1,721,035 research outputs found
Fast, Large-scale Model Predictive Control by Partial Enumeration
No full textPartial 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. © 2007 Elsevier Ltd. All rights reserved
Cooperative Distributed Model Predictive Control
No full textIn this paper we propose a cooperative distributed linear model predictive control strategy applicable to any finite number of subsystems satisfying a stabilizability condition. The control strategy has the following features: hard input constraints are satisfied; terminating the iteration of the distributed controllers prior to convergence retains closed-loop stability; in the limit of iterating to convergence, the control feedback is plantwide Pareto optimal and equivalent to the centralized control solution; no coordination layer is employed. We provide guidance in how to partition the subsystems within the plant. We first establish exponential stability of suboptimal model predictive control and show that the proposed cooperative control strategy is in this class. We also establish that under perturbation from a stable state estimator, the origin remains exponentially stable. For plants with sparsely coupled input constraints, we provide an extension in which the decision variable space of each suboptimization is augmented to achieve Pareto optimality. We conclude with a simple example showing the performance advantage of cooperative control compared to noncooperative and decentralized control strategies. © 2010 Elsevier B.V. All rights reserved
Efficient Cooperative Distributed MPC using Partial Enumeration
No full textWe discuss in this paper a novel and efficient implementation of distributed Model Predictive Control (MPC) systems for large-scale systems. The method is based on Partial Enumeration (PE), an approach that allows to compute the (sub)optimal solution of the Quadratic Program associated to the MPC problem by using a solution table that stores only a few most recently optimal active sets. This method is applied to the each local MPC system with significant improvements in terms of computational efficiency, and the original PE algorithm is modified to guarantee robust stability of the overall closedloop system. We also discuss how input constraints that involve different units, e.g. on the summation of common utility consumption, can be appropriately handled. We illustrate the benefits of proposed method by means a simulated example comprising three units
Is Suboptimal Nonlinear MPC Inherently Robust?
No full textWe study the inherent robust stability properties of nonlinear discrete-time systems controlled by suboptimal model predictive control (MPC). The unique requirement to suboptimal MPC is that it does not increase the cost function with respect to a well-defined warm start, and it is therefore implementable in general nonconvex problems for which no suboptimality margins can be enforced. Because the suboptimal control law is a set-valued map, the closed-loop system is described by a difference inclusion. Under conventional assumptions on the system and cost functions, we establish nominal exponential stability of the equilibrium. If, in addition, a continuity assumption of the feasible input set holds, we prove robust exponential stability with respect to small, but otherwise arbitrary, additive process disturbances and state measurement/estimation errors. To obtain these results, we show that the suboptimal cost is a continuous exponential Lyapunov function for an appropriately augmented closed-loop system. Moreover, we show that robust recursive feasibility is implied by such (nominal) exponential cost decay. We present an illustrative example to clarify the main ideas and assumptions. © 2011 IFAC
Conditions under which suboptimal nonlinear MPC is inherently robust
No full textWe address the inherent robustness properties of nonlinear systems controlled by suboptimal model predictive control (MPC), i.e., when a suboptimal solution of the (generally nonconvex) optimization problem, rather than an element of the optimal solution set, is used for the control. The suboptimal control law is then a set-valued map, and consequently, the closed-loop system is described by a difference inclusion. Under mild assumptions on the system and cost functions, we establish nominal exponential stability of the equilibrium, and with a continuity assumption on the feasible input set, we prove robust exponential stability with respect to small, but otherwise arbitrary, additive process disturbances and state measurement/estimation errors. These results are obtained by showing that the suboptimal cost is a continuous exponential Lyapunov function for an appropriately augmented closed-loop system, written as a difference inclusion, and that recursive feasibility is implied by such (nominal) exponential cost decay. These novel robustness properties for suboptimal MPC are inherited also by optimal nonlinear MPC. We conclude the paper by showing that, in the absence of state constraints, we can replace the terminal constraint with an appropriate terminal cost, and the robustness properties are established on a set that approaches the nominal feasibility set for small disturbances. The somewhat surprising and satisfying conclusion of this study is that suboptimal MPC has the same inherent robustness properties as optimal MPC. © 2011 Elsevier B.V. All rights reserved
Partial Enumeration MPC: Robust Stability Results and Application to an Unstable CSTR
No full textWe revise in this paper the Partial Enumeration (PE) method for the fast computation of a suboptimal solution to linear MPC problems. We derive novel robust exponential stability results for difference inclusions to show that the existence of a continuous Lyapunov function implies Strong Robust Exponential Stability (SRES), i.e. for any sufficiently small perturbation. Given the fact that the suboptimal PE-based control law is non-unique and discontinuous, i.e. a set-valued map, we treat the closed-loop system, appropriately augmented, as a difference inclusion. Such approach allows us to show SRES of the closed-loop system under PE-based MPC. Application to a simulated open-loop unstable CSTR is presented to show the performance and timing results of PE-based MPC, as well as to highlight its robustness to process/model mismatch, disturbances and measurement noise. © 2009 IFAC
Inherently robust suboptimal nonlinear MPC: Theory and application
No full textWe discuss inherent robust stability properties of discrete-time nonlinear systems controlled by Model Predictive Control (MPC) algorithms that do not necessarily attain the global minimum of the optimization problem solved at each sample time. For these implementable suboptimal MPC algorithms, we prove nominal exponential stability of the origin of the closed-loop system. The stability property is robust with respect to (sufficiently small but otherwise arbitrary) process disturbances and state measurement/estimation errors. When (hard) state constraints appear in the control problem, our result requires a (local) continuity assumption of the feasible input space. If (hard) state constraints are not present, robustness of stability can be proved under standard assumptions. We show an example to illustrate the main ideas behind these results. © 2011 IEEE
Existence and computation of infinite horizon model predictive control with active steady-state input constraints
No full textThis material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder
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