37,377 research outputs found

    Robust predictive feedback control for constrained systems

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    A new method for the design of predictive controllers for SISO systems is presented. The proposed technique allows uncertainties and constraints to be concluded in the design of the control law. The goal is to design, at each sample instant, a predictive feedback control law that minimizes a performance measure and guarantees of constraints are satisfied for a set of models that describes the system to be controlled. The predictive controller consists of a finite horizon parametric-optimization problem with an additional constraint over the manipulated variable behavior. This is an end-constraint based approach that ensures the exponential stability of the closed-loop system. The inclusion of this additional constraint, in the on-line optimization algorithm, enables robust stability properties to be demonstrated for the closed-loop system. This is the case even though constraints and disturbances are present. Finally, simulation results are presented using a nonlinear continuous stirred tank reactor model

    Model predictive control techniques for hybrid systems

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    This paper describes the main issues encountered when applying model predictive control to hybrid processes. Hybrid model predictive control (HMPC) is a research field non-fully developed with many open challenges. The paper describes some of the techniques proposed by the research community to overcome the main problems encountered. Issues related to the stability and the solution of the optimization problem are also discussed. The paper ends by describing the results of a benchmark exercise in which several HMPC schemes were applied to a solar air conditioning plant.Ministerio de Eduación y Ciencia DPI2007-66718-C04-01Ministerio de Eduación y Ciencia DPI2008-0581

    Learning an Approximate Model Predictive Controller with Guarantees

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    A supervised learning framework is proposed to approximate a model predictive controller (MPC) with reduced computational complexity and guarantees on stability and constraint satisfaction. The framework can be used for a wide class of nonlinear systems. Any standard supervised learning technique (e.g. neural networks) can be employed to approximate the MPC from samples. In order to obtain closed-loop guarantees for the learned MPC, a robust MPC design is combined with statistical learning bounds. The MPC design ensures robustness to inaccurate inputs within given bounds, and Hoeffding's Inequality is used to validate that the learned MPC satisfies these bounds with high confidence. The result is a closed-loop statistical guarantee on stability and constraint satisfaction for the learned MPC. The proposed learning-based MPC framework is illustrated on a nonlinear benchmark problem, for which we learn a neural network controller with guarantees.Comment: 6 pages, 3 figures, to appear in IEEE Control Systems Letter

    Stochastic Nonlinear Model Predictive Control with Efficient Sample Approximation of Chance Constraints

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    This paper presents a stochastic model predictive control approach for nonlinear systems subject to time-invariant probabilistic uncertainties in model parameters and initial conditions. The stochastic optimal control problem entails a cost function in terms of expected values and higher moments of the states, and chance constraints that ensure probabilistic constraint satisfaction. The generalized polynomial chaos framework is used to propagate the time-invariant stochastic uncertainties through the nonlinear system dynamics, and to efficiently sample from the probability densities of the states to approximate the satisfaction probability of the chance constraints. To increase computational efficiency by avoiding excessive sampling, a statistical analysis is proposed to systematically determine a-priori the least conservative constraint tightening required at a given sample size to guarantee a desired feasibility probability of the sample-approximated chance constraint optimization problem. In addition, a method is presented for sample-based approximation of the analytic gradients of the chance constraints, which increases the optimization efficiency significantly. The proposed stochastic nonlinear model predictive control approach is applicable to a broad class of nonlinear systems with the sufficient condition that each term is analytic with respect to the states, and separable with respect to the inputs, states and parameters. The closed-loop performance of the proposed approach is evaluated using the Williams-Otto reactor with seven states, and ten uncertain parameters and initial conditions. The results demonstrate the efficiency of the approach for real-time stochastic model predictive control and its capability to systematically account for probabilistic uncertainties in contrast to a nonlinear model predictive control approaches.Comment: Submitted to Journal of Process Contro

    Robust MPC of constrained nonlinear systems based on interval arithmetic

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    A robust MPC for constrained discrete-time nonlinear systems with additive uncertainties is presented. The proposed controller is based on the concept of reachable sets, that is, the sets that contain the predicted evolution of the uncertain system for all possible uncertainties. If processes are nonlinear these sets are very difficult to compute. A conservative approximation based on interval arithmetic is proposed for the online computation of these sets. This technique provides good results with a computational effort only slightly greater than the one corresponding to the nominal prediction. These sets are incorporated into the MPC formulation to achieve robust stability. By choosing a robust positively invariant set as a terminal constraint, a robustly stabilising controller is obtained. Stability is guaranteed in the case of suboptimality of the computed solution. The proposed controller is applied to a continuous stirred tank reactor with an exothermic reaction.Ministerio de Ciencia y Tecnología DPI-2001-2380-03- 01Ministerio de Ciencia y Tecnología DPI-2002-4375-C02-0

    Robust stability of min-max MPC controllers for nonlinear systems with bounded uncertainties

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    Sixteenth International Symposium on Mathematical Theory of Networks and Systems 05/07/2004 Leuven, BélgicaThe closed loop formulation of the robust MPC has been shown to be a control technique capable of robustly stabilize uncertain nonlinear systems subject to constraints. Robust asymptotic stability of these controllers has been proved when the uncertainties are decaying. In this paper we extend the existing results to the case of uncertainties that decay with the state but do not tend to zero. This allows us to consider both plant uncertainties and external disturbances in a less conservative way. First, we provide some results on robust stability under the considered kind of uncertainties. Based on these, we prove robust stability of the min-max MPC. In the paper we show how the robust design of the local controller is translated to the min-max controller and how the persistent term of the uncertainties determines the convergence rate of the closed-loop system.Ministerio de Ciencia y Tecnología DPI-2001-2380-03-01Ministerio de Ciencia y Tecnología DPI-2002-4375-C02-0
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