| 1. |
- Farokhi, Farhad, 1987-, et al.
(författare)
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A Game-Theoretic Framework for Studying Truck Platooning Incentives
- 2013
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Ingår i: Proceedings of the 16th International IEEE Annual Conference on Intelligent Transportation Systems (ITSC 2013). - : IEEE conference proceedings. ; , s. 1253-1260
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Konferensbidrag (refereegranskat)abstract
- An atomic congestion game with two types of agents, cars and trucks, is used to model the traffic flow on a road over certain time intervals. In this game, the drivers make a trade-off between the time they choose to use the road, the average velocity of the flow at that time, and the dynamic congestion tax that they are paying to use the road. The trucks have platooning capabilities and therefore, have an incentive for using the road at the same time as their peers. The dynamics and equilibria of this game-theoretic model for the interaction between car traffic and truck platooning incentives are investigated. We use traffic data from Stockholm to validate the modeling assumptions and extract reasonable parameters for the simulations. We perform a comprehensive simulation study to understand the influence of various factors, such as the percentage of the trucks that are equipped with platooning devices on the properties of the pure strategy Nash equilibrium that is learned using a joint strategy fictitious play.
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| 2. |
- Farokhi, Farhad, 1987-, et al.
(författare)
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A Heterogeneous Routing Game
- 2013
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Ingår i: 2013 51st Annual Allerton Conference on Communication, Control, and Computing, Allerton 2013. - : IEEE conference proceedings. - 9781479934096 ; , s. 448-455
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Konferensbidrag (refereegranskat)abstract
- Most literature on routing games make the assumption that drivers or vehicles are of the same type and, hence, experience the same latency or cost when traveling along the edges of the network. In contrast, in this article, we propose a heterogeneous routing game in which each driver or vehicle belongs to a certain type. The type determines the cost of traveling along an edge as a function of the flow of all types of drivers or vehicles over that edge. We examine the existence of a Nash equilibrium in this heterogeneous routing game. We study the conditions for which the problem of finding a Nash equilibrium can be posed as a convex optimization problem and is therefore numerically tractable. Numerical simulations are presented to validate the results.
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| 3. |
- Farokhi, Farhad, 1987-, et al.
(författare)
-
A Study of Truck Platooning Incentives Using a Congestion Game
- 2015
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Ingår i: IEEE transactions on intelligent transportation systems (Print). - 1524-9050 .- 1558-0016. ; 16:2, s. 581-595
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Tidskriftsartikel (refereegranskat)abstract
- We introduce an atomic congestion game with two types of agents, namely, cars and trucks, to model the traffic flow on a road over various time intervals of the day. Cars maximize their utility by finding a tradeoff between the time they choose to use the road, the average velocity of the flow at that time, and the dynamic congestion tax that they pay for using the road. In addition to these terms, the trucks have an incentive for using the road at the same time as their peers because they have platooning capabilities, which allow them to save fuel. The dynamics and equilibria of this game-theoretic model for the interaction between car traffic and truck platooning incentives are investigated. We use traffic data from Stockholm, Sweden, to validate parts of the modeling assumptions and extract reasonable parameters for the simulations. We use joint strategy fictitious play and average strategy fictitious play to learn a pure strategy Nash equilibrium of this game. We perform a comprehensive simulation study to understand the influence of various factors, such as the drivers' value of time and the percentage of the trucks that are equipped with platooning devices, on the properties of the Nash equilibrium.
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| 4. |
- Farokhi, Farhad, 1987-, et al.
(författare)
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Complexity Reduction for Parameter-Dependent Linear Systems
- 2013
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Ingår i: 2013 American Control Conference (ACC). - : American Automatic Control Council. - 9781479901777 ; , s. 2624-2630
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Konferensbidrag (refereegranskat)abstract
- We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with fewer parameters or state variables. To do so, it minimizes the distance (i.e., $H_\infty$-norm of the difference) between the original system and its reduced version. We present a sub-optimal solution to this problem using sum-of-squares optimization methods. We present the results for both continuous-time and discrete-time systems. Lastly, we illustrate the applicability of our proposed algorithm on numerical examples.
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| 5. |
- Farokhi, Farhad, 1987-
(författare)
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Decentralized Control Design with Limited Plant Model Information
- 2012
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Large-scale control systems are often composed of several smaller interconnected units. For these systems, it is common to employ local controllers, which observe and act locally. At the heart of common control design procedures for distributed systems lies the often implicit assumption that the designer has access to the global plant model information when designing a local controller. However, there are several reasons why such plant model information would not be globally known. One reason could be that the designer wants the parameters of each local controller to only depend on local model information, so that the controllers are not modified if the model parameters of a particular subsystem change. It might also be the case that the design of each local controller is done by individual designers with no access to the global plant model, for instance, due to the fact that the designers refuse to share their model information since they consider it private. This class of problems, which we refer to as limited model information control design, is the topic of the thesis. First, we investigate the achievable closed-loop performance of discrete-time linear time-invariant plants under a separable quadratic cost performance with structured static state-feedback controllers. To do so, we introduce control design strategies as mappings, which construct controllers by accessing the plant model information in a constrained way according to a given design graph. We compare control design strategies using the competitive ratio as a performance metric, that is, we compare the worst case control performance for a given design strategy normalized with the optimal control performance based on full model information. An explicit minimizer of the competitive ratio is sought. As this minimizer might not be unique, we further search for the ones that are undominated, that is, there is no other control design strategy in the set of limited model information design strategies with a better closed-loop performance for all possible plants while maintaining the same worst-case ratio. We study the trade-off between the amount of model information exploited by a control design strategy and the best possible closed-loop performance. We generalize this setup to structured dynamic state-feedback controllers for H_2-performance. Surprisingly, the optimal control design strategy with limited model information is still a static one. This is the case even though the optimal decentralized state-feedback controller with full model information is dynamic. Finally, we discuss the design of dynamic controllers for disturbance accommodation under limited model information. This problem is of special interest because the best limited model information control design in this case is a dynamic control design strategy. The optimal controller can be separated into a static feedback law and a dynamic disturbance observer. For constant disturbances, it is shown that this structure corresponds to proportional-integral control.
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| 6. |
- Farokhi, Farhad, 1987-
(författare)
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Decentralized Control of Networked Systems : Information Asymmetries and Limitations
- 2014
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Designing local controllers for networked systems is challenging, because in these systems each local controller can often access only part of the overall information on system parameters and sensor measurements. Traditional control design cannot be easily applied due to the unconventional information patterns, communication network imperfections, and design procedure complexities. How to control large-scale systems is of immediate societal importance as they appear in many emerging applications, such as intelligent transportation systems, smart grids, and energy-efficient buildings. In this thesis, we make three contributions to the problem of designing networked controller under information asymmetries and limitations.In the first contribution, we investigate how to design local controllers to optimize a cost function using only partial knowledge of the model governing the system. Specifically, we derive some fundamental limitations in the closed-loop performance when the design of each controller only relies on local plant model information. Results are characterized in the structure of the networked system as well as in the available model information. Both deterministic and stochastic formulations are considered for the closed-loop performance and the available information. In the second contribution of the thesis, we study decision making in transportation systems using heterogeneous routing and congestion games. It is shown that a desirable global behavior can emerge from simple local strategies used by the drivers to choose departure times and routes. Finally, the third contribution is a novel stochastic sensor scheduling policy for ad-hoc networked systems, where a varying number of control loops are active at any given time. It is shown that the policy provides stochastic guarantees for the network resources dynamically allocated to each loop.
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| 7. |
- Farokhi, Farhad, 1987-, et al.
(författare)
-
Decentralized Disturbance Accommodation with Limited Plant Model Information
- 2013
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Ingår i: SIAM Journal of Control and Optimization. - : Society for Industrial & Applied Mathematics (SIAM). - 0363-0129 .- 1095-7138. ; 51:2, s. 1543-1573
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Tidskriftsartikel (refereegranskat)abstract
- The design of optimal disturbance accommodation and servomechanism controllers with limited plant model information is studied in this paper. We consider discrete-time linear time-invariant systems that are fully actuated and composed of scalar subsystems, each of which is controlled separately and influenced by a scalar disturbance. Each disturbance is assumed to be generated by a system with known dynamics and unknown initial conditions. We restrict ourselves to control design methods that produce structured dynamic state feedback controllers where each subcontroller, at least, has access to the state measurements of those subsystems that can affect its corresponding subsystem. The performance of such control design methods is compared using a metric called the competitive ratio, which is the worst-case ratio of the cost of a given control design strategy to the cost of the optimal control design with full model information. We find an explicit minimizer of the competitive ratio and show that it is undominated, that is, there is no other control design strategy that performs better for all possible plants while having the same worst-case ratio. This optimal controller can be separated into a static feedback law and a dynamic disturbance observer. For step disturbances, it is shown that this structure corresponds to proportional-integral control.
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| 8. |
- Farokhi, Farhad, 1987-, et al.
(författare)
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Decentralized H2 Control Design with Limited Model Information
- 2011
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper deals with designing optimal decentralized H2 controller for interconnected discrete-time time-invariant systems with limited model information. We adapt the notion of limited model information designs to handle the dynamic H2 controllers. The best decentralized control design strategy, in terms of the competitive ratio and domination metrics, is found for different acyclic plant graphs when the control graph is a super-graph of the plant graph.
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| 9. |
- Farokhi, Farhad, 1987-, et al.
(författare)
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Distributed MPC Via Dual Decomposition and Alternating Direction Method of Multipliers
- 2013
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Ingår i: Distributed Model Predictive Control Made Easy. - Dordrecht : Springer. - 9789400770058
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Bokkapitel (refereegranskat)abstract
- A conventional way to handle model predictive control (MPC) problems distributedly is to solve them via dual decomposition and gradient ascent. However, at each time-step, it might not be feasible to wait for the dual algorithm to converge. As a result, the algorithm might be needed to be terminated prematurely. One is then interested to see if the solution at the point of termination is close to the optimal solution and when one should terminate the algorithm if a certain distance to optimality is to be guaranteed. In this chapter, we look at this problem for distributed systems under general dynamical and performance couplings, then, we make a statement on validity of similar results where the problem is solved using alternative direction method of multipliers.
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| 10. |
- Farokhi, Farhad, 1987-, et al.
(författare)
-
Investigating the Interaction Between Traffic Flow and Vehicle Platooning Using a Congestion Game
- 2014
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Ingår i: Proceedings of the 19th IFAC World Congress, 2014. - 9783902823625 - 9781634394567 ; , s. 4170-4177
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Konferensbidrag (refereegranskat)abstract
- We consider a congestion game with two types of agents to describe the traffic flow on a road at various time intervals in each day. The first type of agents (cars) maximize a utility which is determined by a sum of a penalty for using the road at a time other than their preferred time interval, the average velocity of the traffic flow, and the congestion tax. The second type of agents (trucks or heavy-duty vehicles) can benefit from using the road together with other second-type agents. This is because the trucks can form platoons to save fuel through reducing the air drag force. We study a Nash equilibrium of this game to study the interaction between the traffic flow and the platooning incentives. We prove that the introduced congestion game does not admit a potential function unless we devise an appropriate congestion taxing policy. We use joint strategy fictitious play and average strategy fictitious play to learn a pure strategic Nash equilibrium of this congestion game. Lastly, we demonstrate the developed results on a numerical example using data from a highway segment in Stockholm.
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