kinodynamic motion planning kinodynamic planning attempts to solve a robot motion problem subject to simultaneous kinematic and dynamics constraints in the general problem given a robot system we must find a minimal time trajectory that goes from a start position and velocity to a goal position and velocity while avoiding obstacles by a safety margin and respecting constraints on velocity and acceleration we consider the simplified case of a point mass under newtonian mechanics together with velocity and acceleration bounds the point must be flown from a start to a goal amidst polyhedral obstacles in 2d or 3d although exact solutions to this problem are not known we provide the first provably good approximation algorithm and show that it runs in polynomial time

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

transverse vibration of simply supported elliptical and circular plates using boundary characteristic orthogonal polynomials in two variables abstract the first four frequencies and mode shapes have been computed for elliptical and circular plates of uniform thickness with simply supported edges by employing orthogonal polynomials in the rayleigh ritz method in general this is found to give better results than traditional methods successive approximations have been worked out to ensure convergence comparisons have been made with existing results in some cases calculations have been done for several values of b a i e the ratio of the semi major and semi minor axes mode shapes have been used to obtain three dimensional plots of plates in displaced configurations

an infinite ramsey theorem and some banach space dichotomies a problem of banach asks whether every infinite dimensional banach space which is isomorphic to all its infinite dimensional subspaces must be isomorphic to a separable hilbert space in this paper we prove a result of a ramsey theoretic nature which implies an interesting dichotomy for subspaces of banach spaces combined with a result of komorowski and tomczakjaegermann this gives a positive answer to banachxs problem we then generalize the ramsey theoretic result and deduce a further dichotomy for banach spaces with an unconditional basis

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

a c0 saturated banach space with tight structure it is shown that variants of the hi methods could yield objects closely connected to the classical banach spaces thus we present a new c0 saturated space denoted as x0 with rather tight structure the space x0 is not embedded into a space with an unconditional basis and its complemented subspaces have the following structure everyone is either of type i namely contains an isomorph of x0 itself or else is isomorphic to a subspace of c0 type ii furthermore for any analytic decomposition of x0 into two subspaces one is of type i and the other is of type ii the operators of x0 share common features with those of hi spaces

on the hereditary proximity to l1 in the first part of the paper we present and discuss concepts of local and asymptotic hereditary proximity to l1 the second part is devoted to a complete separation of the hereditary local proximity to l1 from the asymptotic one more precisely for every countable ordinal we construct a separable reflexive space x such that every infinite dimensional subspace of it has bourgain l1 index greater than and the space itself has no l1 spreading model we also present a reflexive hi space admitting no lp as a spreading model

free vibration of super elliptical plates with constant and variable thickness by ritz method in this study free vibration of simply supported and clamped super elliptical plates is investigated this class of plates includes a wide range of external boundaries varying from an ellipse to a rectangle although studies on the upper and lower bounds of these plate geometries namely circle and rectangle are quite extensive contributions on the mid shapes especially for simply supported boundary edges are very limited the kirchhoff plate model with isotropic and homogeneous material is studied the super elliptical powers are chosen from 1 to 10 the ritz method is employed for the solution of the energy equations of the plates the effects of poisson s ratio which should not be neglected for simply supported plates with curved boundaries and the aspect ratio of the plate are both examined in detail the effect of thickness variation is also considered in this study in order to avoid long computational run times physically pertinent trial functions are utilized the frequency parameters obtained are presented and compared with published results for plate shapes that match the current cases

a continuation gmres method for fast computation of nonlinear receding horizon control in this paper a fast numerical algorithm for nonlinear receding horizon control is proposed the control input is updated by a differential equation to trace the solution of an associated state dependent two point boundary value problem a linear equation involved in the differential equation is solved by the generalized minimum residual method one of the krylov subspace methods with jacobians approximated by forward differences the error in the entire algorithm is analyzed and is shown to be bounded under some conditions the proposed algorithm is applied to a two link arm whose dynamics is highly nonlinear simulation results show that the proposed algorithm is faster than the conventional algorithms

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

the unconditional basic sequence problem we construct a banach space that does not contain any infinite un conditional basic sequence and investigate further properties of this space for example it has no subspace that can be written as a topological direct sum of two infinite dimensional spaces this property implies that every operator on the space is a strictly singular perturbation of a multiple of the identity in par ticular it is either strictly singular or fredholm with index zero this implies that the space is not isomorphic to any proper subspace trinity college cambridge cb2 1tq england current address department of mathematics university college london gower street lon don wc1e 6bt england e mail address wtg l o phx cam ac uk universit paris vii u f r de mathtmatiques 2 place jussieu 75251 paris cedex 05 france current address equipe d analyse et mathematiques appliquees universite de mamne la vallee 93160 noisy le grand france e mail address maurey logiquejussieu fr this content downloaded from 157 55 39 105 on fri 07 oct 2016 04 30 48 utc all use subject to http about jstor org terms

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

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

tree based trajectory optimization based on local linearity of continuous non linear dynamics this technical note addresses a tradeoff in the tree based trajectory optimization algorithms for open loop optimal control problem of rigid body system in this technical note linear prediction based uniform state sampling method lpuss which relaxes the tradeoff between solutions quality and computational efficiency is proposed on the basis of the local linearity of motion equations lpuss has a lower calculation order than randomized kinodynamic planning rkp and rapid semi optimal motion planning rasmo in the validation using multi degree of freedom dof under actuated manipulator models the solutions quality and the computational efficiency of lpuss were better than those of rkp and rasmo lpuss finished the optimization for the 6 dof model within 40 minutes this was the world s first success of the optimization of the swing up motion of a 6 dof under actuated manipulator model

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

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

proximity to l1and distortion in asymptotic l1spaces abstract for an asymptotic l 1 space x with a basis x i certain asymptotic l 1 constants x are defined for 1 x measures the equivalence between all normalized block bases y i k i 1 of x i which are s admissible with respect to x i s is the th schreier class of sets and the unit vector basis of l k 1 this leads to the concept of the delta spectrum of x x which reflects the behavior of stabilized limits of x the analogues of these constants under all renormings of x are also defined and studied we investigate x both in general and for spaces of bounded distortion we also prove several results on distorting the classical tsirelson s space t and its relatives

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

transverse vibrations of an elliptic plate with variable thickness abstract galerkin s method has been used to obtain the frequencies of symmetric transverse vibrations of an elliptic plate with clamped edges and variable thickness the procedure can be used to generate a sequence of approximations which may be truncated when the required number of frequencies have converged to the desired accuracy the numerical values of the first four frequencies are reported correct to five significant digits for various values of the taper parameter and the ratio of the semi axes mode shapes and the nodal ellipses have also been worked out for the second and third modes the results for an elliptic plate with uniform thickness circular plate with parabolically varying thickness and a circular plate with uniform thickness have been obtained as special cases

the explicit linear quadratic regulator for constrained systems we present a technique to compute the explicit state feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints we show that this closed form solution is piecewise linear and continuous as a practical consequence of the result constrained linear quadratic regulation becomes attractive also for systems with high sampling rates as on line quadratic programming solvers are no more required for the implementation

proximity to lp and c0 in banach spaces abstract we construct a class of minimal trees and use these trees to establish a number of coloring theorems on general trees among the applications of these trees and coloring theorems are quantification of the bourgain l p and c 0 indices dualization of the bourgain c 0 index establishing sharp positive and negative results for constant reduction and estimating the bourgain l p index of an arbitrary banach space x in terms of a subspace y and the quotient x y

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

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

transverse vibrations of a clamped elliptical plate carrying a concentrated mass at an arbitrary position free vibrations of clamped thin elliptical plates carrying a concentrated mass at an arbitrary position are studied in order to analyze the mass effect on the natural frequencies and mode shapes of the plate a variational approach the well known ritz method is used where the displacement amplitude is approximated by polynomial expressions in the cartesian coordinates the present proposal exhibits excellent agreement with particular cases of the problem available in the literature and also with an independent solution obtained by means of the finite element method some new results are presented for the natural frequencies and modes of clamped elliptical plates with a concentrated mass

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

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow