A Class of Team Problems with Discrete Action Spaces: Optimality Conditions Based on Multimodularity

Math. Control Signals Syst.

2009

We consider dynamic systems controlled by boolean signals or decisions. We show that in a number of cases, the receding horizon formulation of the control problem can be solved via linear programming by relaxing the binary constraints on the control. The idea behind our approach is conceptually easy: a feasible control can be forced by imposing that the boolean signal is set to one at least one time over the horizon. We translate this idea into constraints on the controls and analyze the polyhedron of all feasible controls. We specialize the approach to the stabilizability of switched and impulsively-controlled systems.

“…Let the time of the switch be r i + e∆t. Note that the resulting switching control is again of type (15). Fig.…”

Section: Oscillating Systemsmentioning

confidence: 99%

“…Applications include inventory with set up costs (reordering or not from a warehouse in order to meet a demand) [8], distributed computer systems (processing or not the assigned task) [15], air-conditioning systems control, economics and finance (see, e.g., [9] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Boolean-controlled systems via receding horizon and linear programing

Math. Control Signals Syst.

2009

“…Handling integer control requires more than standard convex optimization techniques. It is known that new structural properties of the problem play important roles in mixed integer control; as an example, see multimodularity presented as the counterpart of convexity in discrete action spaces [5]. We should note that there is vast literature on mixed integer programming [6], and it is in this context that we cast the problem addressed in this paper.…”

Section: Introductionmentioning

confidence: 99%

Decomposition and Mean-Field Approach to Mixed Integer Optimal Compensation Problems

Zhu

Başar

2016

J Optim Theory Appl

Mixed integer optimal compensation deals with optimization problems with integer-and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls could lead to intractability in problems of large dimensions. To address this challenge, we introduce a decomposition method which turns the original n-dimensional optimization problem into n independent scalar problems of lot sizing form. Each of these problems can be viewed as a two-player zero-sum game, which introduces some element of conservatism. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon, a step that mirrors a standard procedure in mixed integer programming. We apply the decomposition method to a mean-field coupled multi-agent system problem, where each agent seeks to compensate a combination of an exogenous signal and the local state average. We discuss a large population mean-field type Communicated by

“…It is known that new structural properties of the problem play important roles in mixed integer control. As an example, see multimodularity presented as the counterpart of convexity in discrete action spaces [6]. We should note that there is vast literature on mixed integer programming [13], and it is in this context that we cast the problem addressed in this paper.…”

Section: Introductionmentioning

confidence: 99%

Mixed integer optimal compensation: Decompositions and mean-field approximations

2012 American Control Conference (ACC)

Zhu

Başar

2012

Abstract-Mixed integer optimal compensation deals with optimizing integer-and real-valued control variables to compensate disturbances in dynamic systems. The mixed integer nature of controls might be a cause of intractability for instances of larger dimensions. To tackle this issue, we propose a decomposition method which turns the original n-dimensional problem into n independent scalar problems of lot sizing form. Each scalar problem is then reformulated as a shortest path one and solved through linear programming over a receding horizon. This last reformulation step mirrors a standard procedure in mixed integer programming. We apply the decomposition method to a mean-field coupled multi-agent system problem, where each agent seeks to compensate a combination of the exogenous signal and the local state average. We discuss a large population mean-field type of approximation as well as the application of predictive control methods.