On the state-space design of optimal controllers for distributed systems with finite communication speed

Proceedings of the 2011 American Control Conference

2011

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120

We consider a linear quadratic optimal control problem with an additional penalty on the number of communication links in the distributed controller. We reformulate this combinatorial optimization problem as a sequence of weighted 1 problems, where the weighted 1 norm approximates the counting of the communication links. We identify a class of systems for which the weighted 1 problem can be formulated as a semidefinite program and therefore its solution can be computed efficiently. Application of the developed algorithm to the optimal control of vehicular formations reveals communication topologies that become sparser as the price of inter-vehicular communications is increased.

Section: Introductionmentioning

confidence: 99%

Sparsity-promoting optimal control for a class of distributed systems

Proceedings of the 2011 American Control Conference

2011

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120

“…Over the years a body of literature has been developed that addresses the problem of distributed control of interconnected systems [1]- [13]. The present work is motivated by [14], [15].…”

Section: Introductionmentioning

confidence: 99%

On the dual decomposition of linear quadratic optimal control problems for vehicular formations

49th IEEE Conference on Decision and Control (CDC)

2010

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We use the dual decomposition method along with the dual subgradient algorithm to decouple the linear quadratic optimal control problem for a system of single-integrator vehicles. This produces the optimal control law in a localized manner, in the sense that vehicles can iteratively compute their primal and dual variables by only communicating with their immediate neighbors. In particular, we demonstrate that each vehicle only needs to receive the primal variable of the vehicle ahead and the dual variable of the vehicle behind. We then assume a structured feedback gain relationship between the state and actuation signals, and reformulate the optimization problem to find the optimal feedback gains. We develop an algorithm whereby vehicles can compute structured feedback gains in a localized manner. Convergence properties of the latter algorithm are improved by employing a relaxed version of the augmented Lagrangian method, and numerical examples are provided to demonstrate the utility of our results.

“…The synthesis problem of distributed control for interconnected systems has received considerable attention in recent years [1]- [14]. For linear spatially invariant plants, it was shown in [1] that optimal controllers are themselves spatially invariant.…”

mentioning

confidence: 99%

On the optimal design of structured feedback gains for interconnected systems

Proceedings of the 48h IEEE Conference on Decision and Control (CDC) Held Jointly With 2009 28th Chinese Control Conference

2009

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We consider the design of optimal static feedback gains for interconnected systems subject to architectural constraints on the distributed controller. These constraints are in the form of sparsity requirements for the feedback matrix, which means that each controller has access to information from only a limited number of subsystems. We derive necessary conditions for the optimality of structured static feedback gains in the form of coupled matrix equations. In general these equations have multiple solutions, each of which is a stationary point of the objective function. For stable open-loop systems, we show that in the limit of expensive control, the optimal controller can be found analytically using perturbation techniques. We use this feedback gain to initialize homotopybased gradient and Newton iterations that find an optimal solution to the original (non-expensive) control problem. For unstable open-loop systems, the centralized truncated gain is used as an initial estimate for the iterative schemes aimed at finding the optimal structured feedback gain. We consider both spatially invariant and spatially varying problems and illustrate our developments with several examples.