a distributed model predictive control scheme for leader follower multi agent systems abstractin this paper we present a novel receding horizon control scheme for solving the formation problem of leader follower configurations the algorithm is based on set theoretic ideas and is tuned for agents described by linear time invariant lti systems subject to input and state constraints the novelty of the proposed framework relies on the capability to jointly use sequences of one step controllable sets and polyhedral piecewise state space partitions in order to online apply the better control action in a distributed receding horizon fashion moreover we prove that the design of both robust positively invariant sets and one step ahead controllable regions is achieved in a distributed sense simulations and numerical comparisons with respect to centralised and local based strategies are finally performed on a group of mobile robots to demonstrate the effectiveness of the proposed control strategy

fake algebraic riccati techniques and stability conditions sufficient and necessary for monotonic behavior of the solutions of the riccati differential equation and riccati difference equation are derived for the optimal filtering respectively control equation these results are derived without the usual requirement of detectability respectively stabilizability the monotonic behavior allows proof of stabilizing properties of the solutions subject only to requirements on the initial conditions

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

adaptive fuzzy output feedback control for output constrained nonlinear systems in the presence of input saturation abstract in this paper the problem of adaptive fuzzy output feedback control is investigated for a class of output constrained uncertain nonlinear systems with input saturation and unmeasured states to address output constraint and input constraint a barrier lyapunov function and an auxiliary design system are employed respectively fuzzy logic systems are utilized to approximate the unknown nonlinear functions and a fuzzy state observer is designed to estimate the unmeasured states by utilizing the fuzzy state observer and combining the adaptive backstepping technique with adaptive fuzzy control design an observer based adaptive fuzzy output feedback control approach is developed it is proved that the proposed control approach can guarantee that all the signals in the closed loop system are bounded and the input and output constraints are circumvented simultaneously a numerical example is provided to illustrate the effectiveness of the proposed approach

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

robust event triggered mpc with guaranteed asymptotic bound and average sampling rate we propose a robust event triggered model predictive control mpc scheme for linear time invariant discrete time systems subject to bounded additive stochastic disturbances and hard constraints on the input and state for given probability distributions of the disturbances acting on the system we design event conditions such that the average frequency of communication between the controller and the actuator in the closed loop system attains a given value we employ tube mpc methods to guarantee robust constraint satisfaction and a robust asymptotic bound on the system state moreover we show that instead of a given periodically updated tube mpc scheme an appropriate event triggered mpc scheme can be applied with the same guarantees on constraints and region of attraction but with a reduced number of average communications

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

operators constructed by means of q lagrange polynomials and a statistical approximation in this paper we construct some positive linear operators by means of q lagrange polynomials and prove some approximation results via a statistical convergence we also define and study the rate of a statistical approximation of these operators by using the notion of modulus of continuity and lipschitz class

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

efficient model predictive control for nonlinear systems via function approximation techniques this note deals with the problem of fast implementation of nonlinear model predictive control using approximated control laws at first accuracy properties of a generic approximated controller are introduced together with their influence on closed loop stability and performance then exploiting such results it is shown how set membership sm function approximation theory can be systematically employed to improve the accuracy performance of the resulting controller given by the sum of with a sm approximating function satisfies the above mentioned properties even if they are not met by alone a nonlinear oscillator example shows the effectiveness of the proposed methodology

brief a receding horizon approach to the nonlinear h control problem the receding horizon rh methodology is extended to the design of a robust controller of h type for nonlinear systems using the nonlinear analogue of the fake h algebraic riccati equation we derive an inverse optimality result for the rh schemes for which increasing the horizon causes a decrease of the optimal cost function this inverse optimality result shows that the input output map of the closed loop system obtained with the rh control law has a bounded l 2 gain robustness properties of the nonlinear h control law in face of dynamic input uncertainty are considered

linear predictors for nonlinear dynamical systems koopman operator meets model predictive control this paper presents a class of linear predictors for nonlinear controlled dynamical systems the basic idea is to lift or embed the nonlinear dynamics into a higher dimensional space where its evolution is approximately linear in an uncontrolled setting this procedure amounts to numerical approximations of the koopman operator associated to the nonlinear dynamics in this work we extend the koopman operator to controlled dynamical systems and apply the extended dynamic mode decomposition edmd to compute a finite dimensional approximation of the operator in such a way that this approximation has the form of a linear controlled dynamical system in numerical examples the linear predictors obtained in this way exhibit a performance superior to existing linear predictors such as those based on local linearization or the so called carleman linearization importantly the procedure to construct these linear predictors is completely data driven and extremely simple it boils down to a nonlinear transformation of the data the lifting and a linear least squares problem in the lifted space that can be readily solved for large data sets these linear predictors can be readily used to design controllers for the nonlinear dynamical system using linear controller design methodologies we focus in particular on model predictive control mpc and show that mpc controllers designed in this way enjoy computational complexity of the underlying optimization problem comparable to that of mpc for a linear dynamical system with the same number of control inputs and the same dimension of the state space importantly linear inequality constraints on the state and control inputs as well as nonlinear constraints on the state can be imposed in a linear fashion in the proposed mpc scheme similarly cost functions nonlinear in the state variable can be handled in a linear fashion we treat both the full state measurement case and the input output case as well as systems with disturbances noise numerical examples demonstrate the approach

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

unconstrained receding horizon control of nonlinear systems it is well known that unconstrained infinite horizon optimal control may be used to construct a stabilizing controller for a nonlinear system we show that similar stabilization results may be achieved using unconstrained finite horizon optimal control the key idea is to approximate the tail of the infinite horizon cost to go using as terminal cost an appropriate control lyapunov function roughly speaking the terminal control lyapunov function clf should provide an incremental upper bound on the cost in this fashion important stability characteristics may be retained without the use of terminal constraints such as those employed by a number of other researchers the absence of constraints allows a significant speedup in computation furthermore it is shown that in order to guarantee stability it suffices to satisfy an improvement property thereby relaxing the requirement that truly optimal trajectories be found we provide a complete analysis of the stability and region of attraction operation properties of receding horizon control strategies that utilize finite horizon approximations in the proposed class it is shown that the guaranteed region of operation contains that of the clf controller and may be made as large as desired by increasing the optimization horizon restricted of course to the infinite horizon domain moreover it is easily seen that both clf and infinite horizon optimal control approaches are limiting cases of our receding horizon strategy the key results are illustrated using a familiar example the inverted pendulum where significant improvements in guaranteed region of operation and cost are noted

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

brief paper distributed model predictive control of dynamically decoupled systems with coupled cost this paper considers the distributed model predictive control dmpc of systems with interacting subsystems having decoupled dynamics and constraints but coupled costs an easily verifiable constraint is introduced to ensure asymptotic stability of the overall system in the absence of disturbance the constraint introduced has a parameter which allows for the performance of the dmpc system to approach that controlled by a centralized model predictive controller when the subsystems are linear and additive disturbance is present the added constraint ensures the state of each subsystem converges to its respective minimal disturbance invariant set the approach is demonstrated via several numerical examples

moving horizon control of linear systems with input saturation and plant uncertainty part 2 disturbance rejection and tracking we present a moving horizon feedback system based on constrained optimal control algorithms for linear plants with input saturation the system is a non conventional sampled data system its sampling periods vary from sampling instant to sampling instant and the control during the sampling time is not constant but determined by the solution of an open loop optimal control problem in part 1 we showed that the proposed moving horizon control system is robustly stable in this paper we show that it is capable of asymptotically suppressing a class of l bounded disturbances that are restricted to a subspace and of asymptotically following a class of reference inputs that are continuously differentiable bounded in magnitude and slope and restricted to a subspace

moving horizon control of linear systems with input saturation and plant uncertainty part 1 robustness we present a moving horizon feedback system based on constrained optimal control algorithms for linear plants with input saturation the system is a non conventional sampled data system its sampling periods vary from sampling instant to sampling instant and the control during the sampling time is not constant but determined by the solution of an open loop optimal control problem this is a two part paper in this part we show that the proposed moving horizon control system is robustly stable whether the state of the plant is measurable or not in the second part we show that the proposed moving horizon control system is capable of following a class of reference inputs and suppressing a class of disturbances experimental results show that the behaviour of the moving horizon control system is superior to that resulting from some alternative control laws

some approximation results by p q analogue of bernstein stancu operators in this paper we introduce a new analogue of bernstein stancu operators based on p q integers which we call as p q bernstein stancu operators we study approximation properties for these operators based on korovkin s type approximation theorem and also study some direct theorems furthermore we give comparisons and some illustrative graphics for the convergence of operators to some function

barrier lyapunov functions based adaptive control for a class of nonlinear pure feedback systems with full state constraints in this study an adaptive control technique is developed for a class of uncertain nonlinear parametric systems the considered systems can be viewed as a class of nonlinear pure feedback systems and the full state constraints are strictly required in the systems one remarkable advantage is that only less adjustable parameters are used in the design this advantage is first to take into account the pure feedback systems with the full state constraints the characteristics of the considered systems will lead to a difficult task for designing a stable controller to this end the mean value theorem is employed to transform the pure feedback systems to a strict feedback structure but non affine terms still exist for the transformed systems a novel recursive design procedure is constructed to remove the difficulties for avoiding non affine terms and guarantee that the full state constraints are not violated by introducing barrier lyapunov function blf with the error variables moreover it is proved that all the signals in the closed loop system are global uniformly bounded and the tracking error is remained in a bounded compact set two simulation studies are worked out to show the effectiveness of the proposed approach

receding horizon control of nonlinear systems the receding horizon control strategy provides a relatively simple method for determining feedback control for linear or nonlinear systems the method is especially useful for the control of slow nonlinear systems such as chemical batch processes where it is possible to solve sequentially open loop fixed horizon optimal control problems online the method has been shown to yield a stable closed loop system when applied to time invariant or time varying linear systems it is shown that the method also yields a stable closed loop system when applied to nonlinear systems

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

simultaneous nonlinear model predictive control and state estimation an output feedback approach to model predictive control that combines state estimation and control into a single minmax optimization is introduced for discrete time nonlinear systems specifically a criterion that involves finite forward and backward horizons is minimized with respect to control input variables and is maximized with respect to the unknown initial state as well as disturbance and measurement noise variables under appropriate assumptions that encode controllability and observability we show that the state of the closed loop remains bounded and that a bound on tracking error can be found for trajectory tracking problems we also introduce a primaldual interior point method that can be used to efficiently solve the minmax optimization problem and show in simulation examples that the method succeeds even for severely nonlinear and non convex problems

schur products and matrix completions we prove that a necessary and sufficient condition for a given partially positive matrix to have a positive completion is that a certain schur product map defined on a certain subspace of matrices is a positive map by analyzing the positive elements of this subspace we obtain new proofs of the results of h dym and i gohberg and grone johnson sa and wolkowitz linear algebra appl 58 1984 109 124 linear algebra appl 36 1981 1 24 we also obtain a new proof of a result of u haagerup decomposition of completely bounded maps on operation algebras preprint characterizing the norm of schur product maps and a new hahn banach type extension theorem for these maps finally we obtain generalizations of many of these results to matrices of operators which we apply to the study of representations of certain subalgebras of the n n matrices

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

tauberian conditions under which statistical convergence follows from statistical summability c 1 abstract j a fridly and m k khan have recently extended hardy s and landau s tauberian theorems to the case of statistical convergence which was introduced by h fast in 1951 let x k k 0 1 2 be a sequence of real or complex numbers and set n n 1 1 nk 0xk for n 0 1 2 we present necessary and sufficient conditions under which st limxk l follows from st lim n l where l is a finite number if xk is a sequence of real numbers then these are one sided tauberian conditions if xk is a sequence of complex numbers then these are two sided tauberian conditions in particular our conditions are satisfied if xk is statistically slowly decreasing or increasing in the case of real sequences or if xk is statistically slowly oscillating in the case of complex sequences even these special sufficient conditions imply those given by fridy and khan

robust receding horizon control of constrained nonlinear systems we present a method for the construction of a robust dual mode receding horizon controller which can be employed for a wide class of nonlinear systems with state and control constraints and model error the controller is dual mode in a neighborhood of the origin the control action is generated by a linear feedback controller designed for the linearized system outside this neighborhood receding horizon control is employed existing receding horizon controllers for nonlinear continuous time systems which are guaranteed to stabilize the nonlinear system to which they are applied require the exact solution at every instant of an optimal control problem with terminal equality constraints these requirements are considerably relaxed in the dual mode receding horizon controller presented in this paper stability is achieved by imposing a terminal inequality rather than an equality constraint only approximate minimization is required a variable time horizon is permitted robustness is achieved by employing conservative state and stability constraint sets thereby permitting a margin of error the resultant dual mode controller requires considerably less online computation than existing receding horizon controllers for nonlinear constrained systems

statistical approximation for new positive linear operators of lagrange type abstract in this paper we prove some approximation results in statistical sense and establish some direct theorems for the positive linear operators constructed by the means of lagrange type polynomials we compute error estimation by using modulus of continuity with the help of matlab and give its algorithm furthermore we show graphically the convergence of our operators to various functions

discrete time stability with perturbations application to model predictive control exponential stability and asymptotic perturbed stability results are derived for nonlinear discrete time systems some related results are available in the literature but proofs for the discrete time case are difficult to find our motivation for obtaining these results was to determine conditions under which discrete time nonlinear model predictive control is stabilizing in the face of perturbations this problem has particular relevance when output rather than state feedback is used a nonlinear state estimator is then required to reconstruct the state and it is necessary to identify the class of reconstruction errors for which the cascaded estimator controller assembly is stabilizing

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

weighted statistical convergence and its application to korovkin type approximation theorem abstract the concept of weighted statistical convergence was introduced and studied by karakaya and chishti 2009 7 in this paper we modify the definition of weighted statistical convergence and find its relationship with the concept of statistical summability n p n due to moricz and orhan 2004 10 we apply this new summability method to prove a korovkin type approximation theorem by using the test functions 1 e x e 2 x we apply the classical baskakov operator to construct an example in support of our result

distributed satisficing mpc with guarantee of stability this technical note develops conditions for the closed loop stability of a new class of cooperative distributed model predictive control called satisficing whereby the relative importance of each controller changes dynamically depending on the prevailing conditions instead of being adjusted a priori in the satisficing approach the less satisfied controller will gain more importance the main properties of the proposed approach are illustrated with an unstable dynamic system composed of three subsystems

robust constrained model predictive control using linear matrix inequalities abstract the primary disadvantage of current design techniques for model predictive control mpc is their inability to deal explicitly with plant model uncertainty in this paper we present a new approach for robust mpc synthesis that allows explicit incorporation of the description of plant uncertainty in the problem formulation the uncertainty is expressed in both the time and frequency domains the goal is to design at each time step a state feedback control law that minimizes a worst case infinite horizon objective function subject to constraints on the control input and plant output using standard techniques the problem of minimizing an upper bound on the worst case objective function subject to input and output constraints is reduced to a convex optimization involving linear matrix inequalities lmis it is shown that the feasible receding horizon state feedback control design robustly stabilizes the set of uncertain plants several extensions such as application to systems with time delays problems involving constant set point tracking trajectory tracking and disturbance rejection which follow naturally from our formulation are discussed the controller design is illustrated with two examples

worst case formulations of model predictive control for systems with bounded parameters two different predictive control formulations are developed based on minimization of the worst case quadratic cost for systems with bounded parameters the two formulations differ on the assumptions made about the future inputs in optimizing the current input one assumes open loop control while the other considers closed loop control their closed loop properties such as asymptotic stability are examined we then focus on a moving average model with an integrator and derive computationally simpler suboptimal algorithms

an approach to output feedback mpc of stochastic linear discrete time systems in this paper we propose an output feedback model predictive control mpc algorithm for linear discrete time systems affected by a possibly unbounded additive noise and subject to probabilistic constraints in case the noise distribution is unknown the probabilistic constraints on the input and state variables are reformulated by means of the chebyshev cantelli inequality the recursive feasibility is guaranteed the convergence of the state to a suitable neighbor of the origin is proved under mild assumptions and the implementation issues are thoroughly addressed two examples are discussed in detail with the aim of providing an insight into the performance achievable by the proposed control scheme

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

bilateral generating functions for the erkus srivastava polynomials and the generalized lauricella functions abstract in some recent investigations involving differential operators for the generalized lagrange polynomials chan et al w c c chan c j chyan h m srivastava the lagrange polynomials in several variables integral transforms spec funct 12 2001 139 148 encountered and proved a certain summation identity for the lagrange polynomials in several variables which are popularly known in the literature as the chan chyan srivastava polynomials in the present paper we investigate several families of bilateral generating functions for the erkus srivastava polynomials which are more general than the chan chyan srivastava polynomials and the srivastava daoust or generalized lauricella functions

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

decentralized adaptive control of interconnected systems the adaptive control of a class of large scale systems formed of an arbitrary interconnection of subsystems with unknown parameters nonlinearities and bounded disturbances is investigated it is first shown that no matter how weak the interconnections are a decentralized adaptive control scheme can become unstable approaches are then developed for stabilization and tracking using new decentralized adaptive controllers in the case where the relative degree n of the transfer function of each decoupled subsystem is less than or equal to two sufficient conditions are established which guarantee boundedness and exponential convergence of the state and parameter errors to bounded residual sets in the absence of disturbances and interconnections the decentralized adaptive control schemes guarantee exact convergence of the tracking errors to zero the effectiveness of the proposed adaptive schemes is demonstrated using a simple example

brief paper a predictive controller with artificial lyapunov function for linear systems with input state constraints this paper copes with the problem of satisfying input and or state hard constraints in set point tracking problems stability is guaranteed by synthesizing a lyapunov quadratic function for the system and by imposing that the terminal state lies within a level set of the function procedures to maximize the volume of such an ellipsoidal set are provided and interiorpoint methods to solve on line optimization are considered

on p q analogue of bernstein operators in this paper we introduce a new analogue of bernstein operators and we call it as p q bernstein operators which is a generalization of q bernstein operators we also study approximation properties based on korovkin s type approximation theorem of p q bernstein operators and establish some direct theorems furthermore we show comparisons and some illustrative graphics for the convergence of operators to a function

technical communique stabilizing decentralized model predictive control of nonlinear systems this note presents a stabilizing decentralized model predictive control mpc algorithm for nonlinear discrete time systems no information is assumed to be exchanged between local control laws the stability proof relies on the inclusion of a contractive constraint in the formulation of the mpc problem

weighted statistical approximation by kantorovich type q szasz mirakjan operators abstract in the present paper we introduce a kantorovich type modification of q szasz mirakjan operators and obtain weighted statistical approximation properties of these operators also for introduced operators we give a voronovskaja type theorem related to q derivatives

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

brief paper on receding horizon feedback control receding horizon feedback control rhfc was originally introduced as an easy method for designing stable state feedback controllers for linear systems here those results are generalized to the control of nonlinear autonomous systems and we develop a performance index which is minimized by the rhfc inverse optimal control problem previous results for linear systems have shown that desirable nonlinear controllers can be developed by making the rhfc horizon distance a function of the state that functional dependence was implicit and difficult to implement on line here we develop similar controllers for which the horizon distance is an easily computed explicit function of the state

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

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

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

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

a polyhedral method for solving sparse polynomial systems a continuation method is presented for computing all isolated roots of a semimixed sparse system of polynomial equations we introduce mixed subdivisions of newton polytopes and we apply them to give a new proof and algorithm for bernstein s theorem on the expected number of roots this results in a numerical homotopy with the optimal number of paths to be followed in this homotopy there is one starting system for each cell of the mixed subdivision and the roots of these starting systems are obtained by an easy combinatorial construction

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

on the robustness of receding horizon control with terminal constraints robustness properties of nonlinear receding horizon controllers with zero terminal state constraints are investigated with respect to gain and additive perturbations some robustness margins are derived by extending to the receding horizon case the analysis originally proposed by geromel and da cruz for infinite horizon controllers in the linear case it is shown that the zero terminal state receding horizon controller exhibits worse robustness margins compared to standard infinite horizon lq control

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

brief paper set membership approximation of discontinuous nonlinear model predictive control laws in this paper the use of set membership sm methods is investigated in order to derive off line an approximation of a discontinuous nonlinear model predictive control nmpc law the approximating function can then be evaluated on line instead of solving the nonlinear program embedded in the nmpc scheme this way a significant decrease of computational times may be obtained thus allowing the application of nmpc also to systems with fast dynamics it is shown that the knowledge of the discontinuities is needed to achieve an approximated controller with arbitrarily small approximation error by exploiting such a knowledge sm techniques already developed for the case of continuous nmpc laws are generalized in order to approximate discontinuous ones the stability of the origin of the closed loop system with the approximated control law is analyzed and a numerical example is employed to illustrate the features of the proposed approach

stability of a truncated infinite constrained receding horizon scheme the general discrete nonlinear case some results concerning the constrained receding horizon formulation with infinite and truncated prediction horizon are presented in this formulation a distinction is made between prediction and control horizons the main result is a generalization of a known fact for linear systems namely that under certain technical requirements the asymptotic stability of the above formulation holds for a sufficiently large finite prediction horizon existence results are also provided under stabilizability assumptions

robust model predictive control of stable linear systems a new robust model predictive control mpc algorithm is presented for stable constrained linear plants that is a direct generalization of the nominally stabilizing regulator presented by rawlings and muske model uncertainty is parametrized by a list of possible plants robust stability is achieved through the addition of constraints that prevent the sequence of optimal controller costs from increasing for the true plant asymptotic stability is demonstrated through a lyapunov argument simulation experiments demonstrate the performance of the algorithm for two example processes

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

brief paper control of nonlinear systems with time varying output constraints this paper presents control design for strict feedback nonlinear systems with time varying output constraints an asymmetric time varying barrier lyapunov function blf is employed to ensure constraint satisfaction by allowing the barriers to vary with the desired trajectory in time the initial condition requirements are relaxed through a change of tracking error coordinates we eliminate the explicit dependence of the blf on time thereby simplifying the analysis of constraint satisfaction we show that asymptotic output tracking is achieved without violation of the output constraint and also quantify the transient performance bound as a function of time that converges to zero to handle parametric model uncertainty we present an adaptive controller that ensures constraint satisfaction during the transient phase of online parameter adaptation the performance of the proposed control is illustrated through a simulation example

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 desirability of acyclic database schemes a class of database schemes called acychc was recently introduced it is shown that this class has a number of desirable properties in particular several desirable properties that have been studied by other researchers m very different terms are all shown to be eqmvalent to acydicity in addition several equivalent charactenzauons of the class m terms of graphs and hypergraphs are given and a smaple algorithm for determining acychclty is presented also given are several eqmvalent characterizations of those sets m of multivalued dependencies such that m is the set of murlvalued dependencies that are the consequences of a given join dependency several characterizations for a conflict free in the sense of lien set of muluvalued dependencies are provided

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