polynomial time probabilistic controllability analysis of discrete time piecewise affine systems this paper proposes a probabilistic approach to the controllability analysis for discrete time piecewise affine pwa systems three kinds of randomized algorithms which are based on random sampling of the mode sequence and or the initial state for determining with a probabilistic accuracy if the system is controllable are presented a positive one sided error algorithm a negative one sided error algorithm and a two sided error algorithm it is proven that these are polynomial time algorithms with respect to several variables of the problem it is also shown with some examples for which it is hopeless to check the controllability in a deterministic way that these algorithms are efficient

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

control for safety specifications of systems with imperfect information on a partial order in this paper we consider the control problem for uncertain systems with imperfect information in which an output of interest must be kept outside an undesired region the bad set in the output space the state input output and disturbance spaces are equipped with partial orders the system dynamics are either input output order preserving with output in r2 or given by the parallel composition of input output order preserving dynamics each with scalar output we provide necessary and sufficient conditions under which an initial set of possible system states is safe that is the corresponding outputs are steerable away from the bad set with open loop controls a closed loop control strategy is explicitly constructed which guarantees that the current set of possible system states as obtained from an estimator generates outputs that never enter the bad set the complexity of algorithms that check safety of an initial set of states and implement the control map is quadratic with the dimension of the state space the algorithms are illustrated on two application examples a ship maneuver to avoid an obstacle and safe navigation of an helicopter among buildings

technical communique who needs qp for linear mpc anyway conventional mpc uses quadratic programming qp to minimise on line a cost over n linearly constrained control moves however stability constraints often require the use of large n thereby increasing the on line computation rendering the approach impracticable in the case of fast sampling here we explore an alternative that requires a fraction of the computational cost which increases only linearly with n and propose an extension which in all but a small class of models matches to within a fraction of a percent point the performance of the optimal solution obtained through qp the provocative title of the paper is intended to point out that the proposed approach offers a very attractive alternative to qp based mpc

a positive mass theorem in three dimensional cauchy riemann geometry in this note we summarize the results from 6 on the positive mass problem in 3 dimensional cr cauchy riemann geometry

pseudo einstein structures on cr manifolds etant donne une variete cr compacte non degeneree on cherche une structure pseudohermitienne associee pour laquelle le tenseur de ricci pseudohermitien est un multiple scalaire de la forme de levi

corrigendum corrigendum to the explicit linear quadratic regulator for constrained systems automatica 38 1 2002 3 20 we apologize that example 7 1 as publishedin bemporad morari dua andpistikopoulos 2002 is incorrect due to a miscalculation of the weight matrix p on the terminal state

a predictive control scheme for systems with variable time delay this article deals with the robust control design problem for linear time invariant systems affected by variable feedback delay constraints on the system state are considered in the system description the starting point is the construction of a predictive control law which guarantees the existence of a nonempty robust positive invariant rpi set with respect to the closed loop dynamics subsequently an iterative algorithm is proposed in order to obtain an approximation of the maximal rpi set the problem can be treated in the framework of piecewise affine systems due to the explicit formulations of the control law obtained via multiparametric programming

lagrange stability and performance analysis of discrete time piecewise affine systems with logic states in this paper we consider discrete time piecewise affine systems with boolean inputs outputs and states and show that they can be represented in a logic canonical form where the logic variables influence the switching between different submodels but not the continuous valued dynamics we exploit this representation for studying lagrange stability and developing performance analysis procedures based on linear matrix inequalities moreover by using arguments from dissipativity theory for non linear systems we generalize our approach to solve the h analysis problem

computational complexity certification for real time mpc with input constraints based on the fast gradient method this paper proposes to use nesterov s fast gradient method for the solution of linear quadratic model predictive control mpc problems with input constraints the main focus is on the method s a priori computational complexity certification which consists of deriving lower iteration bounds such that a solution of pre specified suboptimality is obtained for any possible state of the system we investigate cold and warm starting strategies and provide an easily computable lower iteration bound for cold starting and an asymptotic characterization of the bounds for warm starting moreover we characterize the set of mpc problems for which small iteration bounds and thus short solution times are expected the theoretical findings and the practical relevance of the obtained lower iteration bounds are underpinned by various numerical examples and compared to certification results for a primal dual interior point method

cardinality constrained linear quadratic optimal control as control implementation often incurs not only a variable cost associated with the magnitude or energy of the control but also a setup cost we consider a discrete time linear quadratic lq optimal control problem with a limited number of control implementations termed in this technical note the cardinality constrained linear quadratic optimal control cclq we first derive a semi analytical feedback policy for cclq problems using dynamic programming dp due to the exponential growth of the complexity in calculating the action regions however dp procedure is only efficient for cclq problems with a scalar state space recognizing this fact we develop then two lower bounding schemes and integrate them into a branch and bound bnb solution framework to offer an efficient algorithm in solving general cclq problems adopting the devised solution algorithm for cclq problems we can solve efficiently the linear quadratic optimal control problem with setup costs

new speech harmonic structure measure and its applications to speech processing the harmonic structure can be easily recognized in time frequency representation of speech signals in adverse environment the harmonicity is a measure of the completeness of a harmonic structure this paper presents a new harmonic structure measure that extends the conventional harmonicity to a set of harmonicities they are expressed in terms of the grid harmonicity the temporal harmonicity the segment spectral harmonicity and the segmental harmonicity the grid harmonicity measures the completeness of individual harmonics in each frame the grid harmonicities in a frame are summed up to form a temporal harmonicity for representing the strength of harmonicity the segment spectral harmonicity computed by summing specific grid harmonicity over a segment evaluates the integrity of individual harmonics across a segment the segmental harmonicity evaluates the total strength of harmonic structure within a segment this set of harmonicities is available for a systematic analysis of the harmonic structure and effective to several speech processing tasks the applications to speech distortion analysis robust fundamental frequency estimation robust voicing detection and speech enhancement are demonstrated

fast algorithm for a constrained infinite horizon lq problem this paper presents an efficient algorithmic solution to the infinite horizon linear quadratic optimal control problem for a discrete time siso plant subject to bound constraints on a scalar variable the solution to the corresponding quadratic programming problem is based on the active set method and on dynamic programming it is shown that the optimal solution can be updated after inclusion or removal of an active constraint by a simple procedure requiring in the order of kn operations n being the system order and k the time at which the constraint is included or removed

computation of maximal safe sets for switching systems the problem of determining maximal safe sets and hybrid controllers is computationally intractable because of the mathematical generality of hybrid system models given the practical and theoretical relevance of the problem finding implementable procedures that could at least approximate the maximal safe set is important to this end we begin by restricting our attention to a special class of hybrid systems switching systems we exploit the structural properties of the graph describing the discrete part of a switching system to develop an efficient procedure for the computation of the safe set this procedure requires the computation of a maximal controlled invariant set we then restrict our attention to linear discrete time systems for which there is a wealth of results available in the literature for the determination of maximal controlled invariant sets however even for this class of systems the computation may not converge in a finite number of steps we then propose to compute inner approximations that are controlled invariant and for which a procedure that terminates in a finite number of steps can be obtained a tight bound on the error can be given by comparing the inner approximation with the classical outer approximation of the maximal controlled invariant set our procedure is applied to the idle speed regulation problem in engine control to demonstrate its efficiency

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

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

a dynamic game approach to distributionally robust safety specifications for stochastic systems abstract this paper presents a new safety specification method that is robust against errors in the probability distribution of disturbances our proposed distributionally robust safe policy maximizes the probability of a system remaining in a desired set for all times subject to the worst possible disturbance distribution in an ambiguity set we propose a dynamic game formulation of constructing such policies and identify conditions under which a non randomized markov policy is optimal based on this existence result we develop a practical design approach to safety oriented stochastic controllers with limited information about disturbance distributions however an associated bellman equation involves infinite dimensional minimax optimization problems since the disturbance distribution may have a continuous density to alleviate computational issues we propose a duality based reformulation method that converts the infinite dimensional minimax problem into a semi infinite program that can be solved using existing convergent algorithms we prove that there is no duality gap and that this approach thus preserves optimality the results of numerical tests confirm that the proposed method is robust against distributional errors in disturbances while a standard stochastic safety verification tool is not

performance bounds for linear stochastic control we develop computational bounds on performance for causal state feedback stochastic control with linear dynamics arbitrary noise distribution and arbitrary input constraint set this can be very useful as a comparison with the performance of suboptimal control policies which we can evaluate using monte carlo simulation our method involves solving a semidefinite program a linear optimization problem with linear matrix inequality constraints a convex optimization problem which can be efficiently solved numerical experiments show that the lower bound obtained by our method is often close to the performance achieved by several widely used suboptimal control policies which shows that both are nearly optimal as a by product our performance bound yields approximate value functions that can be used as control lyapunov functions for suboptimal control policies

inverse minimax optimality of model predictive control policies we present novel results linking model predictive control mpc and minimax optimal control theory specifically we show that for linear discrete time systems with constraints and disturbance inputs the closed loop optimal solutions of a particular class of minimax optimal control problems are a class of typical mpc policies we also present conditions which ensure that the inverse optimal mpc policies achieve a prescribed regional l2 gain from the disturbance input

speech enhancement using a minimum mean square error short time spectral amplitude estimator this paper focuses on the class of speech enhancement systems which capitalize on the major importance of the short time spectral amplitude stsa of the speech signal in its perception a system which utilizes a minimum mean square error mmse stsa estimator is proposed and then compared with other widely used systems which are based on wiener filtering and the spectral subtraction algorithm in this paper we derive the mmse stsa estimator based on modeling speech and noise spectral components as statistically independent gaussian random variables we analyze the performance of the proposed stsa estimator and compare it with a stsa estimator derived from the wiener estimator we also examine the mmse stsa estimator under uncertainty of signal presence in the noisy observations in constructing the enhanced signal the mmse stsa estimator is combined with the complex exponential of the noisy phase it is shown here that the latter is the mmse estimator of the complex exponential of the original phase which does not affect the stsa estimation the proposed approach results in a significant reduction of the noise and provides enhanced speech with colorless residual noise the complexity of the proposed algorithm is approximately that of other systems in the discussed class

stabilizing polynomial approximation of explicit mpc a given explicit piecewise affine representation of an mpc feedback law is approximated by a single polynomial computed using linear programming this polynomial state feedback control law guarantees closed loop stability and constraint satisfaction the polynomial feedback can be implemented in real time even on very simple devices with severe limitations on memory storage

an algebraic approach to bounded controllability of linear systems in this paper we present an algebraic approach to the proof that a linear system with matrices a b is null controllable using bounded inputs if and only if it is null controllable with unbounde

a unified framework for the study of anti windup designs we present a unified framework for the study of linear time invariant lti systems subject to control input nonlinearities the framework is based on the following two step design paradigm design the linear controller ignoring control input nonlinearities and then add anti windup bumpless transfer awbt compensation to minimize the adverse eflects of any control input nonlinearities on closed loop performance the resulting awbt compensation is applicable to multivariable controllers of arbitrary structure and order all known lti anti windup and or bumpless transfer compensation schemes are shown to be special cases of this framework it is shown how this framework can handle standard issues such as the analysis of stability and performance with or without uncertainties in the plant model the actual analysis of stability and performance and robustness issues are problems in their own right and hence not detailed here the main result is the unification of existing schemes for awbt compensation under a general framework

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

robust model predictive control of nonlinear systems with bounded and state dependent uncertainties in this note a robust model predictive control scheme for constrained discrete time nonlinear systems affected by bounded disturbances and state dependent uncertainties is presented in order to guarantee the robust satisfaction of the state constraints restricted constraint sets are introduced in the optimization problem by exploiting the state dependent nature of the considered class of uncertainties moreover unlike the nominal model predictive control algorithm a stabilizing state constraint is imposed at the end of the control horizon in place of the usual terminal constraint posed at the end of the prediction horizon the regional input to state stability of the closed loop system is analyzed a simulation example shows the effectiveness of the proposed approach

ultra fast stabilizing model predictive control via canonical piecewise affine approximations this paper investigates the use of canonical piecewise affine pwa functions for approximation and fast implementation of linear mpc controllers the control law is approximated in an optimal way over a regular simplicial partition of a given set of states of interest the stability properties of the resulting closed loop system are analyzed by constructing a suitable pwa lyapunov function the main advantage of the proposed approach to the implementation of mpc controllers is that the resulting stabilizing approximate mpc controller can be implemented on chip with sampling times in the order of tens of nanoseconds

brief paper reachability and stabilization of discrete time affine systems with disturbances this paper studies the fundamental problems whether an affine system affected by additive disturbances is robustly transferable from a source set simplex to a target set polytope and whether it is robustly stabilizable with its state constrained in a simplex first a necessary and sufficient condition is derived for the existence of affine feedback control that solves the robust reachability problem further investigation is provided for two situations relying on whether the union of the source set and the target set is convex or non convex for the former one a necessary and sufficient condition is obtained in the form of linear inequalities while for the latter several computationally feasible sufficient conditions are found second we show that robust stabilization subject to a state constraint is equivalent to find a feasible solution to a linear equation once it is known that either of the problems has a solution by checking the derived conditions design of control laws is then straightforward

a relative index on the space of embeddable cr structures i we study the problem of embeddability for three dimensional cr manifolds let m m0b denote a compact embeddable strictly pseudoconvex cr manifold and os the orthogonal projection on ker 0 b if 16b denotes a deformation of this cr structure then 1 b is embeddable if and only if

reachability analysis of discrete time systems with disturbances this paper presents new results that allow one to compute the set of states that can be robustly steered in a finite number of steps via state feedback control to a given target set the assumptions that are made in this paper are that the system is discrete time nonlinear and time invariant and subject to mixed constraints on the state and input a persistent disturbance dependent on the current state and input acts on the system existing results are not able to address state and input dependent disturbances and the results in this paper are therefore a generalization of previously published results one of the key aims of this paper is to present results such that one can perform the relevant set computations using polyhedral algebra and computational geometry software provided the system is piecewise affine and the constraints are polygonal existing methods are only applicable to piecewise affine systems that either have no control inputs or no disturbances whereas the results in this paper remove this limitation some simple examples are also given that show that even if all the relevant sets are convex and the system is linear convexity of the set of controllable states cannot be guaranteed

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

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

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

brief multiplier theory for stability analysis of anti windup control systems we apply the passivity theorem with appropriate choice of multipliers to develop a general framework for analyzing stability of anti windup bumpless transfer awbt schemes for appropriate choices of the multipliers we reduce the resulting sufficient conditions for stability to equivalent linear matrix inequalities lmis we show that a number of previously reported attempts to analyze awbt stability using seemingly diverse techniques such as the popov circle and off axis circle criteria the optimally scaled small gain theorem generalized m upper bound and describing functions can all be generalized within the framework of this paper

projection free parallel quadratic programming for linear model predictive control a key component in enabling the application of model predictive control mpc in fields such as automotive aerospace and factory automation is the availability of low complexity fast optimisation algorithms to solve the mpc finite horizon optimal control problem in architectures with reduced computational capabilities in this paper we introduce a projection free iterative optimisation algorithm and discuss its application to linear mpc the algorithm originally developed by brand for non negative quadratic programs is based on a multiplicative update rule and it is shown to converge to a fixed point which is the optimum an acceleration technique based on a projection free line search is also introduced to speed up the convergence to the optimum the algorithm is applied to mpc through the dual of the quadratic program qp formulated from the mpc finite time optimal control problem we discuss how termination conditions with guaranteed degree of suboptimality can be enforced and how the algorithm

a patchy approximation of explicit model predictive control the explicit solution of multi parametric optimisation problems mpop has been used to construct an off line solution to relatively small and medium sized constrained control problems the control design principles are based on receding horizon optimisation and generally use linear prediction models for the system dynamics in this context it can be shown that the optimal control law is a piecewise linear pwl state feedback defined over polytopic cells of the state space however as the complexity of the related optimisation problems increases the memory footprint and implementation of such explicit optimal solution may be burdensome for the available hardware principally due to the high number of polytopic cells in the state space partition in this article we provide a solution to this problem by proposing a patchy pwl feedback control law which intend to approximate the optimal control law the construction is based on the linear interpolation of the exact solution at the vertices of a feasibl

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

admissible sets for slowly varying discrete time systems abstract this note describes a method to calculate admissible sets for dynamical systems with slowly varying parameters a set of initial states is said to be admissible if all state trajectories starting within this set respect safety critical constraints for all future time instances for many classes of systems the maximal admissible set mas equals the maximal robust positive invariant mrpi set therefore much of the literature focus on algorithms that produce approximations of the mrpi set however for slowly varying systems it turns out that the mas can be larger than the mrpi set a property referred to as the m proximal contraction property is defined for such systems to state sufficient conditions for sets to be admissible it is then shown that algorithm 2 produces an admissible set that is a superset of the mrpi set

metriques autoduales sur la boule a conformal metric on a 4 ball induces on the boundary 3 sphere a conformal metric and a trace free second fundamental form conversely such a data on the 3 sphere is the boundary of a unique selfdual conformal metric defined in a neighborhood of the sphere in this paper we characterize the conformal metrics and trace free second fundamental forms on the 3 sphere close to the standard round metric which are boundaries of selfdual conformal metrics on the whole 4 ball when the data on the boundary is reduced to a conformal metric the trace free part of the second fundamental form vanishes one may hope to find in the conformal class of the filling metric an einstein metric with a pole of order 2 on the boundary we determine which conformal metrics on the 3 sphere are boundaries of such selfdual einstein metrics on the 4 ball in particular this implies the positive frequency conjecture of lebrun the proof uses twistor theory which enables to translate the problem in terms of complex analysis this leads us to prove a criterion for certain integrable cr structures of signature 1 1 to be fillable by a complex domain finally we solve an analogous higher dimensional problem selfdual einstein metrics are replaced by quaternionic kahler metrics and conformal structures on the boundary by quaternionic contact structures previously introduced by the author in contrast with the 4 dimensional case we prove that any small deformation of the standard quaternionic contact structure on the 4m 1 sphere is the boundary of a quaternionic kahler metric on the 4m ball

multi resolution explicit model predictive control delta model formulation and approximation this paper deals with the explicit solution and approximation of the constrained linear finite time optimal control problem for systems with fast sampling rates to this aim the recently developed explicit model predictive control empc is reformulated and characterized using the operator to enjoy its promising advantages compared to the time shift operator using the proposed model empc formulation a systematic method is proposed for first designing a low complexity approximate empc solution and then improving its closed loop action without first determining an exact optimal solution that might be of prohibitive complexity it is shown that the stability and feasibility of the proposed sub optimal solution is guaranteed

stability and invariance analysis of uncertain discrete time piecewise affine systems this note proposes a method to analyze uniform asymptotic stability and uniform ultimate boundedness of uncertain piecewise affine systems whose dynamics are only defined in a bounded and possibly non invariant set x of states the approach relies on introducing fake dynamics outside x and on synthesizing a piecewise affine and possibly discontinuous lyapunov function via linear programming the existence of such a function proves stability properties of the original system and allows the determination of a region of attraction contained in x the procedure is particularly useful in practical applications for analyzing the stability of piecewise affine control systems that are only defined over a bounded subset x of the state space and to determine whether for a given set of initial conditions the trajectories of the state vector remain within the domain x

computation of the constrained infinite time linear quadratic regulator this paper presents an efficient algorithm for computing the solution to the constrained infinite time linear quadratic regulator clqr problem for discrete time systems the algorithm combines multi parametric quadratic programming with reachability analysis to obtain the optimal piecewise affine pwa feedback law the algorithm reduces the time necessary to compute the pwa solution for the clqr when compared to other approaches it also determines the minimal finite horizon email protected s such that the constrained finite horizon lqr problem equals the clqr problem for a compact set of states s the on line computational effort for the implementation of the clqr can be significantly reduced as well either by evaluating the pwa solution or by solving the finite dimensional quadratic program associated with the clqr for a horizon of email protected s

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

minimising conservatism in infinite horizon lqr control this paper studies the formulation of the constrained infinite horizon linear quadratic regulator control law cihlqr results from recent studies in this area are extended to show that conditions used in the standard formulation of the cihlqr law are not necessary but merely sufficient through the use of a novel proof it is shown that for a general siso system with input constraints and certain conditions imposed saturated lqr provides the same control sequence as cihlqr it is further shown that saturated lqr is equivalent to the cihlqr in the case of first order systems subject to both state and control constraints finally the region of constrained stabilisability is characterised for the case of open loop unstable first order systems

bounded strictly pseudoconvex domains in c2 with obstruction flat boundary ii abstract on a bounded strictly pseudoconvex domain in c n n 1 the smoothness of the cheng yau solution to fefferman s complex monge ampere equation up to the boundary is obstructed by a local cr invariant of the boundary for a bounded strictly pseudoconvex domain c 2 diffeomorphic to the ball we prove that the global vanishing of this obstruction implies biholomorphic equivalence to the unit ball subject to the existence of a holomorphic vector field satisfying a mild approximate tangency condition along the boundary in particular by considering the euler vector field multiplied by i the result applies to all domains in a large c 1 open neighborhood of the unit ball in c 2 the proof rests on establishing an integral identity involving the cr curvature of for any holomorphic vector field defined in a neighborhood of the boundary the notion of ambient holomorphic vector field along the cr boundary generalizes naturally to the abstract setting and the corresponding integral identity still holds in the case of abstract cr 3 manifolds

brief paper fast large scale model predictive control by partial enumeration partial enumeration pe is presented as a method for treating large linear model predictive control applications that are out of reach with available mpc methods pe uses both a table storage method and online optimization to achieve this goal versions of pe are shown to be closed loop stable pe is applied to an industrial example with more than 250 states 32 inputs and a 25 sample control horizon the performance is less than 0 01 suboptimal with average speedup factors in the range of 80 220 and worst case speedups in the range of 4 9 39 2 compared to an existing mpc method small tables with only 25 200 entries were used to obtain this performance while full enumeration is intractable for this example

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

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

admissible sets and feedback control for discrete time linear dynamical systems with bounded controls and states for linear discrete time dynamical systems necessary and sufficient conditions are given for a control sequence belonging to a polyhedral constraint set to stabilize the system under the condition that the state is restricted to a polyhedral state constraint set a variable structure linear state feedback controller given in terms of the controls at the vertices of the polyhedral state constraint set is presented

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

temporal and spectral estimations of harmonics to noise ratio in human voice signals the quantity harmonic to noise ratio hnr has been used to estimate the level of noise in human voice signals hnr estimation can be accomplished in two ways 1 on a time domain basis in which hnr is computed directly from the acoustic waveform and 2 on a frequency domain basis in which hnr is computed from a transformed representation of the waveform an algorithm for computing hnr in the frequency domain was modified and tested in the work described here the modifications were designed to reduce the influence of spectral leakage in the computation of harmonic energy and to remove the necessity of spectral baseline shifting prescribed in one existing algorithm g de krom j speech hear res 36 254 266 1993 frequency domain estimations of hnr based on this existing algorithm and our modified algorithm were compared to time domain estimations on synthetic signals and human pathological voice samples results indicated a highly significant linear correlation between frequency and time domain estimations of hnr for our modified approach

asymptotically exact stabilisation for constrained discrete takagisugeno systems via set invariance given a takagisugeno ts system this paper proposes a novel methodology to obtain the state feedback controller guaranteeing asymptotically as a polya related complexity parameter grows the largest membership shape independent possible domain of attraction with contraction rate performance based on polyhedral contractive sets from constrained linear systems literature the resulting controller is valid for any realisation of the memberships as usual in most ts literature for a finite complexity parameter an inner estimate of such largest set is obtained the frontier of such approximation can be understood as the level set of a polyhedral control lyapunov function convergence of a proposed iterative algorithm is asymptotically necessary and sufficient for ts system stabilisation for a high enough value of the complexity parameter any conceivable shape independent lyapunov controller design procedure will yield a proven domain of attraction smaller or equal to the algorithm s output

on the robustness of nominal nonlinear minimum time control and extension to non robustly controllable target sets this work deals with the analysis and the design of minimum time control laws for a class of nonlinear discrete time dynamical systems characterized by k continuous transition maps and bounded control inputs in the paper it is shown that the reachability properties of the target set even if not robust positively controllable in one state transition can be exploited to assess the existence of a robust positively controllable set including the target in its interior this result allows the formulation of a robustified minimum time control policy based on iterated online optimizations and guaranteeing the ultimate boundedness of the state trajectories in the presence of bounded uncertainties even if the target set is not robust positively controllable

impulse differential inclusions a viability approach to hybrid systems impulse differential inclusions are introduced as a framework for modeling hybrid phenomena connections to standard problems in the area of hybrid systems are discussed conditions are derived that allow one to determine whether a set of states is viable or invariant under the action of an impulse differential inclusion for sets that violate these conditions methods are developed for approximating their viability and invariance kernels that is the largest subset that is viable or invariant under the action of the impulse differential inclusion the results are demonstrated on examples

embeddability for three dimensional cr manifolds a question of principal interest in the theory of compact three dimensional cr manifolds is to understand when a given strictly pseudoconvex cr structure can be realized by an embedding in c we call a structure for which this is possible embeddable and nonembeddable otherwise this question is only of interest in three dimensions as a theorem of boutet de monvel states that any strictly pseudoconvex cr structure on a compact 2d 1 manifold is realizable as an embedding in some c provided d 1 on the other hand there is a classical example of rossi which shows that an arbitrarily small real analytic perturbation of the standard structure on the three sphere may fail to be embeddable ros later nirenberg constructed w perturbations for which the associated ob equation fails to have even local solutions n in fact this situation is generic in the f topology it is now understood principally from the work of eliashberg that cr structures with

a global invariant for three dimensional cr manifolds in this note we define a global r valued invariant of a compact strictly pseudoconvex 3 dimensional cr manifold m whose holomorphic tangent bundle is trivial the invariant arises as the evaluation of a derham cohomology class on the fundamental class of the manifold to construct the relevant form we start with the cr structure bundle y over m see ch mo whose notation we follow the form is a secondary characteristic form of this structure by fixing a contact form and coframe i e a section of y we obtain a form on m surprisingly this form is well defined up to an exact term and thus its cohomology class is well defined in h 3 m r our motivation for studying this invariant was its analogy with the r z secondary characteristic number associated by chern and simons to the conforreal class of a riemannian 3 manifold n which provides an obstruction to the conformal immersion of n in r 4 though several formal analogies to the conformal case are valid for our invariant this one does not hold up specifically in w below we calculate examples which show that the cr invariant can take on any positive real value for hypersurfaces embedded in c 2 it is also clear that the invariant is neither a homotopy nor concordance invariant but depends in an elusive way on the cr structure our inspiration came from the seminal papers of chern and moser and chern and simons the idea of looking at secondary characteristic forms of higher order geometric structures in general appears in ko oc though with a different intention in w 2 we will quickly review the definition of a cr structure the construction of y and its reduction to a pseudo hermitian structure ld webster we in w 3 we define the invariant and prove that it is in fact r valued and not r z valued as in the riemannian case we also prove that if the invariant is stationary as a function of the cr structure then m is locally cr equivalent to the standard three sphere in c 2 paralleling a result of chern and simons as noted already w 4 is devoted to the calculation of several examples

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

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

adaptive comb filtering for harmonic signal enhancement a new algorithm is presented for adaptive comb filtering and parametric spectral estimation of harmonic signals with additive white noise the algorithm is composed of two cascaded parts the first estimates the fundamental frequency and enhances the harmonic component in the input and the second estimates the harmonic amplitudes and phases performance analysis provides new results for the asymptotic cramer rao bound crb on the parameters of harmonic signals with additive white noise results of simulations indicate that the variances of the estimates are of the same order of magnitude as the crb for sufficiently large data sets and illustrate the performance in enhancing noisy artificial periodic signals

a dynamic programming approach to solving constrained linear quadratic optimal control problems abstract the solution of a constrained linear quadratic regulator problem is determined by the set of its optimal active sets we propose an algorithm that constructs this set of active sets for a desired horizon n from that for horizon n 1 while it is not obvious how to extend the optimal feedback law itself for horizon n 1 to horizon n a simple relation between the optimal active sets for two successive horizon lengths has recently been established essentially we show how to use this recent result to improve the efficiency of existing active set enumeration algorithms

reachability analysis of linear dynamic systems with constant arbitrary and lipschitz continuous inputs abstract this paper sets forth a method for reachability analysis of linear dynamic systems in continuous time that can be used to compute time domain bounds of states and outputs with floating point precision the focus is on the particular initial conditions and inputs that cause state or output trajectories to attain their extreme values in time inputs can be constant arbitrary or lipschitz continuous waveforms uncertainties in initial conditions and inputs are modeled using zonotopes the calculations exploit the definition of zonotopes and the modal information of the linear system dynamics

zames falb multipliers for quadratic programming in constrained linear model predictive control a quadratic program must be solved on line at each control step and this constitutes a nonlinearity if zero is a feasible point for this quadratic program then the resultant nonlinearity is sector bounded we show that if the nonlinearity is static then it is also monotone and slope restricted hence we show the existence of zames falb multipliers for such a nonlinearity the multipliers may be used in a general and versatile analysis of the robust stability of input constrained model predictive control

computing robust controlled invariant sets of linear systems we consider controllable linear discrete time systems with bounded perturbations and present two methods to compute robust controlled invariant sets the first method tolerates an arbitrarily small constraint violation to compute an arbitrarily precise outer approximation of the maximal robust controlled invariant set while the second method provides an inner approximation the outer approximation scheme is delta complete given that the constraint sets are formulated as finite unions of polytopes

a lyapunov method for stability analysis of piecewise affine systems over non invariant domains this paper analyses stability of discrete time piecewise affine systems defined on possibly non invariant domains taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system an algorithm based on linear programming is proposed in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction the results are based on the definition of a piecewise affine lyapunov function which is in general discontinuous on the boundaries of the regions the proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach two numerical examples are shown among which a case where the proposed method is applied to a closed loop system to which model predictive control was applied without a priori guarantee of stability

brief paper constrained linear systems with hard constraints and disturbances an extended command governor with large domain of attraction this paper considers a nonlinear feedback control policy that is an extension of those provided by command governors and reference governors as in these control approaches it applies to discrete time linear systems with hard constraints and set bounded disturbances the control policy retains the main properties of traditional governors such as straightforward direct implementation and finite settling time response to arbitrarily specified set points its principal advantage over traditional governors is a significantly larger domain of attraction that may compete in size with those obtained by dynamic programming connections to model predictive control are made numerical examples illustrate advantageous features of the proposed approach