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

dual mode predictive control algorithm for constrained hammerstein systems in the process industry there exist many systems which can be approximated by a hammerstein model moreover these systems are usually subjected to input magnitude constraints in this paper a multi channel identification algorithm mcia is proposed in which the coefficient parameters are identified by least squares estimation lse together with a singular value decomposition svd technique compared with traditional single channel identification algorithms the present method can enhance the approximation accuracy remarkably and provide consistent estimates even in the presence of coloured output noises under relatively weak assumptions on the persistent excitation pe condition of the inputs then to facilitate the following controller design this mcia is converted into a two stage single channel identification algorithm ts scia which preserves most of the advantages of mcia with this ts scia as the inner model a dual mode non linear model predictive control nmpc algorithm is developed in detail over a finite horizon an optimal input profile found by solving a open loop optimal control problem drives the non linear system state into the terminal invariant set afterwards a linear output feedback controller steers the state to the origin asymptotically in contrast to the traditional algorithms the present method has a maximal stable region a better steady state performance and a lower computational complexity finally simulation results on a heat exchanger are presented to show the efficiency of both the identification and the control algorithms

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

robust model predictive control of singular systems this note is concerned with model predictive control for linear singular systems with time varying uncertainties a piecewise constant control sequence is calculated by minimizing the worst case linear quadratic objective function at each sample time the sufficient conditions on the existence of the model predictive control are derived and expressed as linear matrix inequalities the robust stability of the closed loop systems is guaranteed by the proposed design method

brief paper stochastic tube mpc with state estimation an output feedback model predictive control mpc strategy for linear systems with additive stochastic disturbances and probabilistic constraints is proposed given the probability distributions of the disturbance input the measurement noise and the initial state estimation error the distributions of future realizations of the constrained variables are predicted using the dynamics of the plant and a linear state estimator from these distributions a set of deterministic constraints is computed for the predictions of a nominal model the constraints are incorporated in a receding horizon optimization of an expected quadratic cost which is formulated as a quadratic program the constraints are constructed so as to provide a guarantee of recursive feasibility and the closed loop system is stable in a mean square sense all uncertainties in this paper are taken to be bounded in most control applications this gives a more realistic representation of process and measurement noise than the more traditional gaussian assumption

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

time optimal model predictive control for linear systems based on ellipsoidal and polytopic sets time optimal model predictive control mpc strategies are investigated in this paper we first derive a series of controllable sets described by ellipsoids or convex polytopes offline then obtain

input to state stability of efficient robust h mpc scheme for nonlinear systems propose an efficient constrained h nmpc with guaranteed iss w r t bounded disturbances use piecewise affine h control and augmented pldi models to decrease conservatism of nmpc use pldi method to turn the non convex min max problem into a semi definite programming present a sufficient condition in form of lmis to ensure the iss of the proposed nmpc scheme apply the proposed nmpc to some fast systems such as mass carts and vehicular platoon in this work we present an efficient h model predictive control mpc scheme with guaranteed input to state stability iss for constrained nonlinear systems subject to unknown but bounded disturbances the nonlinear system is represented by using some given inclusion polytope the notion of iss is introduced to derive the sufficient condition in terms of linear matrix inequalities lmis which ensures the iss of the closed loop system in order to reduce the online computational demand of mpc the non convex min max optimization problem is converted to a minimization problem in form of lmis a suboptimal mpc algorithm is then addressed to further decrease the computational demand the applicability of the proposed results is illustrated by two numerical examples of a mass cart and a vehicular platoon

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

robust triple mode mpc this paper reviews triple mode predictive control for linear time invariant systems and then proposes a new algorithm for robust triple mode predictive control for constrained linear systems described by polytopic uncertainty models the approach significantly enlarges the feasibility region compared to recently proposed robust dual mode approaches the efficacy of the approach is demonstrated with numerical examples

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

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

constrained predictive control of linear distributed parameter systems the model predictive control problem with guaranteed stability for a class of linear distributed parameter systems with simultaneous amplitude and rate control constraints is investigated the approach is developed using a finite dimensional input output modelling technique for distributed parameter systems based on a distributed output projection onto a finite basis set the paper employs a dual mode prediction strategy in conjunction with the projection based state space system description and proposes algorithms for the design of polyhedral positive invariant and feasible sets which serve as terminal target sets for predicted states an extension to predictive control with integral action is described the proposed algorithms are shown to work well by means of both simulations and experimental results

t s model based nonlinear moving horizon h control and applications using a t s fuzzy model we propose a formulation for a moving horizon h control problem for nonlinear systems our main contribution is combination of t s fuzzy models and a moving horizon h control scheme by chen and scherer to address the disturbance attenuation of nonlinear constrained system a sufficient condition for the disturbance amplitude is given to guarantee the feasibility of the optimization problem at each time a parameter dependent state feedback control law is adopted and the corresponding optimization problem is reduced to a convex optimization problem involving linear matrix inequalities lmis the h attenuation index for the nonlinear moving horizon h control problem is adapted online to satisfy time domain constraints finally the effectiveness of the proposed scheme is successfully demonstrated by control of a continuous stirred tank reactor and active queue management for routers

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

brief paper explicit use of probabilistic distributions in linear predictive control the guarantee of feasibility given feasibility at initial time is an issue that has been overlooked by many of the recent papers on stochastic model predictive control effective solutions have recently been proposed but these carry considerable online computational load and a degree of conservativism for the case that the elements of the random additive disturbance vector are independent the current paper ensures that probabilistic constraints are met and that a quadratic stability condition is satisfied a numerical example illustrates the efficacy of the proposed algorithm which achieves tight satisfaction of constraints and thereby attains near optimal performance

probabilistic tubes in linear stochastic model predictive control this paper considers constrained control of linear systems with additive and multiplicative stochastic uncertainty and linear input state constraints both hard and soft constraints are considered and bounds are imposed on the probability of soft constraint violation assuming the plant parameters to be finitely supported a method of constraint handling is proposed in which a sequence of tubes corresponding to a sequence of confidence levels on the predicted future plant state is constructed online around nominal state trajectories a set of linear constraints is derived by imposing bounds on the probability of constraint violation at each point on an infinite prediction horizon through constraints on one step ahead predictions a guarantee of the recursive feasibility of the online optimization ensures that the closed loop system trajectories satisfy both the hard and probabilistic soft constraints the approach is illustrated by a numerical example

model predictive control for systems with stochastic multiplicative uncertainty and probabilistic constraints abstract robust predictive control handles constrained systems that are subject to stochastic uncertainty but propagating the effects of uncertainty over a prediction horizon can be computationally expensive and conservative this paper overcomes these issues through an augmented autonomous prediction formulation and provides a method of handling probabilistic constraints and ensuring closed loop stability through the use of an extension of the concept of invariance namely invariance with probability p

a feedback theory of two degree of freedom optimal wiener hopf design the design of linear two degree of freedom stabilizing controllers is treated in a quadratic cost setting the class of all such controllers which give finite cost is established and the tradeoff possible between optimum performance tracking cost sensitivity and stability margins is discussed

receding horizon control strategies for constrained lpv systems based on a class of nonlinearly parameterized lyapunov functions in this technical note we present a receding horizon control rhc design method for linear parameter varying lpv systems subject to input and or state constraints based on a class of nonlinearly parameterized lyapunov functions recently introduced by guerra and vermeiren as it will be made clear their use gives rise to less conservative stabilizability conditions w r t those arising from quadratic lyapunov functions a workable convex optimization procedure is first presented for control design purposes which allows the synthesis of stabilizing scheduling state feedback control laws complying with the prescribed constraints this control design method is then arranged into a receding horizon framework and its feasibility and stability properties are carefully analyzed numerical comparisons with existing rhc methods for lpv systems are reported in the final example

constrained robust feedback model predictive control for uncertain systems with polytopic description for the constrained uncertain systems with polytopic description a new design method of robust feedback model predictive control is proposed by using a sequence of feedback control laws and designing the parameter dependent lyapunov function for each model the design method provides more degrees of freedom and then can improve the control performance and enlarge the feasible region based on the characteristic property of the design method an offline design algorithm is developed to reduce the mpc controller s online computation burden the numerical examples verify the effectiveness of the results presented in this article

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

constrained generalized predictive control a generalized predictive controller for systems with constrained input and output signals is presented the optimum values of the future control signals are obtained by transforming the quadratic optimization problem into a linear complementarity problem a simple algorithm to decrease the number of constraints and a modification to a standard algorithm for solving the linear complementarity problem are proposed in order to reduce the amount of computation required

a limiting absorption principle for schrodinger operators with generalized von neumann wigner potentials ii the proof in this series of papers we prove the limiting absorption principle over a given interval for a class of hamiltonians which contains the original one of von neumann and wigner more specifically the hamiltonians are of the form c sin b x x v x where 2 3 1 v x is a short range potential and i is a given compact subinterval of the open positive axis which does not contain the pointb2 4

explicit reference governor for constrained nonlinear systems this technical note introduces a novel control law that dynamically modifies the reference of a pre compensated nonlinear system to ensure the satisfaction of constraints this is done by translating the state space constraints into an upper bound on the value of the lyapunov function and by manipulating the velocity of the applied reference to enforce this bound the main advantage of this approach is that it systematically provides a closed form control law able to enforce constraints the theory is introduced for general nonlinear systems subject to constraints and is then specialized to the large and highly relevant class of nonlinear systems admitting a lyapunov function lower bounded by a quadratic form and subject to linear constraints numerical simulations show the effectiveness of the proposed method

technical communique improving off line approach to robust mpc based on nominal performance cost this paper gives two alternative off line synthesis approaches to robust model predictive control rmpc for systems with polytopic description in each approach a sequence of explicit control laws that correspond to a sequence of nested asymptotically invariant ellipsoids are constructed off line in order to accommodate a wider class of systems nominal performance cost is chosen to substitute the worst case one in an existing technique in the design of control law for a larger ellipsoid the second approach further incorporates the knowledge of control laws associated with all smaller ellipsoids so as to further improve feasibility and optimality the effectiveness of the alternative approaches is illustrated by a simulation example

brief optimizing the end point state weighting matrix in model based predictive control in this paper a linear model based predictive control mpc algorithm is presented for which nominal closed loop stability is guaranteed the input is obtained by minimizing a quadratic performance index over a finite horizon plus an end point state eps penalty subject to input state and output constraints under certain conditions the weighting matrix in the eps penalty enables one to specify an invariant ellipsoid in which the input state and output constraints are satisfied in existing mpc algorithms this weighting matrix is calculated off line the main contribution of this paper is to incorporate the calculation of the eps weighting matrix into the on line optimization problem of the controller the main advantage of this approach is that a natural and automatic trade off between feasibility and optimality is obtained this is demonstrated in a simulation example

efficient robust predictive control predictive constrained control of time varying and or uncertain linear systems has been effected through the use of ellipsoidal invariant sets kothare et al 1996 linear matrix inequalities lmis have been used to design a state dependent state feedback law that maintains the state vector inside invariant feasible sets for the purposes of prediction however at each time instant the state feedback law is assumed constant in addition due to the large number of lmis involved online computation becomes intractable for anything other than small dimensional systems here we propose an approach that deploys a fixed state feedback law but introduces extra degrees of freedom through the use of perturbations on the fixed state feedback law the problem is so formulated that all demanding computations can be performed offline leaving only a simple optimization problem to be solved online over and above the very significant reduction in computational cost the extra degrees of freedom allow for better performance and wider applicability

robust stability in constrained predictive control through the youla parameterisations in this article we take advantage of the primary and dual youla parameterisations to set up a soft constrained model predictive control mpc scheme in this framework it is possible to guarantee stability in face of norm bounded uncertainties under special conditions guarantees are also given for hard input constraints in more detail we parameterise the mpc predictions in terms of the primary youla parameter and use this parameter as the on line optimisation variable the uncertainty is parameterised in terms of the dual youla parameter stability can then be guaranteed through small gain arguments on the loop consisting of the primary and dual youla parameter this is included in the mpc optimisation as a constraint on the induced gain of the optimisation variable we illustrate the method with a numerical simulation example

robust digital model predictive control for linear uncertain systems with saturations actuator saturation constraint is inevitable in industrial process in this note we consider a discrete receding horizon control a piecewise constant robust model predictive control for a continuous time plant with actuator saturation constraint through a sampled data control approach the solution is formulated as an optimization problem subject to linear matrix inequalities a numerical example is used to demonstrate the effectiveness of the proposed design procedure

an interpolation strategy for discrete time bilinear mpc problems input output i o feedback linearization suffers from a number of restrictions which have limited its use in model based predictive control some of these restrictions do not apply to the case of bilinear systems but problems with input constraints and unstable zero dynamics persist this paper overcomes these difficulties by means of an interpolation strategy involved in this interpolation is a feasible and stabilizing trajectory which is computed through the use of invariant feasible sets and a more aggressive trajectory which can be chosen to be either the unconstrained optimal trajectory or any alternative one

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

convex liftings based robust control design this paper presents a new approach for control design of constrained linear systems affected by bounded additive disturbances and polytopic uncertainties this method hinges on so called convex liftings which emulate control lyapunov function by providing a constructive framework for optimization based control implementation it will be shown that this method can guarantee the recursive feasibility and robust stability finally a numerical example will be presented to illustrate this method