symmetric prismatic tensegrity structures part ii symmetry adapted formulations this paper presents analytical formulations for the symmetry adapted equilibrium force density and geometrical stiffness matrices for prismatic tensegrity structures with dihedral symmetries an analytical expression for the infinitesimal mechanisms is also derived

rigidity and energy suppose one holds two sticks in the form of a cross in one hand and places a rubber band in tension around the four ends when it is released it comes to rest in the shape of a convex quadrilateral in a plane it always returns to the same shape no matter how it is distorted as long as the ends do not slip and the rubber band does not break this is a very simple example of a rigid framework of the type we discuss here energy explains why a framework such as the one above is rigid the rubber band deforms in such a way as to minimize the total energy in the framework only in the final deformed shape will the framework have a minimum energy this idea of introducing energy functions is very useful it can be used to prove a key lemma that was used by cauchy 5 in 1813 to show that convex polyhedral surfaces are rigid it can explain why some and perhaps all of r buckminster fuller s tensegrity structures 10 stay up when applied to spider webs it shows why they can only take on certain geometric shapes it also can be used to prove conjecture 6 of branko gri inbaum and g c shephard in their lectures on lost mathematics 12 this conjecture says that if a framework in the shape of a convex polygon with rods sticks on the boundary and cables inside is rigid in the plane so is the framework obtained by reversing the roles of rods and cables it is interesting to compare some of these results with the opening a rm theorem of axel schur 18 see chern 6 also which is a very close smooth analogue to cauchy s lemma schur s theorem says that if a convex planar smooth arc the arm is opened that is it is moved to another position with the same length but with corresponding points having smaller curvature then the two ends are moved apart another amusing application is to show that a regular pentagon in 4 space a pentagon with all 5 sides equal and all 5 angles between the sides equal has its angles bounded between 36 and 108 a comment of o bottema in 4

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

constrained linear quadratic regulation the paper is a contribution to the theory of the infinite horizon linear quadratic regulator lqr problem subject to inequality constraints on the inputs and states extending an approach first proposed by sznaier and damborg 1987 a solution algorithm is presented which requires solving a finite number of finite dimensional positive definite quadratic programs the constrained lqr outlined does not feature the undesirable mismatch between open loop and closed loop nominal system trajectories which is present in the other popular forms of model predictive control mpc that can be implemented with a finite quadratic programming algorithm the constrained lqr is shown to be both optimal and stabilizing the solution algorithm is guaranteed to terminate in finite time with a computational cost that has a reasonable upper bound compared to the minimal cost for computing the optimal solution inherent to the approach is the removal of a tuning parameter the control horizon which is present in other mpc approaches and for which no reliable tuning guidelines are available two examples are presented that compare constrained lqr and two other popular forms of mpc the examples demonstrate that constrained lqr achieves significantly better performance than the other forms of mpc on some plants and the computational cost is not prohibitive for online implementation

implementation of dynamic programming for chaos control in discrete systems in this paper the control of discrete chaotic systems by designing linear feedback controllers is presented the linear feedback control problem for nonlinear systems has been formulated under the viewpoint of dynamic programming for suppressing chaos with minimum control effort the system is stabilized on its first order unstable fixed point ufp the presented method also could be employed to make any desired nth order fixed point of the system stable two different methods for higher order ufps stabilization are suggested afterwards these methods are applied to two well known chaotic discrete systems the logistic and the henon maps for each of them the first and second ufps in their chaotic regions are stabilized and simulation results are provided for the demonstration of performance

positive semidefinite matrix completion universal rigidity and the strong arnold property this paper addresses the following three topics positive semidenite psd matrix completions universal rigidity of frameworks and the strong arnold property sap we show some strong connections among these topics using semidenite programming as unifying theme our main contribution is a sufcient condition for constructing partial psd matrices which admit a unique completion to a full psd matrix such partial matrices are an essential tool in the study of the gram dimension gd g of a graph g a recently studied graph parameter related to the low psd matrix completion problem additionally we derive an elementary proof of connelly s sucient condition for universal rigidity of tensegrity frameworks and we investigate the links between these two sucient conditions we also give a geometric characterization of psd matrices satisfying the strong arnold property in terms of nondegeneracy of an associated semidenite program which we use to establish some links between the gram dimension gd and the colin de verdi ere type graph parameter

nonlinear control of constrained linear systems via predictive reference management a method based on conceptual tools of predictive control is described for solving set point tracking problems wherein pointwise in time input and or state inequality constraints are present it consists of adding to a primal compensated system a nonlinear device called command governor cg whose action is based on the current state set point and prescribed constraints the cg selects at any time a virtual sequence among a family of linearly parameterized command sequences by solving a convex constrained quadratic optimization problem and feeds the primal system according to a receding horizon control philosophy the overall system is proved to fulfill the constraints be asymptotically stable and exhibit an offset free tracking behavior provided that an admissibility condition on the initial state is satisfied though the cg can be tailored for the application at hand by appropriately choosing the available design knobs the required online computational load for the usual case of affine constraints is well tempered by the related relatively simple convex quadratic programming problem

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

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

calculating the free energy of nearly jammed hard particle packings using molecular dynamics we present a new event driven molecular dynamics md algorithm for measuring the free energy of nearly jammed packings of spherical and non spherical hard particles this bounding cell molecular dynamics bcmd algorithm exactly calculates the free energy of a single occupancy cell soc model in which each particle is restricted to a neighborhood of its initial position using a hard wall bounding cell our md algorithm generalizes previous ones in the literature by enabling us to study non spherical particles as well as to measure the free energy change during continuous irreversible transformations moreover we make connections to the well studied problem of computing the volume of convex bodies in high dimensions using random walks we test and verify the numerical accuracy of the method by comparing against rigorous asymptotic results for the free energy of jammed and isostatic disordered packings of both hard spheres and ellipsoids for which the free energy can be calculated directly as the volume of a high dimensional simplex we also compare our results to previously published monte carlo results for hard sphere crystals near melting and jamming and find excellent agreement we have successfully used the bcmd algorithm to determine the configurational and free volume contributions to the free energy of glassy states of binary hard disks a donev f h stillinger s torquato do binary hard disks exhibit an ideal glass transition phys rev lett 96 22 2006 225502 the algorithm can also be used to determine phases with locally or globally minimal free energy to calculate the free energy cost of point and extended crystal defects or to calculate the elastic moduli of glassy or crystalline solids among other potential applications

global registration of multiple point clouds using semidefinite programming consider n points in r d and m local coordinate systems that are related through unknown rigid transforms for each point we are given possibly noisy measurements of its local coordinates in some of the coordinate systems alternatively for each coordinate system we observe the coordinates of a subset of the points the problem of estimating the global coordinates of the n points up to a rigid transform from such measurements comes up in distributed approaches to molecular conformation and sensor network localization and also in computer vision and graphics the least squares formulation of this problem although nonconvex has a well known closed form solution when m 2 based on the singular value decomposition svd however no closed form solution is known for m geq 3 in this paper we demonstrate how the least squares formulation can be relaxed into a convex program namely a semidefinite program sdp by setting up connections between the uniqueness of this sdp and results fr

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

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

percolation of the loss of tension in an infinite triangular lattice we introduce a new class of bootstrap percolation models where the local rules are of a geometric nature as opposed to simple counts of standard bootstrap percolation our geometric bootstrap percolation comes from rigidity theory and convex geometry we outline two percolation models a poisson model and a lattice model our poisson model describes how defects holes is one of the possible interpretations of these defects imposed on a tensed membrane result in a redistribution or loss of tension in this membrane the lattice model is motivated by applications of hooke spring networks to problems in material sciences an analysis of the poisson model is given by menshikov et al 4 in the discrete set up we consider regular and generic triangular lattices on the plane where each bond is removed with probability 1 p the problem of the existence of tension on such lattice is solved by reducing it to a bootstrap percolation model where the set of local rules follows from the geometry of stresses we show that both regular and perturbed lattices cannot support tension for any p 1 moreover the complete relaxation of tension as defined in section 4 occurs in a finite time almost surely furthermore we underline striking similarities in the properties of the poisson and lattice models

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

moving horizon control of linear systems with input saturation and plant uncertainty part 2 disturbance rejection and tracking 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 in part 1 we showed that the proposed moving horizon control system is robustly stable in this paper we show that it is capable of asymptotically suppressing a class of l bounded disturbances that are restricted to a subspace and of asymptotically following a class of reference inputs that are continuously differentiable bounded in magnitude and slope and restricted to a subspace

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

reshaping of tensegrities using a geometrical variation approach abstract we propose a novel approach for the reshaping of tensegrities and pre stressed pin jointed frameworks both free standing and restrained frameworks are studied first a geometrical variation is introduced and considered as an initial geometrical change to a self equilibrated tensegrity a new nonlinear set of equilibrium equations is then established based on this variation and subsequently linearized using an expansion the linearization provides us with an underdetermined system of linear equations with a rectangular jacobian matrix which is derived in a very simple and compact matrix form the system is finally solved iteratively using a newton raphson method employing a moore penrose pseudo inverse operation to establish a new equilibrium state the method promises to generate very accurate results with a remarkable convergence rate the outstanding features and performance of the proposed method are demonstrated and studied comprehensively through three examples

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

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

a new approach to the analytical and numerical form finding of tensegrity structures we develop a new formulation for the form finding of tensegrity structures in which the primary variables are the cartesian components of element lengths both an analytical and a numerical implementation of the formulation are described each require a description of the connectivity of the tensegrity with the iterative numerical method also requiring a random starting vector of member force densities the analytical and numerical form finding of tensegrity structures is demonstrated through six examples and the results obtained are compared and contrasted with those available in the literature to verify the accuracy and viability of the suggested methods

advanced form finding for cable strut structures a numerical method is presented for form finding of cable strut structures the topology and the types of members are the only information that is required in this form finding process dummy members are used to transform the cable strut structure with supports into self stressed system without supports the requirement on rank deficiencies of the force density and equilibrium matrices for the purpose of obtaining a non degenerate d dimensional self stressed structure has been explicitly discussed the spectral decomposition of the force density matrix and the singular value decomposition of the equilibrium matrix are performed iteratively to find the feasible sets of nodal coordinates and force densities which satisfy the minimum required rank deficiencies of the force density and equilibrium matrices respectively based on numerical examples it is found that the proposed method is very efficient robust and versatile in searching self equilibrium configurations of cable strut structures

polytopic approximation of explicit model predictive controllers a model predictive control law mpc is given by the solution to a parametric optimization problem that can be precomputed offline which provides an explicit map from state to input that can be rapidly evaluated online however the primary limitations of these optimal explicit solutions are that they are applicable to only a restricted set of systems and that the complexity can grow quickly with problem size in this paper we compute approximate explicit control laws that trade off complexity against approximation error for mpc controllers that give rise to convex parametric optimization problems the algorithm is based on the classic double description method and returns a polyhedral approximation to the optimal cost function the proposed method has three main advantages from a control point of view it is an incremental approach meaning that an approximation of any specified complexity can be produced it operates on implicitly defined convex sets meaning that the prohibitively complex optimal explicit solution is not required and finally it can be applied to any convex parametric optimization problem a sub optimal controller based on barycentric interpolation is then generated from this approximate polyhedral cost function that is feasible and stabilizing the resulting control law is continuous although non linear and defined over a non simplical polytopic partition of the state space the non simplical nature of the partition generates significantly simpler approximate control laws which is demonstrated on several examples

advances in the theory and practice of graph drawing the visualization of conceptual structures is a key component of support tools for complex applications in science and engineering foremost among the visual representations used are drawings of graphs and ordered sets in this talk we survey recent advances in the theory and practice of graph drawing specific topics include bounds and tradeoffs for drawing properties three dimensional representations methods for constraint satisfaction and experimental studies

on constrained infinite time linear quadratic optimal control abstract this work presents a solution to the infinite time linear quadratic optimal control itlqoc problem with state and control constraints it is shown that a single finite dimensional convex program of known size can yield this solution properties of the resulting value function with respect to initial conditions are also established and are shoen to be useful in determining the aforementioned problem size an example illustrating the method is finally presented

formulation of closed loop min max mpc as a quadratically constrained quadratic program in this note we show that min max model predictive control mpc for linearly constrained polytopic systems with quadratic cost can be cast as a quadratically constrained quadratic program qcqp we use the rigorous closed loop formulation of min max mpc and show that any such min max mpc problem with convex costs and constraints can be cast as a finite dimensional convex optimization problem with the qcqp arising from quadratic costs as a special case at the base of the proof is a lemma showing the convexity of the dynamic programming cost to go which implies that the worst case on an infinite polytopic set is assumed on one of its finitely many vertices as the approach is based on a scenario tree formulation the number of variables in this problem grows exponentially with the horizon length fortunately the qcqp is tree structured and can thus be efficiently solved by specially tailored interior point methods whose computational costs are linear in the number of variables the new formulation as a tree sparse qcqp promises to facilitate online solution of the rigorous min max mpc problem with quadratic costs

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

contractive model predictive control for constrained nonlinear systems this paper addresses the development of stabilizing state and output feedback model predictive control mpc algorithms for constrained continuous time nonlinear systems with discrete observations moreover we propose a nonlinear observer structure for this class of systems and derive sufficient conditions under which this observer provides asymptotically convergent estimates the mpc scheme proposed consists of a basic finite horizon nonlinear mpc technique with the introduction of an additional state constraint which has been called a contractive constraint the resulting mpc scheme has been denoted contractive mpc this is a lyapunov based approach in which a lyapunov function chosen a priori is decreased not continuously but discretely it is allowed to increase at other times we show in this work that the implementation of this additional constraint into the online optimization makes it possible to prove strong nominal stability properties of the closed loop system

robust dynamic programming for min max model predictive control of constrained uncertain systems we address min max model predictive control mpc for uncertain discrete time systems by a robust dynamic programming approach and develop an algorithm that is suitable for linearly constrained polytopic systems with piecewise affine cost functions the method uses polyhedral representations of the cost to go functions and feasible sets and performs multiparametric programming by a duality based approach in each recursion step we show how to apply the method to robust mpc and give conditions guaranteeing closed loop stability finally we apply the method to a tutorial example a parking car with uncertain mass

path planning for active tensegrity structures abstract this paper presents a path planning method for actuated tensegrity structures with quasi static motion the valid configurations for such structures lay on an equilibrium manifold which is implicitly defined by a set of kinematic and static constraints the exploration of this manifold is difficult with standard methods due to the lack of a global parameterization thus this paper proposes the use of techniques with roots in differential geometry to define an atlas i e a set of coordinated local parameterizations of the equilibrium manifold this atlas is exploited to define a rapidly exploring random tree which efficiently finds valid paths between configurations however these paths are typically long and jerky and therefore this paper also introduces a procedure to reduce their control effort a variety of test cases are presented to empirically evaluate the proposed method

moufang polygons and irreducible spherical bn pairs of rank 2 i let g be a group with an irreducible spherical bn pair of rank 2 satisfying the additional condition there exists a normal nilpotent subgroup u of b with b tu where t b n and jw ja16 forthe weyl gr oup w n b n we show that g corresponds to a moufang polygon and hence is essentially known r 2003 elsevier science usa all rights reserved

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

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

computation approximation and stability of explicit feedback min max nonlinear model predictive control this paper presents an approximate multi parametric nonlinear programming mp nlp approach to explicit solution of feedback min max nmpc problems for constrained nonlinear systems in the presence of bounded disturbances and or parameter uncertainties it is based on an orthogonal search tree structure of the state space partition and consists in constructing a piecewise nonlinear pwnl approximation to the optimal sequence of feedback control policies conditions guaranteeing the robust stability of the closed loop system in terms of a finite l 2 gain are derived

approximate robust dynamic programming and robustly stable mpc we present a technique for approximate robust dynamic programming that is suitable for linearly constrained polytopic systems with piecewise affine cost functions the approximation method uses polyhedral representations of the cost to go function and feasible set and can considerably reduce the computational burden compared to recently proposed methods for exact robust dynamic programming bemporad a borrelli f morari m 2003 min max control of constrained uncertain discrete time linear systems ieee transactions on automatic control 48 9 1600 1606 diehl m bjornberg j 2004 robust dynamic programming for min max model predictive control of constrained uncertain systems ieee transactions on automatic control 49 12 2253 2257 we show how to apply the method to robust mpc and give conditions that guarantee closed loop stability we finish by applying the method to a state constrained tutorial example a parking car with uncertain mass

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

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

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

a fast ellipsoidal mpc scheme for discrete time polytopic linear parameter varying systems this paper proposes a fast ellipsoidal model predictive control mpc strategy to address feedback regulation problems for constrained polytopic linear parameter varying lpv systems subject to bounded disturbances in order to deal with the specific non convex structure of the state prediction tubes arising in lpv contexts a new convexification procedure is proposed and based on the off line computation of a sequence of inner ellipsoidal approximations of exact one step controllable sets a computationally low demanding mpc algorithm is presented comparisons with state of the art mpc control algorithms for lpv systems are reported in a final numerical example where several methods are contrasted in terms of achievable domains of attraction control performance numerical burdens and memory requirements

equilibrium conditions of a tensegrity structure this paper characterizes the necessary and sufficient conditions for tensegrity equilibria static models of tensegrity structures are reduced to linear algebra problems after first characterizing the problem in a vector space where direction cosines are not needed this is possible by describing the components of all member vectors while our approach enlarges by a factor of 3 the vector space required to describe the problem the advantage of enlarging the vector space makes the mathematical structure of the problem amenable to linear algebra treatment using the linear algebraic techniques many variables are eliminated from the final existence equations

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

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

on affine motions and universal rigidity of tensegrity frameworks abstract recently alfakih and ye 2013 4 proved that if an r dimensional bar framework g p on n r 2 nodes in general position in r r admits a positive semidefinite stress matrix with rank n r 1 then g p is universally rigid in this paper we generalize this result in two directions first we extend this result to tensegrity frameworks second we replace the general position assumption by the weaker assumption that in configuration p each point and its neighbors in g affinely span r r

stability conditions for tensegrity structures stability conditions for tensegrity structures are derived based on positive definiteness of the tangent stiffness matrix which is the sum of the linear and geometrical stiffness matrices a necessary stability condition is presented by considering the affine motions that lie in the null space of the geometrical stiffness matrix the condition is demonstrated to be equivalent to that derived from the mathematical rigidity theory so as to resolve the discrepancy between the stability theories in the fields of engineering and mathematics furthermore it is shown that the structure is guaranteed to be stable if the structure satisfies the necessary stability condition and the geometrical stiffness matrix is positive semidefinite with the minimum rank deficiency for non degeneracy

moving horizon observers and observer based control in this paper two topics are explored a new approach to the problem of obtaining an estimate of the state of a nonlinear system is proposed the moving horizon observer produces an estimate of the state of the nonlinear system at time t either by minimizing or approximately minimizing a cost function over the preceding interval horizon t t t as t advances so does the horizon convergence of the estimator is established under the assumption that the corresponding global optimization problem can be approximately solved and a uniform reconstructability condition is satisfied the latter condition is automatically satisfied for linear observable systems the utility of the estimator for receding horizon control is explored in particular stability of a composite moving horizon system comprising a moving horizon regulator and a moving horizon observer is established

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

stability of model predictive control with mixed constraints we derive stability conditions for model predictive control mpc with hard constraints on the inputs and soft constraints on the outputs for an infinitely long output horizon we show that with state feedback mpc is globally asymptotically stabilizing if and only if all the eigenvalues of the open loop system are in the closed unit disk with output feedback we show that the results hold if all the eigenvalues are strictly inside the unit circle the online optimization problem defining mpc can be posed as a finite dimensional quadratic program even though the output constraints are specified over an infinite horizon

on the dual rigidity matrix abstract a novel characterization of bar and joint framework rigidity was introduced in a y alfakih graph rigidity via euclidean distance matrices linear algebra appl 310 2000 149 165 a y alfakih on rigidity and realizability of weighted graphs linear algebra appl 325 2001 57 70 this characterization uses the notion of normal cones of convex sets to define a matrix r whose rank determines whether or not a given generic framework is rigid furthermore this characterization was derived under the assumption that the framework of interest g p has an equivalent framework g q in r n 1 where n is the number of vertices of g p in this paper we show that the matrix r corresponding to a framework g p contains the same information as the well known rigidity matrix r whereas the entries of r are a function of the positions of the vertices of g p the entries of r are a function of the gale matrix corresponding to g p furthermore while the number of rows of r is equal to the number of edges of g p the number of columns of r is equal to the number of missing edges of g p we also show that the assumption of the existence of an equivalent framework g q in r n 1 can be dropped and we give the precise relation between the left nullspaces and consequently the nullspaces of r and r

min max control of constrained uncertain discrete time linear systems for discrete time uncertain linear systems with constraints on inputs and states we develop an approach to determine state feedback controllers based on a min max control formulation robustness is achieved against additive norm bounded input disturbances and or polyhedral parametric uncertainties in the state space matrices we show that the finite horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs when the optimal control law is implemented in a receding horizon scheme only a piecewise affine function needs to be evaluated on line at each time step the technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state space

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

new simple groups with a bn pair abstract we show that there are simple groups with a spherical bn pair of rank 2 which are non moufang and hence not of algebraic origin

on affine motions and bar frameworks in general position abstract a configuration p in r dimensional euclidean space is a finite collection of points p 1 p n that affinely span r r a bar framework denoted by g p in r r is a simple graph g on n vertices together with a configuration p in r r a given bar framework g p is said to be universally rigid if there does not exist another configuration q in any euclidean space not obtained from p by a rigid motion such that q i q j p i p j for each edge i j of g it is known 2 7 that if configuration p is generic and bar framework g p in r r admits a positive semidefinite stress matrix s of rank n r 1 then g p is universally rigid connelly asked 9 whether the same result holds true if the genericity assumption of p is replaced by the weaker assumption of general position we answer this question in the affirmative in this paper

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

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

form finding of tensegrity structures via genetic algorithm abstract we propose an efficient method for the form finding of tensegrity structures the force densities of each tensegrity are obtained by the minimisation of a particular objective function leading to a semi positive definite force density matrix a super stable tensegrity with a required rank deficiency a genetic algorithm is used as a global search technique for the minimisation the geometry of a tensegrity is subsequently formed based on those eigenvectors of the force density matrix corresponding to zero eigenvalues furthermore two other methods are introduced to convert the asymmetrical geometry obtained from the main algorithm into its symmetrical counterparts this transformation in geometry is performed by finding a suitable linear combination of the mentioned eigenvectors examples from well known tensegrities including prismatic truncated tetrahedron expandable octahedron and truncated icosahedron tensegrities are studied using the present method and the results obtained are compared with those documented in the literature to verify the efficiency of the present method

every continuous nonlinear control system can be obtained by parametric convex programming in this short note we define parametric convex programming pcp in a slightly different manner than it is usually done by extending convexity not only to variables but also to the parameters and we show that the widely applied model predictive control mpc technique is a particular case of pcp the main result of the note is an answer to the inverse question of pcp which feedback laws can be generated by pcp by employing results of convex analysis we provide a constructive proof yet not computational that allows us to conclude that every continuous feedback law can be obtained by pcp

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

effective insights into the geometric stability of symmetric skeletal structures under symmetric variations abstract geometric stability is a necessary criterion to guarantee stable equilibrium in engineering structures however we generally encounter enormous calculations to examine the geometric stability when we make variations on the geometry or the connectivity of a given kinematically and statically indeterminate structure this study describes how symmetry is utilized to enhance the mobility and geometric stability analysis of symmetric skeletal structures symmetry extended mobility distinguishes representations of the internal mechanisms and self stress states from relative mobility based on their inherent symmetries using group theoretic method thus it acts as an efficient tool to evaluate the order of internal mechanisms that may be indistinguishable by traditional structural approaches further it is used to gain effective insights into the mobility and geometric stability of a symmetric skeletal structure with symmetrically perturbed connectivity or geometry the first order changes of symmetry extended mobility are deduced to describe the changes induced by the variations of nodal coordinates members and kinematic constraints respectively examples are given to verify the correctness and effectiveness of the proposed method we show that the geometry or connectivity of kinematically indeterminate symmetric skeletal structures can be altered while at the same time retaining geometric stability and some or all of the original symmetry the results have potential application in the design of novel deployable structures

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

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

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

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

suboptimal model predictive control feasibility implies stability practical difficulties involved in implementing stabilizing model predictive control laws for nonlinear systems are well known stabilizing formulations of the method normally rely on the assumption that global and exact solutions of nonconvex nonlinear optimization problems are possible in limited computational time in the paper we first establish conditions under which suboptimal model predictive control mpc controllers are stabilizing the conditions are mild holding out the hope that many existing controllers remain stabilizing even if optimality is lost second we present and analyze two suboptimal mpc schemes that are guaranteed to be stabilizing provided an initial feasible solution is available and for which the computational requirements are more reasonable

dihedral star tensegrity structures this paper presents conditions for self equilibrium and super stability of dihedral star tensegrity structures based on their dihedral symmetry it is demonstrated that the structures are super stable if and only if they have an odd number of struts and the struts are as close as possible to each other numerical investigations show that their prestress stability is sensitive to the geometry realisation

an ellipsoidal off line mpc scheme for uncertain polytopic discrete time systems an off line model predictive control mpc method based on ellipsoidal calculus and viability theory is described in order to address control problems in the presence of state and input constraints for uncertain polytopic linear plants subject to persistent disturbances in order to reduce the computational burdens and conservativeness of traditional polytopic mpc schemes the present approach carries out off line most of the computations and it makes use of closed loop predictions to improve the control performance this is done by recursively pre computing suitable ellipsoidal inner approximations of the exact controllable sets and solving on line a simple and numerically low demanding optimization problem subject to a set membership constraint comparisons with three other recent off line mpc approaches are also provided in the final example

a nonlinear sum of squares model predictive control approach this note presents a novel model predictive control mpc strategy for input saturated nonlinear systems having a polynomial structure the results here proposed are a significant generalization w r t similar existing algorithms which are tailored only for linearized or multi model plant descriptions a first key aim is to present sum of squares sos conditions under which off line one step controllable sets for nonlinear polynomial systems can be derived a second relevant contribution is to describe an on line mpc strategy that leads to less conservative performance w r t most existing methods based on global linearization approaches an illustrative example is finally provided in order to show the effectiveness of the proposed sos based mpc algorithm

pair correlation function characteristics of nearly jammed disordered and ordered hard sphere packings we study the approach to jamming in hard sphere packings and in particular the pair correlation function g2srd around contact both theoretically and computationally our computational data unambiguously separate the narrowing d function contribution to g2 due to emerging interparticle contacts from the background contribution due to near contacts the data also show with unprecedented accuracy that disordered hard sphere packings are strictly isostatic i e the number of exact contacts in the jamming limit is exactly equal to the number of degrees of freedom once rattlers are removed for such isostatic packings we derive a theoretical connection between the probability distribution of interparticle forces pfsfd which we measure computationally and the contact contribution to g2 we verify this relation for computationally generated isostatic packings that are representative of the maximally random jammed state we clearly observe a maximum in pf and a nonzero probability of zero force shedding light on long standing questions in the granular media literature we computationally observe an unusual power law divergence in the near contact contribution to g2 persistent even in the jamming limit with exponent 0 4 clearly distinguishable from previously proposed inversesquare root divergence additionally we present high quality numerical data on the two discontinuities in the split second peak of g2 and use a shared neighbor analysis of the graph representing the contact network to study the local particle clusters responsible for the peculiar features finally we present the computational data on the contact contribution to g2 for vacancy diluted fcc crystal packings and also investigate partially crystallized packings along the transition from maximally disordered to fully ordered packings we find that the contact network remains isostatic even when ordering is present unlike previous studies we find that ordering has a significant impact on the shape of pf for small forces

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

split bn pairs of rank 2 the octagons abstract let g be a group with an irreducible spherical bn pair of rank 2 where b contains a normal nilpotent subgroup u with b u b n then g is essentially a group of lie type this completes the classification of split bn pairs of rank 2 generalizing the corresponding result for finite groups due to fong and seitz

the explicit constrained min max model predictive control of a discrete time linear system with uncertain disturbances in this technical brief we develop an algorithm to determine the explicit solution of the constrained min max model predictive control problem for a discrete time linear system with bounded additive uncertain disturbance the control law is determined to be piecewise affine from a quadratic cost function and the state space is partitioned into corresponding polyhedral cones by moving the on line implementation to an off line explicit evaluation the computational burden is decreased and the applicability of min max optimization is broadened the results of this approach are shown via computer simulations