K.I. Kouramas

Imperial College London, Londinium, England, United Kingdom

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Publications (28)12 Total impact

  • [Show abstract] [Hide abstract]
    ABSTRACT: A new algorithm for robust explicit/multi-parametric Model Predictive Control (MPC) for uncertain, linear discrete-time systems is proposed. Based on previous work on Dynamic Programming (DP), multi-parametric Programming and Robust Optimization, the proposed algorithm features, (i) a DP reformulations of the MPC optimization problem, (ii) a robust reformulation of the constraints, and (iii) a multi-parametric programming step, where the control variables are obtained as explicit functions of the state variable, such that the state and input constraints are satisfied for all admissible values of the uncertainty. A key feature of the proposed procedure is that, as opposed to previous methods, it only solves a convex multi-parametric programming problem for each stage of the DP procedure.
    Automatica. 02/2013; 49(2):381–389.
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    ABSTRACT: We present an analytical dynamic model and a general framework for the optima control design of a PEM fuel cell system. The mathematical model consists of a detailed model for the PEM fuel cell stack and simplified models for the compressor, humidifier and cooling system. The framework features (i) a detailed dynamic process model, (ii) a reduced order approximating model obtained by performing dynamic simulations of the system and (iii) the design of an explicit/multi-parametric model predictive controller. The derived explicit/multi-parametric controller is tested and validated off-line on several operating conditions.
    Chemical Engineering Science 01/2012; 67(1):15-25. · 2.61 Impact Factor
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    ABSTRACT: This work presents a new algorithm for solving the explicit/multi-parametric model predictive control (or mp-MPC) problem for linear, time-invariant discrete-time systems, based on dynamic programming and multi-parametric programming techniques. The algorithm features two key steps: (i) a dynamic programming step, in which the mp-MPC problem is decomposed into a set of smaller subproblems in which only the current control, state variables, and constraints are considered, and (ii) a multi-parametric programming step, in which each subproblem is solved as a convex multi-parametric programming problem, to derive the control variables as an explicit function of the states. The key feature of the proposed method is that it overcomes potential limitations of previous methods for solving multi-parametric programming problems with dynamic programming, such as the need for global optimization for each subproblem of the dynamic programming step.
    Automatica. 08/2011; 47(8):1638–1645.
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    ABSTRACT: In this work, we demonstrate how constrained Moving Horizon Estimation (MHE) and Model Predictive Control (MPC) can be simultaneously addressed via multi-parametric programming. First, we present a method for obtaining the error dynamics of constrained MHE for linear, time-invariant systems by solving the constrained optimization problem of the MHE by multi-parametric programming methods. Set-theoretical methods are then used to derive bounds on the estimation error - it is shown that the estimation error is bounded in an invariant set for the error dynamics described by a set of linear inequalities. The error dynamics and the error bounds can then be used for the design of a robust output feedback explicit/multi-parametric MPC yielding a simultaneous estimation and control design which is illustrated with an example of robust tube-based MPC.
    Decision and Control (CDC), 2010 49th IEEE Conference on; 01/2011
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    ABSTRACT: We present a general framework for the optimal design and control of a metal-hydride bed under hydrogen desorption operation. The framework features: (i) a detailed two-dimension dynamic process model, (ii) a design and operational dynamic optimization step, and (iii) an explicit/multi-parametric model predictive controller design step. For the controller design, a reduced order approximate model is obtained, based on which nominal and robust multi-parametric controllers are designed.
    Computers & Chemical Engineering 09/2010; 34(9):1341–1347. · 2.09 Impact Factor
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    ABSTRACT: We present an analytical dynamic model and a general framework for the optimal design and control of a PEM fuel cell system. The mathematical model includes detailed model for the PEM fuel cell stack and simplified models for the compressor, humidifier and cooling system. The framework features (i) a detailed dynamic process model, and (ii) an explicit/multi-parametric model predictive controller design step. For the model based controller design, a reduced order approximate model is obtained from the dynamic simulation of the system.
    01/2010;
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    ABSTRACT: Explicit robust multi–parametric feedback control laws are designed for constrained dynamic systems involving uncertainty in the left-hand side(LHS) of the underlying MPC optimization model. Our proposed procedure features: (i) a robust reformulation/optimization step, (ii) a dynamic programming framework for the model predictive control (MPC) problem formulation, and (iii) a multi-parametric programming solution step.
    01/2009;
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    Efstrations N. Pistikopoulos, Konstantinos I. Kouramas, Nuno P. Faísca
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    ABSTRACT: In this work we present the fundamental theoretical developments for a unified and general framework for the design of Robust Multi-Parametric Controllers. Given a dynamic system, with model uncertainties appearing both in the left-hand side and the right-hand side of the underlying MPC optimisation problem, the proposed framework uses a dynamic programming and robust multi-parametric optimization approach to obtain the current and future control actions as a function of the initial system state i.e. a feedback control law.
    Computer Aided Chemical Engineering 01/2009; 26:297-302.
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    ABSTRACT: Multi-parametric model-based control (mp-MPC) is a control method that is widely acknowledged for its ability to solve the on-line optimisation problem, involved in traditional MPC, off-line via parametric optimisation. Its main advantage is that it obtains the control actions as explicit functions of the plant measurements. This allows for the control actions to be obtained on-line via simple function evaluations instead of solving repetitively a computationally demanding on-line optimisation. This allows mp-MPC to be implemented on the simplest, low-cost hardware. In this paper we report on recent developments on industrial and experimental applications of mp-MPC, where the ability of mp-MPC to be applied on systems with fast dynamics and sampling times is demonstrated, which maybe prohibitive for traditional MPC that relies on on-line optimisation methods.
    Computers & Chemical Engineering. 01/2008;
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    ABSTRACT: In this work, we present a new algorithm for solving complex multi-stage optimization problems involving hard constraints and uncertainties, based on dynamic and multi-parametric programming techniques. Each echelon of the dynamic programming procedure, typically employed in the context of multi-stage optimization models, is interpreted as a multi-parametric optimization problem, with the present states and future decision variables being the parameters, while the present decisions the corresponding optimization variables. This reformulation significantly reduces the dimension of the original problem, essentially to a set of lower dimensional multi-parametric programs, which are sequentially solved. Furthermore, the use of sensitivity analysis circumvents non-convexities that naturally arise in constrained dynamic programming problems. The potential application of the proposed novel framework to robust constrained optimal control is highlighted.
    Optimization Letters 01/2008; 2:267-280. · 1.65 Impact Factor
  • S V Rakovi'c, K I Kouramas
    Proceedings of the 46th IEEE Conference on Decision and Control, CDC 2007; 12/2007
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    ABSTRACT: The benefits of parametric programming for the design of optimal controllers for constrained systems are widely acknowledged, especially for the case of linear systems. In this work we attempt to exploit these benefits and further extend the theoretical contributions to multi-parametric Model Predictive Control (mp-MPC) for non-linear systems with state and input constraints. The aim is to provide an insight and understanding of multi-parametric control and its benefits for non-linear systems and outline key issues for ongoing research work.
    09/2007: pages 193-205;
  • S V Rakovi'c, K I Kouramas
    Proceedings of the International Congress Nonlinear Dynamical Analysis -- 2007 dedicated to the 150th anniversary of A.M.Lyapunov; 06/2007
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    ABSTRACT: This paper introduces the concept of optimized robust control invariance for discrete-time linear time-invariant systems subject to additive and bounded state disturbances. A novel characterization of two families of robust control invariant sets is given. The existence of a constraint admissible member of these families can be checked by solving a single and tractable convex programming problem in the generic linear-convex case and a standard linear/quadratic program when the constraints are polyhedral or polytopic. The solution of the same optimization problem yields the corresponding feedback control law that is, in general, set-valued. A procedure for selection of a point-valued, nonlinear control law is provided.
    Automatica 05/2007; 43(5):831-841. · 2.92 Impact Factor
  • S.V. Raković, K.I. Kouramas
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    ABSTRACT: This paper provides results on the minimal robust positively invariant set and its robust positively invariant approximations of an asymptotically stable, continuous-time, linear time-invariant system. The minimal robust positively invariant set is characterized as an infinite time Aumann Integral. A novel family of robust positively invariant sets, defined as a simple scaling of a finite time Aumann Integral, is characterized. Adequate members of this family are robust positively invariant sets and are arbitrarily close outer approximations of the minimal robust positively invariant set. A practical result, based on the optimal control theory, for the construction of safe polytopic sets is also provided. Computational procedures are briefly discussed and some simple, illustrative, examples are provided.
    Decision and Control, 2007 46th IEEE Conference on; 01/2007
  • S.V. Rakovic, K.I. Kouramas
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    ABSTRACT: This paper considers the minimal robust positively invariant set for linear discrete time systems and its robust positively invariant approximations. Efficient approximating techniques proposed by Rakovic et al., (2005) are extended to degenerate cases when the disturbance set is not necessarily full-dimensional. Two methods for handling degenerate case are proposed and two novel families of robust positively invariant sets are characterized. The minimal robust positively invariant set can be approximated arbitrarily closely with appropriate members of these families. The presented results are exploited, under mild assumptions, to construct robust positively invariant sets for the case when the state is also uncertain and only its estimate, obtained by the standard Luenberger type observer, is known. A simple example illustrates the proposed methods
    Decision and Control, 2006 45th IEEE Conference on; 12/2006
  • S V Rakovi'c, K I Kouramas
    Proceedings of the 45th IEEE Conference on Decision and Control, CDC 2006; 12/2006
  • S.V. Rakovic, K.I. Kouramas
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    ABSTRACT: A state decomposition principle in set invariance theory for linear discrete time systems is analyzed. The proposed approach allows for an appropriate use of the superposition principle, for linear time invariant discrete time systems, in the set invariance theory. It is shown how to obtain a characterization of a novel family of robust control/positively invariant sets, given a collection of robust positively invariant sets for the system with respect to relaxed state and control constraints. The corresponding feedback control strategy is generally a selection from an appropriately defined set valued map. It is shown how to define a point-valued selection that, is in general case, non-linear function of state. The potential benefits of the proposed method are illustrated by a simple and illuminating example
    Decision and Control, 2006 45th IEEE Conference on; 12/2006
  • S V Rakovi'c, K I Kouramas
    Proceedings of the 45th IEEE Conference on Decision and Control, CDC 2006; 12/2006
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    ABSTRACT: This paper provides a new and efficient method for the computation of an arbitrarily close outer robust positively invariant (RPI) approximation to the minimal robust positively invariant (mRPI) set for linear difference inclusions. It is assumed that the linear difference inclusion is absolutely asymptotically stable (AAS) in the absence of an additive state disturbance, which is the case for parametrically uncertain or switching linear discrete-time systems controlled by a stabilizing linear state feedback controller.
    Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC '05. 44th IEEE Conference on; 12/2005

Publication Stats

159 Citations
12.00 Total Impact Points

Institutions

  • 2003–2013
    • Imperial College London
      • • Department of Chemical Engineering
      • • Department of Electrical and Electronic Engineering
      Londinium, England, United Kingdom
  • 2009
    • Process Systems Enterprise Limited
      Londinium, England, United Kingdom
  • 2005
    • University of Cambridge
      • Department of Engineering
      Cambridge, ENG, United Kingdom