Least inventory control of multi-storage systems with non-stochastic unknown inputs

Blanchini, Franco; Rinaldi, Franca; Ukovich, Walter

doi:10.1109/acc.1997.609681

Cited by 16 publications

(22 citation statements)

References 24 publications

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“…Second, we show that a stricter version of the above condition is sufficient to guarantee global convergence of all state trajectories to the invariant set. Finally, we show that these two results when specialized to the scalar case share striking similarities to existing results in the literature where the inputs are assumed to be analog [6] [7].…”

Section: Introductionsupporting

confidence: 68%

“…For the example in Fig. 1 borrowed from [7], we have three resourses/products x i , i = 1, 2, 3, four controlled flows u i , i = 1, . .…”

Section: B Significance Of the Problem Statementmentioning

confidence: 99%

“…Questions of existence of robustly control invariant sets, as well as their properties when they do exist, are thus of interest. Of course, this problem has been previously considered in the literature, for instance in [6] [7] where polytopic invariant sets as considered and in [5] where ellipsoidal sets are considered. Restricting the discussion to polytopic sets has the advantage of reducing the problem to linear programs, with the relative computational benefits: The problem turns into a robust quadratic programming problem involving linear matrix inequalities when the sets are ellipsoidal.…”

Section: Introductionmentioning

confidence: 99%

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Control of production-distribution systems under discrete disturbances and control actions

Bauso

Tarraf

2011

IEEE Conference on Decision and Control and European Control Conference

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Abstract-This paper deals with the robust control and optimization of production-distribution systems. The model used in our problem formulation is a general network flow model that describes production, logistics, and transportation applications. The novelty in our formulation is in the discrete nature of the control and disturbance inputs. We highlight three main contributions: First, we derive a necessary and sufficient condition for the existence of robustly control invariant hyperboxes. Second, we show that a stricter version of the same condition is sufficient for global convergence to an invariant set. Third, for the scalar case, we show that these results parallel existing results in the setting where the control actions and disturbances are analog. We conclude with two simple illustrative examples.

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Section: Introductionsupporting

confidence: 68%

“…For the example in Fig. 1 borrowed from [7], we have three resourses/products x i , i = 1, 2, 3, four controlled flows u i , i = 1, . .…”

Section: B Significance Of the Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Control of production-distribution systems under discrete disturbances and control actions

Bauso

Tarraf

2011

IEEE Conference on Decision and Control and European Control Conference

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“…1), inventory [5][6][7], and supply-chain applications [26] and traffic [2,14]. The control and demand are assumed subject to capacity constraints…”

Section: Problem Statement and Preliminary Resultsmentioning

confidence: 99%

“…Although the literature on flow networks is quite wide, "robustness" has been brought into the picture only recently [1,4,7,20,23]. A robust decentralized strategy has been proposed in [8], where the authors present a Lyapunov based control that guarantees robustness against uncertain demand in the presence of both buffer and arc flow constraints.…”

Section: Introductionmentioning

confidence: 99%

The linear saturated decentralized strategy for constrained flow control is asymptotically optimal

et al. 2013

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We present an algorithm for constrained network flow control in the presence of an unknown demand. Our algorithm is decentralized in the sense that it is implemented by a team of agents, each controlling just the flow on a single arc of the network based only on the buffer levels at the nodes at the extremes of the arc, while ignoring the actions of other agents and the network topology. We prove that our algorithm is also stabilizing and steady-state optimal. Specifically, we show that it asymptotically produces the minimum-norm flow. We finally generalize our algorithm to networks with a linear dynamics and we prove that certain least-square optimality properties still hold.

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Robust Control Strategies for Multi–Inventory Systems with Average Flow Constraints

Bauso

Blanchini

Pesenti

2006

Analysis and Design of Hybrid Systems 2006

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In this paper we consider multi-inventory systems in presence of uncertain demand. We assume that i) demand is unknown but bounded in an assigned compact set and ii) the control inputs (controlled flows) are subject to assigned constraints. Given a long-term average demand, we select a nominal flow that feeds such a demand. In this context, we are interested in a control strategy that meets at each time all possible current demands and achieves the nominal flow in the average. We provide necessary and sufficient conditions for such a strategy to exist and we characterize the set of achievable flows. Such conditions are based on linear programming and thus they are constructive. In the special case of a static flow (i.e. a system with 0-capacity buffers) we show that the strategy must be affine. The dynamic problem can be solved by a linear-saturated control strategy (inspired by the previous one). We provide numerical analysis and illustrating examples.

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Least inventory control of multi-storage systems with non-stochastic unknown inputs

Cited by 16 publications

References 24 publications

Control of production-distribution systems under discrete disturbances and control actions

Control of production-distribution systems under discrete disturbances and control actions

The linear saturated decentralized strategy for constrained flow control is asymptotically optimal

Robust Control Strategies for Multi–Inventory Systems with Average Flow Constraints

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