient fashion using convex optimization methods this equivalence result is used to design a robust receding horizon control rhc state feedback policy such that the closed loop system is input to state stable iss and the constraints are satisfied for all time and all allowable disturbance sequences the cost to be minimized in the associated finite horizon optimal control problem is quadratic in the disturbance free state and input sequences the value of the receding horizon control law can be calculated at each sample instant using a single tractable and convex quadratic program qp if the disturbance set is polytopic or a tractable second order cone program socp if the disturbance set is given by a 2 norm bound

first order lub approximations characterization and algorithms one of the major approaches to approximation of logical theories is the upper and lower bounds approach introduced by selman and kautz 1991 1996 in this paper we address the problem of lowest upper bound lub approximation in a general setting we characterize lub approximations for arbitrary target languages both propositional and first order and describe algorithms of varying generality and efficiency for all target languages proving their correctness we also examine some aspects of the computational complexity of the algorithms both propositional and first order show that they can be used to characterize properties of whole families of resolution procedures discuss the quality of approximations and relate lub approximations to other approaches existing in the literature which are not typically seen in the approximation framework and which go beyond the knowledge compilation perspective that led to the introduction of lubs

min max feedback model predictive control for constrained linear systems min max feedback formulations of model predictive control are discussed both in the fixed and variable horizon contexts the control schemes the authors discuss introduce in the control optimization the notion that feedback is present in the receding horizon implementation of the control this leads to improved performance compared to standard model predictive control and resolves the feasibility difficulties that arise with the min max techniques that are documented in the literature the stabilizing properties of the methods are discussed as well as some practical implementation details

robust model predictive control using tubes a form of feedback model predictive control mpc that overcomes disadvantages of conventional mpc but which has manageable computational complexity is presented the optimal control problem solved on line yields a tube and an associated piecewise affine control law that maintains the controlled trajectories in the tube despite uncertainty computational complexity is linear rather than exponential in horizon length asymptotic stability of the controlled system is established

robust time optimal control of constrained linear systems a version of dynamic programming which computes level sets of the value function rather than the value function set itself is used to design robust non linear controllers for linear discrete time dynamical systems subject to hard constraints on controls and states the controller stabilizes the system and steers all trajectories emanating in a prescribed set to a control invariant set in minimum time for the robust regulator problem the control invariant terminal set is a neighborhood preferably small of the origin for the robust tracking problem the control invariant terminal set is a neighborhood of the invariant set in which the tracking error is zero two non linear controllers which utilize the level sets of the value function are described the first requires the controller to solve on line a modest linear program whose dimension is approximately the same as that of the control variable the second decomposes each level set into a set of simplices a piecewise linear control law affine in each simplex is then constructed

systems with persistent disturbances predictive control with restricted constraints predictive regulation of linear discrete time systems subject to unknown but bounded disturbances and to state control constraints is addressed an algorithm based on constraint restrictions is presented and its stability properties are analysed

dimension splitting for simplifying diffusion in lattice gas models we introduce a simplified technique for incorporating diffusive phenomena into lattice gas molecular dynamics models in this method spatial interactions take place one dimension at a time with a separate fractional timestep devoted to each dimension and with all dimensions treated identically we show that the model resulting from this technique is equivalent to the macroscopic diffusion equation in the appropriate limit this technique saves computational resources and reduces the complexity of model design programming debugging simulation and analysis for example a reaction diffusion simulation can be designed and tested as a one dimensional system and then directly extended to two or more dimensions we illustrate the use of this approach in constructing a microscopically reversible model of diffusion limited aggregation as well as in a model of growth of biological films

efficient robust predictive control predictive constrained control of time varying and or uncertain linear systems has been effected through the use of ellipsoidal invariant sets kothare et al 1996 linear matrix inequalities lmis have been used to design a state dependent state feedback law that maintains the state vector inside invariant feasible sets for the purposes of prediction however at each time instant the state feedback law is assumed constant in addition due to the large number of lmis involved online computation becomes intractable for anything other than small dimensional systems here we propose an approach that deploys a fixed state feedback law but introduces extra degrees of freedom through the use of perturbations on the fixed state feedback law the problem is so formulated that all demanding computations can be performed offline leaving only a simple optimization problem to be solved online over and above the very significant reduction in computational cost the extra degrees of freedom allow for better performance and wider applicability

parameterized robust control invariant sets for linear systems theoretical advances and computational remarks we characterize a family of parametrized robust control invariant sets for linear discrete time systems subject to additive but bounded state disturbances the existence of a member of the introduced family of parametrized robust control invariant sets can be verified by solving a tractable convex optimization problem in the linear convex case which reduces to the standard linear or convex quadratic programme in the linear polytopic case the developed method can also be utilized to detect and obtain an implicit representation of local control lyapunov functions in the linear convex case from the solution of a single and tractable convex optimization problem the offered method permits for the computation of polytopic robust control invariant sets and local control lyapunov functions of indirectly controlled and limited complexity in the linear polytopic case

invariant approximations of the minimal robust positively invariant set this note provides results on approximating the minimal robust positively invariant mrpi set also known as the 0 reachable set of an asymptotically stable discrete time linear time invariant system it is assumed that the disturbance is bounded persistent and acts additively on the state and that the constraints on the disturbance are polyhedral results are given that allow for the computation of a robust positively invariant outer approximation of the mrpi set conditions are also given that allow one to a priori specify the accuracy of this approximation

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

the satisfiability problem for a class consisting of horn sentences and some non horn sentences in porportional logic in this paper the satisfiability problem for a class of proportional sentences is considered here a sentence is a set of clauses a clause is a set of literals first it is proposed that a class s 0 of propositional sentences which properly includes the class of propositional horn sentences a sentence c 1 c n is in s 0 if there are sets p 1 p n of positive literals such that 1 p 1 p 2 p n 2 p i c i for 1 i n and 3 c i p i is a horn clause for 1 i n then it is proposed that a new inference rule based on the resolution principle by which un satisfiability for s 0 in polynomial time can be decided

homothetic tube model predictive control the robust model predictive control for constrained linear discrete time systems is solved through the development of a homothetic tube model predictive control synthesis method the method employs several novel features including a more general parameterization of the state and control tubes based on homothety and invariance a more flexible form of the terminal constraint set and a relaxation of the controlled dynamics of the sets that define the state and control tubes under natural assumptions the proposed method is computationally efficient and it induces strong system theoretic properties

convex liftings based robust control design this paper presents a new approach for control design of constrained linear systems affected by bounded additive disturbances and polytopic uncertainties this method hinges on so called convex liftings which emulate control lyapunov function by providing a constructive framework for optimization based control implementation it will be shown that this method can guarantee the recursive feasibility and robust stability finally a numerical example will be presented to illustrate this method