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Mayuresh V. Kothare - One of the best experts on this subject based on the ideXlab platform.
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Comments on: “Efficient robust Constrained Model predictive control with a time varying terminal constraint set” by Wan and Kothare
Systems & Control Letters, 2006Co-Authors: Z. Wan, Bert Pluymers, Mayuresh V. Kothare, B. De MoorAbstract:Abstract We present an algorithm that modifies the original formulation proposed in Wan and Kothare [Efficient robust Constrained Model predictive control with a time-varying terminal constraint set, Systems Control Lett. 48 (2003) 375–383]. The modified algorithm can be proved to be robustly stabilizing and preserves all the advantages of the original algorithm, thereby overcoming the limitation pointed out recently by Pluymers et al. [Min–max feedback MPC using a time-varying terminal constraint set and comments on “Efficient robust Constrained Model predictive control with a time-varying terminal constraint set”, Systems Control Lett. 54 (2005) 1143–1148].
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efficient robust Constrained Model predictive control with a time varying terminal constraint set
Systems & Control Letters, 2003Co-Authors: Mayuresh V. KothareAbstract:Abstract An efficient robust Constrained Model predictive control algorithm with a time varying terminal constraint set is developed for systems with Model uncertainty and input constraints. The approach is novel in that it off-line constructs a continuum of terminal constraint sets and on-line achieves robust stability by using a relatively short control horizon (even N =0) with a time varying terminal constraint set. This algorithm not only dramatically reduces the on-line computation but also significantly enlarges the size of the allowable set of initial conditions. Moreover, this control scheme retains the unConstrained optimal performance in the neighborhood of the equilibrium. The controller design is illustrated through a benchmark problem.
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robust Constrained Model predictive control using linear matrix inequalities
Automatica, 1996Co-Authors: Mayuresh V. Kothare, V Balakrishnan, Manfred MorariAbstract: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.
Manfred Morari - One of the best experts on this subject based on the ideXlab platform.
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soft Constrained Model predictive control with robust stability guarantees
IEEE Transactions on Automatic Control, 2014Co-Authors: Melanie N Zeilinger, Manfred Morari, Colin N JonesAbstract:Soft Constrained Model predictive control (MPC) is frequently applied in practice in order to ensure feasibility of the optimization during online operation. Standard techniques offer global feasibility by relaxing state or output constraints, but cannot ensure closed-loop stability. This paper presents a new soft Constrained MPC approach for tracking that provides stability guarantees even for unstable systems. Two types of soft constraints and slack variables are proposed to enlarge the terminal constraint and relax the state constraints. The approach ensures feasibility of the MPC problem in a large region of the state space, depending on the imposed hard constraints, and stability is guaranteed by design. The optimal performance of the MPC control law is preserved whenever all state constraints can be enforced. Asymptotic stability of all feasible reference steady-states under the proposed control law is shown, as well as input-to-state stability for the system under additive disturbances. The soft Constrained method can be combined with a robust MPC approach, in order to exploit the benefits of both techniques. The properties of the proposed methods are illustrated by numerical examples.
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An improved discrete-time robust approach for Constrained Model predictive control
2001 European Control Conference (ECC), 2001Co-Authors: Francesco Alessandro Cuzzola, Jose C. Geromel, Manfred MorariAbstract:In this paper we present a new technique to face the so-called Constrained Model Predictive Control. The main advantage of this new approach with respect to other well-known techniques is represented by the reduced conservativeness. More precisely, the technique described in this paper can be applied to polytopic uncertain systems and is based on the use of several Lyapunov functions each one corresponding to a different vertex of the uncertainty's polytope.
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robust Constrained Model predictive control using linear matrix inequalities
Automatica, 1996Co-Authors: Mayuresh V. Kothare, V Balakrishnan, Manfred MorariAbstract: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.
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robust stability of Constrained Model predictive control
American Control Conference, 1993Co-Authors: Zhi Q Zheng, Manfred MorariAbstract:A new design technique for a robust Model predictive controller is proposed using an uncertainty description expressed in the time-domain. Robust stability of the resulting closed-loop system is guaranteed for a set of Finite Impulse Response (FIR) Models. Both necessary and sufficient conditions for asymptotic stability are stated. If the uncertainty is described as lower and upper bounds on impulse response coefficients, then the resulting optimization problem can be cast as a linear program of moderate size.
B.h. Krogh - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear stability-Constrained Model predictive control with input and state constraints
Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207), 1998Co-Authors: Xu Cheng, B.h. KroghAbstract:In stability-Constrained Model predictive control (SCMPC) a stability constraint is propagated from stage to stage to limit magnitude of the state vector in a controllable form. For the unConstrained case, a sufficient condition that can be easily evaluated guarantees the stability constraint is a feasible contraction mapping. This paper presents sufficient conditions for guaranteed asymptotic stability when SCMPC is applied to nonlinear systems with arbitrary constraints on the control and state.
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Stability Constrained Model predictive control for nonlinear systems
Proceedings of the 36th IEEE Conference on Decision and Control, 1Co-Authors: Xu Cheng, B.h. KroghAbstract:A new method for nonlinear Model predictive control with guaranteed stability is proposed as an extension to the stability Constrained Model predictive control (SCMPC) for linear time-invariant systems. The method applies to a class of nonlinear systems that can be transformed to a controllable companion form and depends on the existence of a nonlinear deadbeat control (although this is not necessarily the control that is used). Asymptotic stability is proved for the case when all state variables are measurable.
Juan P. Garrahan - One of the best experts on this subject based on the ideXlab platform.
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dynamics and large deviation transitions of the xor fredrickson andersen kinetically Constrained Model
arXiv: Statistical Mechanics, 2020Co-Authors: Luke Causer, Igor Lesanovsky, Mari Carmen Banuls, Juan P. GarrahanAbstract:We study a one-dimensional classical stochastic kinetically Constrained Model (KCM) inspired by Rydberg atoms in their "facilitated" regime, where sites can flip only if a single of their nearest neighbours is excited. We call this Model "XOR-FA" to distinguish it from the standard Fredrickson-Andersen (FA) Model. We describe the dynamics of the XOR-FA Model, including its relation to simple exclusion processes in its domain wall representation. The interesting relaxation dynamics of the XOR-FA is related to the prominence of large dynamical fluctuations that lead to phase transitions between active and inactive dynamical phases as in other KCMs. By means of numerical tensor network methods we study in detail such transitions in the dynamical large deviation regime.
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Renormalization group study of a kinetically Constrained Model for strong glasses.
Physical Review E, 2005Co-Authors: Stephen Whitelam, Ludovic Berthier, Juan P. GarrahanAbstract:We derive a dynamic field theory for a kinetically Constrained Model, based on the Fredrickson-Andersen Model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d>/=2 , the behavior of the Model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We argue that in d=1 its behavior is that of compact directed percolation. We perform detailed numerical simulations of the corresponding Fredrickson-Andersen Model on the lattice in various dimensions, and find reasonable quantitative agreement with the field theory predictions.
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Renormalization group study of a kinetically Constrained Model for strong glasses
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2005Co-Authors: Stephen Whitelam, Ludovic Berthier, Juan P. GarrahanAbstract:We derive a dynamic field theory for a kinetically Constrained Model, based on the Fredrickson--Andersen Model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d \\geq 2, the behaviour of the Model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We argue that in d=1 its behaviour is that of compact directed percolation. We perform detailed numerical simulations of the corresponding Fredrickson-Andersen Model on the lattice in various dimensions, and find reasonable quantitative agreement with the field theory predictions.
Stephen Whitelam - One of the best experts on this subject based on the ideXlab platform.
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Two-stage coarsening mechanism in a kinetically Constrained Model of an attractive colloid.
Physical Review E, 2006Co-Authors: Stephen Whitelam, Phillip L. GeisslerAbstract:We study an attractive version of the East Model using the real-space renormalization group (RG) introduced by Stella et al. The former is a kinetically Constrained Model with an Ising-like interaction between excitations and shows striking agreement with the phenomonology of attractive colloidal systems. We find that the RG predicts two nonuniversal dynamic exponents, which suggests that in the out-of-equilibrium regime the Model coarsens via a two-stage mechanism. We explain this mechanism physically and verify this prediction numerically. In addition, we predict that the characteristic relaxation time of the Model is a nonmonotonic function of attraction strength, again in agreement with numerical results.
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Renormalization group study of a kinetically Constrained Model for strong glasses.
Physical Review E, 2005Co-Authors: Stephen Whitelam, Ludovic Berthier, Juan P. GarrahanAbstract:We derive a dynamic field theory for a kinetically Constrained Model, based on the Fredrickson-Andersen Model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d>/=2 , the behavior of the Model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We argue that in d=1 its behavior is that of compact directed percolation. We perform detailed numerical simulations of the corresponding Fredrickson-Andersen Model on the lattice in various dimensions, and find reasonable quantitative agreement with the field theory predictions.
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Renormalization group study of a kinetically Constrained Model for strong glasses
Physical Review E : Statistical Nonlinear and Soft Matter Physics, 2005Co-Authors: Stephen Whitelam, Ludovic Berthier, Juan P. GarrahanAbstract:We derive a dynamic field theory for a kinetically Constrained Model, based on the Fredrickson--Andersen Model, which we expect to describe the properties of an Arrhenius (strong) supercooled liquid at the coarse-grained level. We study this field theory using the renormalization group. For mesoscopic length and time scales, and for space dimension d \\geq 2, the behaviour of the Model is governed by a zero-temperature dynamical critical point in the directed percolation universality class. We argue that in d=1 its behaviour is that of compact directed percolation. We perform detailed numerical simulations of the corresponding Fredrickson-Andersen Model on the lattice in various dimensions, and find reasonable quantitative agreement with the field theory predictions.