Results 1  10
of
52
Optimal control of spatially distributed systems
 IEEE Tran. on Automatic Control, September 2006, accepted. [Online]. Available: http://www.grasp.upenn.edu/ ∼ motee/ TACMoteeJ06SD.pdf
"... Abstract — In this paper, we study the structural properties of optimal control of spatially distributed systems. Such systems consist of an infinite collection of possibly heterogeneous linear control systems that are spatially interconnected via certain distant dependent coupling functions over ar ..."
Abstract

Cited by 37 (5 self)
 Add to MetaCart
(Show Context)
Abstract — In this paper, we study the structural properties of optimal control of spatially distributed systems. Such systems consist of an infinite collection of possibly heterogeneous linear control systems that are spatially interconnected via certain distant dependent coupling functions over arbitrary graphs. The key idea of the paper is the introduction of a special class of operators called spatially decaying (SD) operators. We study the structural properties of infinitehorizon linear quadratic optimal controllers for such systems by analyzing the spatial structure of the solution to the corresponding operator Lyapunov and Riccati equations. We prove that the kernel of the optimal feedback of each subsystem decays in the spatial domain at a rate proportional to the inverse of the corresponding coupling function of the system. I.
Design of optimal sparse feedback gains via the alternating direction method of multipliers
 IEEE Trans. Automat. Control
"... Abstract—We design sparse and block sparse feedback gains that minimize the variance amplification (i.e., the norm) of distributed systems. Our approach consists of two steps. First, we identify sparsity patterns of feedback gains by incorporating sparsitypromoting penalty functions into the optim ..."
Abstract

Cited by 33 (8 self)
 Add to MetaCart
Abstract—We design sparse and block sparse feedback gains that minimize the variance amplification (i.e., the norm) of distributed systems. Our approach consists of two steps. First, we identify sparsity patterns of feedback gains by incorporating sparsitypromoting penalty functions into the optimal control problem, where the added terms penalize the number of communication links in the distributed controller. Second, we optimize feedback gains subject to structural constraints determined by the identified sparsity patterns. In the first step, the sparsity structure of feedback gains is identified using the alternating direction method of multipliers, which is a powerful algorithm wellsuited to large optimization problems. This method alternates between promoting the sparsity of the controller and optimizing the closedloop performance, which allows us to exploit the structure of the corresponding objective functions. In particular, we take advantage of the separability of the sparsitypromoting penalty functions to decompose the minimization problem into subproblems that can be solved analytically. Several examples are provided to illustrate the effectiveness of the developed approach. Index Terms—Alternating direction method of multipliers (ADMM), communication architectures, continuation methods, minimization, optimization, separable penalty functions, sparsitypromoting optimal control, structured distributed design. I.
R.: Distributed utilization control for realtime clusters with load balancing
 In: Proceedings of 27th IEEE International Realtime Systems Symposium (RTSS’06), pp.137–146. Riode Janeiro 5–8
, 2006
"... Recent years have seen rapid growth of online services that rely on largescale server clusters to handle high volume of requests. Such clusters must adaptively control the CPU utilizations of many processors in order to maintain desired soft realtime performance and prevent system overload in face ..."
Abstract

Cited by 13 (1 self)
 Add to MetaCart
(Show Context)
Recent years have seen rapid growth of online services that rely on largescale server clusters to handle high volume of requests. Such clusters must adaptively control the CPU utilizations of many processors in order to maintain desired soft realtime performance and prevent system overload in face of unpredictable workloads. This paper presents DUCLB, a novel distributed utilization control algorithm for clusterbased soft realtime applications. Compared to earlier works on utilization control, a distinguishing feature of DUCLB is its capability to handle system dynamics caused by load balancing, which is a common and essential component of most clusters today. Simulation results and controltheoretic analysis demonstrate that DUCLB can provide robust utilization control and effective load balancing in largescale clusters.... Read complete abstract on page 2.
Design of Optimal Sparse Interconnection Graphs for Synchronization of Oscillator Networks
 IEEE TRANSACTIONS ON AUTOMATIC CONTROL
, 2014
"... We study the optimal design of a conductance network as a means for synchronizing a given set of oscillators. Synchronization is achieved when all oscillator voltages reach consensus, and performance is quantified by the meansquare deviation from the consensus value. We formulate optimization probl ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
We study the optimal design of a conductance network as a means for synchronizing a given set of oscillators. Synchronization is achieved when all oscillator voltages reach consensus, and performance is quantified by the meansquare deviation from the consensus value. We formulate optimization problems that address the tradeoff between synchronization performance and the number and strength of oscillator couplings. We promote the sparsity of the coupling network by penalizing the number of interconnection links. For identical oscillators, we establish convexity of the optimization problem and demonstrate that the design problem can be formulated as a semidefinite program. Finally, for special classes of oscillator networks we derive explicit analytical expressions for the optimal conductance values.
Distributed Control: A Sequentially SemiSeparable Approach for Spatially Heterogeneous Linear Systems
, 2009
"... We consider the problem of designing controllers for spatiallyvarying interconnected systems distributed in one spatial dimension. The matrix structure of such systems can be exploited to allow fast analysis and design of centralized controllers with simple distributed implementations. Iterative al ..."
Abstract

Cited by 8 (1 self)
 Add to MetaCart
We consider the problem of designing controllers for spatiallyvarying interconnected systems distributed in one spatial dimension. The matrix structure of such systems can be exploited to allow fast analysis and design of centralized controllers with simple distributed implementations. Iterative algorithms are provided for stability analysis, analysis and suboptimal controller synthesis. For practical implementation of the algorithms, approximations can be used, and the computational efficiency and accuracy are demonstrated on an example.
Minimal Interconnection Topology in Distributed Control Design
 Proceedings of the American Control Conference, ACC
, 2006
"... Abstract. In this paper, we consider a distributed control design problem. Multiple agents (or subsystems) that are dynamically uncoupled need to be controlled to optimize a joint cost function. An interconnection graph specifies the topology according to which the agents can access information abou ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
(Show Context)
Abstract. In this paper, we consider a distributed control design problem. Multiple agents (or subsystems) that are dynamically uncoupled need to be controlled to optimize a joint cost function. An interconnection graph specifies the topology according to which the agents can access information about each others ’ state. We propose and partially analyze a new model for determining the influence of the topology of the interconnection graph on the performance achieved by the subsystems. We consider the classical LQR cost function and propose making one of the weight matrices to be topologydependent to capture the extra cost incurred when more communication between the agents is allowed. We present results about optimal topologies for some models of the dependence of the weight matrix on the communication graph. We also give some results about the existence of “critical prices ” at which adding supplementary edges becomes detrimental to closedloop performance. One conclusion of the work is that if the communication between the agents comes at a cost, then adding communication edges may be harmful for the system performance. 1. Introduction. The
1 A Suboptimal Algorithm to Synthesize Control Laws for a Network of Dynamic Agents
"... We study the synthesis problem of an LQR controller when the matrix describing the control law is constrained to lie in a particular vector space. Our motivation is the use of such control laws to stabilize networks of autonomous agents in a decentralized fashion, with the information flow being dic ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
We study the synthesis problem of an LQR controller when the matrix describing the control law is constrained to lie in a particular vector space. Our motivation is the use of such control laws to stabilize networks of autonomous agents in a decentralized fashion, with the information flow being dictated by the constraints of a prespecified topology. In this paper, we consider the finitehorizon version of the problem and provide both a computationally intensive optimal solution and a suboptimal solution that is computationally more tractable. Then we apply the technique to the decentralized vehicle formation control problem. It is numerically illustrated that while the loss in performance due to the use of the suboptimal solution is not huge, the topology can have a large effect on performance.