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

mpc for tracking periodic references in this technical note a new model predictive controller for tracking arbitrary periodic references is presented the proposed controller is based on a single layer that unites dynamic trajectory planning and control a design procedure to guarantee that the closed loop system converges asymptotically to the optimal admissible periodic trajectory while guaranteeing constraint satisfaction is provided in addition the constraints of the optimization problem solved by the controller do not depend on the reference allowing for sudden changes in the reference without loosing feasibility the properties of the proposed controller are demonstrated with a simulation example of a ball and plate system

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

weak limit and blowup of approximate solutions to h systems abstract let h r 3 r be a continuous function such that h p h 0 r as p fixing a domain in r 2 we study the behaviour of a sequence u n of approximate solutions to the h system u 2 h u u x u y in assuming that sup p r 3 h p h 0 p 1 we show that the weak limit of the sequence u n solves the h system and u n u strongly in h 1 apart from a countable set s made by isolated points moreover if in addition h p h 0 o 1 p as p then in correspondence of each point of s we prove that the sequence u n blows either an h bubble or an h 0 sphere

bubbles with prescribed mean curvature the variational approach abstract let h r 3 r be a c 1 mapping such that h p h 0 as p we show that when h satisfies some global conditions then there exists an h bubble namely a sphere s in r 3 such that the mean curvature of s at any regular point p s equals h p

blow up analysis for the prescribed mean curvature equation on r2 abstract we consider the h system u 2 h u u x u y on r 2 where h c 0 r 3 r satisfies h q h o 1 q as q and sup q r 3 h q h q 1 for some h r 0 we show that a sequence of approximate solutions of the h system on r 2 admits a limit configuration made by h bubbles namely nonconstant solutions of h systems on r 2 and h can be the mapping h or the constant h

on real time robust model predictive control high speed applications impose a hard real time constraint on the solution of a model predictive control mpc problem which generally prevents the computation of the optimal control input as a result in most mpc implementations guarantees on feasibility and stability are sacrificed in order to achieve a real time setting in this paper we develop a real time mpc approach for linear systems that provides these guarantees for arbitrary time constraints allowing one to trade off computation time vs performance stability is guaranteed by means of a constraint enforcing that the resulting suboptimal mpc cost is a lyapunov function the key is then to guarantee feasibility in real time which is achieved by the proposed algorithm through a warm starting technique in combination with robust mpc design we address both regulation and tracking of piecewise constant references as a main contribution of this paper a new warm start procedure together with a lyapunov function for real time tracking is presented in addition to providing strong theoretical guarantees the proposed method can be implemented at high sampling rates simulation examples demonstrate the effectiveness of the real time scheme and show that computation times in the millisecond range can be achieved

systematic and effective embedding of feedforward of target information into mpc discussions on how to make effective use of advance information on target changes are discussed relatively rarely in the predictive control literature while earlier work has indicated that the def

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

on the complexity of fixed parameter clique and dominating set we provide simple faster algorithms for the detection of cliques and dominating sets of fixed order our algorithms are based on reductions to rectangular matrix multiplication we also describe an improved algorithm for diamonds detection

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

on syntactic versus computational views of approximability we attempt to reconcile the two distinct views of approximation classes syntactic and computational syntactic classes such as max snp permit structural results and have natural complete problems while computational classes such as apx allow us to work with classes of problems whose approximability is well understood our results provide a syntactic characterization of computational classes and give a computational framework for syntactic classes we compare the syntactically defined class max snp with the computationally defined class apx and show that every problem in apx can be placed i e has approximation preserving reduction to a problem in max snp our methods introduce a simple yet general technique for creating approximation preserving reductions which shows that any well approximable problem can be reduced in an approximation preserving manner to a problem which is hard to approximate to corresponding factors the reduction then follows easily from the recent nonapproximability results for max snp hard problems we demonstrate the generality of this technique by applying it to other classes such as max snp rmax 2 and min f pi 2 1 which have the clique problem and the set cover problem respectively as complete problems the syntactic nature of max snp was used by papadimitriou and yannakakis j comput system sci 43 1991 pp 425 440 to provide approximation algorithms for every problem in the class we provide an alternate approach to demonstrating this result using the syntactic nature of max snp we develop a general paradigm nonoblivious local search useful for developing simple yet efficient approximation algorithms we show that such algorithms can find good approximations for all max snp problems yielding approximation ratios comparable to the best known for a variety of specific max snp hard problems nonoblivious local search provably outperforms standard local search in both the degree of approximation achieved and the efficiency of the resulting algorithms

multiple solutions of h systems and rellich s conjecture soit x y r 2 x 2 y 2 1 on considere une fonction u r 3 satisfaisant le systeme h u 2hu x u y sur avec l une des conditions suivantes soit dirichlet u sur soit plateau u x 2 u y 2 u x u y 0 sur u et u non decroissante sur

generalized terminal state constraint for model predictive control a terminal state equality constraint for model predictive control mpc laws is investigated where the terminal state input pair is not fixed a priori but it is a free variable in the optimization the approach named generalized terminal state constraint can be used for both tracking mpc i e when the objective is to track a given steady state and economic mpc i e when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state it is shown that the proposed technique provides in general a larger feasibility set with respect to the existing approaches given the same prediction horizon moreover a new receding horizon strategy is introduced exploiting the generalized terminal state constraint under mild assumptions the new strategy is guaranteed to converge in finite time with arbitrarily good accuracy to an mpc law with an optimally chosen terminal state constraint while still enjoying a larger feasibility set the features of the new technique are illustrated by an inverted pendulum example in both the tracking and the economic contexts

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

on approximating the number of k cliques in sublinear time we study the problem of approximating the number of k cliques in a graph when given query access to the graph we consider the standard query model for general graphs via 1 degree queries 2

induced subgraph isomorphism the complexity of the subgraph isomorphism problem where the pattern graph is of fixed size is well known to depend on the topology of the pattern graph here we present two results which in contrast provide evidence that no topology of an induced subgraph of fixed size can be substantially easier to detect or count than an independent set of related size we show that any fixed pattern graph having a maximum independent set of size k that is disjoint from other maximum independent sets is not easier to detect as an induced subgraph than an independent set of size k it follows in particular that an induced path on 2 k 1 vertices is not easier to detect than an independent set on k vertices and that an induced cycle on 2k vertices is not easier to detect than an independent set on k vertices in view of linear time upper bounds on the detection of induced path of length two and three our lower bound is tight similar corollaries hold for the detection of induced complete bipartite graphs and an induced paw and its generalizations we show also that for an arbitrary pattern graph h on k vertices with no isolated vertices there is a simple subdivision of h resulting from splitting each edge into a path of length four and attaching a distinct path of length three at each vertex of degree one that is not easier to detect or count than an independent set on k vertices respectively next we show that the so called diamond and its generalizations on k vertices are not easier to detect as induced subgraphs than an independent set on three vertices or an independent set on k vertices respectively for c 4 we give a weaker evidence of its hardness in terms of an independent set on three vertices finally we derive several results relating the complexity of the edge colored variant of induced subgraph isomorphism to that of the standard variant

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

on dynamic output feedback robust mpc for constrained quasi lpv systems this paper considers the dynamic output feedback robust model predictive control mpc of a quasi linear parameter varying quasi lpv system with bounded noise in our previous works for the unknown true state either its ellipsoidal bounds or its polyhedral bounds were solely applied in the main optimisation problem the recursive feasibility of the main optimisation problem was guaranteed by a simple refreshment of the ellipsoidal bound but might be lost by applying the polyhedral bounds this paper shows how and to what extent the recursive feasibility can be restored when the polyhedral bounds are still utilised first we propose a new approach which at each sampling time utilises either the ellipsoidal bound or the polyhedral bound in the main optimisation problem the latter being used if and only if it is contained in the former then we show the sufficient conditions under which the approaches based on polyhedral bounds preserve the property of recursive feasibility a numerical example is

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

nonlinear offset free model predictive control this paper addresses offset free reference tracking of asymptotically constant reference signals using model predictive control existing results for linear models are extended to general nonlinear models the core of the proposed method employs a disturbance model and an observer to estimate its state typical disturbance models are shown and the implications of using them are discussed conditions are given for which this setup eliminates the tracking error asymptotically basically we prove that error free output estimation and error free nominal tracking imply offset free model predictive control

technical communique improvements in the efficiency of linear mpc a model predictive control mpc strategy based on augmented autonomous predictions enables a highly efficient online optimization by imposing a terminal constraint at the current time near optimal performance is obtained by delaying the imposition of the terminal constraint by one sampling period however under certain conditions the degree of optimality can be affected an extension is proposed to remove this difficulty yielding significant improvements in the degree of optimality and achieving this at modest computational cost

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

the dirichlet problem for h systems with small boundary data blowup phenomena and nonexistence results given h 3 of class c1 and bounded we consider a sequence un of solutions of the h system open image in new window in the unit open disc open image in new window satisfying the boundary condition un n on open image in new window in the first part of this paper assuming that un is bounded in h1 open image in new window 3 we study the behavior of un when the boundary data n shrink to zero we show that either un 0 strongly in h1 open image in new window 3 or un blows up at least one h bubble namely a nonconstant conformal solution of the h system on 2 under additional assumptions on h we can obtain more precise information on the blow up in the second part of this paper we investigate the multiplicity of solutions for the dirichlet problem on the disc with small boundary datum we detect a family of nonconstant functions h even close to a nonzero constant in any reasonable topology for which the dirichlet problem cannot admit a large solution at a mountain pass level when the boundary datum is small

constrained infinite horizon model predictive control for fuzzy discrete time systems the problem of constrained infinite horizon model predictive control for fuzzy discrete systems is considered in this paper new sufficient conditions are proposed in terms of linear matrix inequalities based on the optimal solutions of these sufficient conditions at each sampling instant we design both parallel distributed compensation and nonparallel distributed compensation state feedback controllers which can guarantee that the resulting closed loop fuzzy discrete system is asymptotically stable in addition the fuzzy feedback controllers meet the specifications for the fuzzy discrete systems with both input and output constraints numerical examples are presented to demonstrate the effectiveness of the proposed techniques

predictive inverse model allocation for constrained over actuated linear systems the paper presents a model predictive allocation scheme for constrained over actuated linear systems for which input redundancy entails the existence of multiple trajectories in the state space yielding a given reference output the method relies upon the concept of inverse model allocation where dynamic allocation of reference state and input trajectories is accomplished within the framework of output regulation while maintaining invariance of the error zeroing subspace the study focuses on the design of model predictive allocator to achieve constraint satisfaction and asymptotic evolution of the trajectories to a pre computed steady state target in particular the objective of this study is the analysis of the stability and feasibility properties of the proposed schemes and the characterization of suitable sufficient conditions for stability in geometric terms in support of the theoretical findings this study presents an example where the proposed methodology is applied to solve a constrained tracking control problem for the linearized model of the air path system of a turbocharged diesel engine

reference tracking mpc using dynamic terminal set transformation among the many different formulations of model predictive control mpc with guaranteed stability one that has attracted significant attention is the formulation with a terminal cost and terminal constraint set the so called dual mode formulation

brief paper mpc for tracking piecewise constant references for constrained linear systems in this paper a novel model predictive control mpc for constrained non square linear systems to track piecewise constant references is presented this controller ensures constraint satisfaction and asymptotic evolution of the system to any target which is an admissible steady state therefore any sequence of piecewise admissible setpoints can be tracked without error if the target steady state is not admissible the controller steers the system to the closest admissible steady state these objectives are achieved by i adding an artificial steady state and input as decision variables ii using a modified cost function to penalize the distance from the artificial to the target steady state iii considering an extended terminal constraint based on the notion of invariant set for tracking the control law is derived from the solution of a single quadratic programming problem which is feasible for any target furthermore the proposed controller provides a larger domain of attraction for a given control horizon than the standard mpc and can be explicitly computed by means of multiparametric programming tools on the other hand the extra degrees of freedom added to the mpc may cause a loss of optimality that can be arbitrarily reduced by an appropriate weighting of the offset cost term

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

h bubbles in a perturbative setting the finite dimensional reduction s method given a regular function h colon mathbb r 3 to mathbb r we look for h bubbles that is regular surfaces in mathbb r 3 parametrized on the sphere mathbb s 2 with mean curvature h at every point here we study the case of h u h 0 varepsilon h 1 u h varepsilon u where h 0 is a nonzero constant varepsilon is the smallness parameter and h 1 is any c 2 function we prove that if bar p in mathbb r 3 is a good stationary point for the melnikov type function gamma p int q p h 0 1 h 1 q dq then for varepsilon small there exists an h varepsilon bubble omega varepsilon that converges to a sphere of radius h 0 1 centered at bar p as varepsilon to 0

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

reference tracking with guaranteed error bound for constrained linear systems we propose a control design for a constrained linear system to track reference signals within a given bounded error the admissible reference signals are generated as output trajectories of a reference generator which is a constrained linear system driven by unknown bounded inputs the controller has to track the reference signals and to never violate a given tracking error bound while satisfying state and input constraints for any admissible reference the design is based on a model predictive controller mpc enforcing a polyhedral robust control invariant set defined by the system and reference generator models and constraints we describe an algorithm to compute the robust control invariant set and how to design the tracking mpc law that guarantees satisfaction of the tracking error bound and of the system constraints and achieves persistent feasibility we demonstrate the proposed method in two case studies

siso linear system control via saturating actuator l2 tracking performance in the presence of arbitrary shaped inputs most studies on linear system control in the presence of actuator saturation have focused on closed loop asymptotic stabilisation available tracking results are generally limited to constraint compatible inputs references disturbances with known exogenous input models the problem of output reference tracking in the presence of arbitrary shaped not necessarily constraint compatible inputs has yet to be investigated in this study we show that an tracking performance is achievable for siso linear systems using a given class of saturated controllers accordingly the tracking error energy resp power is bounded by the energy resp power of a well defined mismatch input depending on the disturbance and reference compatibility in the disturbance free case this entails perfect asymptotic tracking of arbitrary shaped constraint compatible reference signals otherwise the average tracking quality is proportional to the mismatch input power in the case of periodic inputs constraint compatible or not

dual mode predictive tracking of piecewise constant references for constrained linear systems in this paper the attention is focused on the tracking of a piecewise constant reference for an lti system in presence of state control constraints and bounded disturbance inputs exploiting robust controlled invariant sets in the extended state setpoint space we propose a novel predictive tracking algorithm which yields robust constraint satisfaction and good tracking performance with a reasonable on line computational burden the main idea is to adopt a dual mode controller that operates as a predictive regulator whenever the desired setpoint is feasible or in feasibility recovery mode otherwise simulation results demonstrate the improved tracking performance of the proposed method with respect to available techniques

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

adaptive receding horizon control for constrained mimo systems an adaptive control algorithm for open loop stable constrained linear multiple input multiple output systems is presented the proposed approach can deal with both input and output constraints as well as measurement noise and output disturbances the adaptive controller consists of an iterative set membership identification algorithm that provides a set of candidate plant models at each time step and a model predictive controller that enforces input and output constraints for all the plants inside the model set the algorithm relies only on the solution of standard convex optimization problems that are guaranteed to be recursively feasible the experimental results obtained by applying the proposed controller to a quad tank testbed are presented

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

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

hardness of rna folding problem with four symbols abstract an rna sequence is a string composed of four types of nucleotides a c g and u the goal of the rna folding problem is to find a maximum cardinality set of crossing free pairs of the form a u or c g in a given rna sequence the problem is central in bioinformatics and has received much attention over the years abboud backurs and williams focs 2015 demonstrated a conditional lower bound for a generalized version of the rna folding problem based on a conjectured hardness of the k clique problem their lower bound requires the rna sequence to have at least 36 types of symbols making the result not applicable to the rna folding problem in real life i e alphabet size 4 in this paper we present an improved lower bound that works for the alphabet size 4 case we also investigate the dyck edit distance problem which is a string problem closely related to rna folding we demonstrate a reduction from rna folding to dyck edit distance with alphabet size 10 this leads to a much simpler proof of the conditional lower bound for dyck edit distance problem given by abboud backurs and williams focs 2015 and lowers the alphabet size requirement

robust tracking model predictive control for input constrained uncertain linear time invariant systems this paper presents a robust tracking model predictive control mpc strategy for offset free regulation of the output of input constrained uncertain systems to a non zero reference signal to this end a feedback control law with integral action is proposed and a feasible and invariant set is explicitly derived on the basis of the feedback law finally a robust one step ahead tracking mpc is devised on the basis of the feasible and invariant set in order to improve the control performance simulation results show that the proposed tracking mpc successfully achieves robust tracking in terms of both control performance and the size of the feasible set

model predictive tracking control for constrained linear systems using integrator resets in this technical note we propose a model predictive tracking control algorithm for linear dynamical systems with input constraints to achieve setpoint tracking an integrator is inserted into the feedback loop in the standard control strategy integral action is used for all the time to remove steady state error in the proposed control approach the value of the integrator state is reset at each sampling time to improve tracking control performance until upper bound of the cost becomes sufficiently small then the integral action is used to achieve offset free tracking the control algorithm is reduced to a convex optimization problem under linear matrix inequality constraints

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

arboricity h index and dynamic algorithms we propose a new data structure for manipulating graphs called h graph which is particularly suited for designing dynamic algorithms the structure itself is simple consisting basically of a triple of elements for each vertex of the graph the overall size of all triples is o n m for a graph with n vertices and m edges we describe algorithms for performing the basic operations related to dynamic applications as insertions and deletions of vertices or edges and adjacency queries the data structure employs a technique first described by chiba and nishizeki chiba nishizeki arboricity and subgraph listing algorithms siam j comput 14 1 1985 210 223 and relies on the arboricity of graphs using the proposed data structure we describe several dynamic algorithms for solving problems as listing the cliques of a given size recognizing diamond free graphs and finding simple simplicial and dominated vertices these algorithms are the first of their kind to be proposed in the literature in fact the dynamic algorithms for the above problems lead directly to new static algorithms and using the data structure we also design new static algorithms for the problems of counting subgraphs of size 4 recognizing cop win graphs and recognizing strongly chordal graphs the complexities of all of the proposed static algorithms improve over the complexities of the so far existing algorithms for graphs of low arboricity in addition for the problems of counting subgraphs of size 4 and recognizing diamond free graphs the improvement is general

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

multiple solutions to the plateau problem for nonconstant mean curvature we prove the existence of at least two solutions to the plateau problem for any curvature function h close enough in l norm to a nonzero constant h 0 such that h 0 1 where denotes the l norm of the boundary condition

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

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

map graphs having witnesses of large girth abstract a half square of a bipartite graph b x y e b has one color class of b as vertex set say x two vertices are adjacent whenever they have a common neighbor in y if g v e g is the half square of a planar bipartite graph b v w e b then g is called a map graph and b is a witness of g map graphs generalize planar graphs and have been introduced and investigated by chen grigni and papadimitriou stoc 1998 j acm 2002 they proved that recognizing map graphs is in np by proving the existence of a witness soon later thorup focs 1998 claimed that recognizing map graphs is in p by providing an n 120 time algorithm for n vertex input graphs in this note we give good characterizations and efficient recognition for half squares of bipartite graphs with girth at least a given integer g 8 it turns out that map graphs having witnesses of girth at least g are precisely the graphs whose vertex clique incidence bipartite graph is planar and of girth at least g our structural characterization implies an o n 2 m time algorithm for recognizing if a given n vertex m edge graph g is such a map graph

extended dynamic subgraph statistics using h index parameterized data structures we present techniques for maintaining subgraph frequencies in a dynamic graph using data structures that are parameterized in terms of h the h index of the graph our methods extend previous results of eppstein and spiro for maintaining statistics for undirected subgraphs of size three to directed subgraphs and to subgraphs of size four for the directed case we provide a data structure to maintain counts for all 3 vertex induced subgraphs in o h amortized time per update for the undirected case we maintain the counts of size four subgraphs in o h 2 amortized time per update these extensions enable a number of new applications in bioinformatics and social networking research

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

any domain of attraction for a linear constrained system is a tracking domain of attraction in the stabilization problem for systems with control and state constraints a domain of attraction is a set of initial states that can be driven to the origin by a feedback control without incurring constraints violations if the problem is that of tracking a reference signal that converges to a constant constraint admissible value a tracking domain of attraction is a set of initial states from which the reference signal can be asymptotically approached without constraints violation during the transient clearly since the zero signal is an admissible reference signal any tracking domain of attraction is a domain of attraction we show that the opposite is also true for constant reference signals we establish a connection between the convergence speed of the stabilization problem and tracking convergence which turns out to be independent of the reference signal we also show that the tracking controller can be inferred from the stabilizing possibly nonlinear controller associated with the domain of attraction

fixed parameter tractability and completeness ii on completeness for w 1 abstract for many fixed parameter problems that are trivially solvable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is solvable in time bounded by a polynomial of degree c where c is a constant independent of k in a previous paper the w hierarchy of parameterized problems was defined and complete problems were identified for the classes w t for t 2 our main result shows that independent set is complete for w 1

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

on the parameterized complexity of approximating dominating set we study the parameterized complexity of approximating the k dominating set domset problem where an integer k and a graph g on n vertices are given as input and the goal is to find a dominating set of size at most f k k whenever the graph g has a dominating set of size k when such an algorithm runs in time t k poly n i e fpt time for some computable function t it is said to be an f k fpt approximation algorithm for k domset whether such an algorithm exists is listed in the seminal book of downey and fellows 2013 as one of the most infamous open problems in parameterized complexity this work gives an almost complete answer to this question by showing the non existence of such an algorithm under w 1 fpt and further providing tighter running time lower bounds under stronger hypotheses specifically we prove the following for every computable functions t f and every constant e 0 assuming w 1 fpt there is no f k fpt approximation algorithm for k domset assuming the exponential time hypothesis eth there is no f k approximation algorithm for k domset that runs in t k no k time assuming the strong exponential time hypothesis seth for every integer k 2 there is no f k approximation algorithm for k domset that runs in t k nk e time assuming the k sum hypothesis for every integer k 3 there is no f k approximation algorithm for k domset that runs in t k n k 2 e time previously only constant ratio fpt approximation algorithms were ruled out under sf w 1 fpt and log1 4 m k fpt approximation algorithms were ruled out under eth chen and lin focs 2016 recently the non existence of an f k fpt approximation algorithm for any function f was shown under gap eth chalermsook et al focs 2017 note that to the best of our knowledge no running time lower bound of the form nd this allows us to easily apply known techniques to solve them