Results 11  20
of
187
H2 optimal decentralized control over posets: A state space solution for statefeedback
 in Proceedings of the 49th IEEE Conference on Decision and Control
"... We develop a complete statespace solution to H2optimal decentralized control of posetcausal systems with statefeedback. Our solution is based on the exploitation of a key separability property of the problem, that enables an efficient computation of the optimal controller by solving a small numb ..."
Abstract

Cited by 47 (2 self)
 Add to MetaCart
(Show Context)
We develop a complete statespace solution to H2optimal decentralized control of posetcausal systems with statefeedback. Our solution is based on the exploitation of a key separability property of the problem, that enables an efficient computation of the optimal controller by solving a small number of uncoupled standard Riccati equations. Our approach gives important insight into the structure of optimal controllers, such as controller degree bounds that depend on the structure of the poset. A novel element in our statespace characterization of the controller is a remarkable pair of transfer functions, that belong to the incidence algebra of the poset, are inverses of each other, and are intimately related to prediction of the state along the different paths on the poset. The results are illustrated by a numerical example. I.
An Elementary Counterexample to the Finiteness Conjecture
 SIAM JOURNAL ON MATRIX ANALYSIS
, 2001
"... ..."
Randomized algorithms for probabilistic robustness with real and complex structured uncertainty
 IEEE Trans. Autom. Control
, 2000
"... Abstract—In recent years, there has been a growing interest in developing randomized algorithms for probabilistic robustness of uncertain control systems. Unlike classical worst case methods, these algorithms provide probabilistic estimates assessing, for instance, if a certain design specification ..."
Abstract

Cited by 45 (13 self)
 Add to MetaCart
(Show Context)
Abstract—In recent years, there has been a growing interest in developing randomized algorithms for probabilistic robustness of uncertain control systems. Unlike classical worst case methods, these algorithms provide probabilistic estimates assessing, for instance, if a certain design specification is met with a given probability. One of the advantages of this approach is that the robustness margins can be often increased by a considerable amount, at the expense of a small risk. In this sense, randomized algorithms may be used by the control engineer together with standard worst case methods to obtain additional useful information. The applicability of these probabilistic methods to robust control is presently limited by the fact that the sample generation is feasible only in very special cases which include systems affected by real parametric uncertainty bounded in rectangles or spheres. Sampling in more general uncertainty sets is generally performed through overbounding, at the expense of an exponential rejection rate. In this paper, randomized algorithms for stability and performance of linear time invariant uncertain systems described by a general1 configuration are studied. In particular, efficient polynomialtime algorithms for uncertainty structures 1 consisting of an arbitrary number of full complex blocks and uncertain parameters are developed. Index Terms—Random matrices, randomized algorithms, robust control, uncertainty. I.
Computationally efficient approximations of the joint spectral radius
 SIAM J. Matrix Anal
, 2005
"... Abstract. The joint spectral radius of a set of matrices is a measure of the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from the set. This quantity appears in a number of application contexts but is notoriously difficult to compute and to approxima ..."
Abstract

Cited by 38 (7 self)
 Add to MetaCart
(Show Context)
Abstract. The joint spectral radius of a set of matrices is a measure of the maximal asymptotic growth rate that can be obtained by forming long products of matrices taken from the set. This quantity appears in a number of application contexts but is notoriously difficult to compute and to approximate. We introduce in this paper a procedure for approximating the joint spectral radius of a finite set of matrices with arbitrary high accuracy. Our approximation procedure is polynomial in the size of the matrices once the number of matrices and the desired accuracy are fixed. For the special case of matrices with nonnegative entries we give elementary proofs of simple inequalities that we then use to obtain approximations of arbitrary high accuracy. From these inequalities it follows that the spectral radius of matrices with nonnegative entries is given by the simple expression ρ(A1,...,Am) = lim k→ ∞ ρ1/k (A ⊗k 1 + ···+ A⊗k m), where it is somewhat surprising to notice that the righthand side does not directly involve any mixed product between the matrices. (A ⊗k denotes the kth Kronecker power of A.)
Decentralized control information structures preserved under feedback
 In Proc. IEEE Conference on Decision and Control
, 2002
"... We consider the problem of constructing decentralized control systems. We formulate this problem as one of minimizing the closedloop norm of a feedback system subject to constraints on the controller structure. We de¯ne the notion of quadratic invariance of a constraint set with respect to a system ..."
Abstract

Cited by 38 (16 self)
 Add to MetaCart
(Show Context)
We consider the problem of constructing decentralized control systems. We formulate this problem as one of minimizing the closedloop norm of a feedback system subject to constraints on the controller structure. We de¯ne the notion of quadratic invariance of a constraint set with respect to a system, and show that if the constraint set has this property, then the constrained minimum norm problem may be solved via convex programming. We also show that quadratic invariance is necessary and su±cient for the constraint set to be preserved under feedback. We develop necessary and su±cient conditions under which the constraint set is quadratically invariant, and show that many examples of decentralized synthesis which have been proven to be solvable in the literature are quadratically invariant. As an example, we show that a controller which minimizes the norm of the closedloop map may be e±ciently computed in the case where distributed controllers can communicate faster than the propagation delay of the plant dynamics.
An adaptive sampling algorithm for solving Markov decision processes
 Operations Research
, 2005
"... Based on recent results for multiarmed bandit problems, we propose an adaptive sampling algorithm that approximates the optimal value of a finite horizon Markov decision process (MDP) with infinite state space but finite action space and bounded rewards. The algorithm adaptively chooses which actio ..."
Abstract

Cited by 37 (8 self)
 Add to MetaCart
Based on recent results for multiarmed bandit problems, we propose an adaptive sampling algorithm that approximates the optimal value of a finite horizon Markov decision process (MDP) with infinite state space but finite action space and bounded rewards. The algorithm adaptively chooses which action to sample as the sampling process proceeds, and it is proven that the estimate produced by the algorithm is asymptotically unbiased and the worst possible bias is bounded by a quantity that converges to zero at rate O � � H ln N N,whereHis the horizon length and N is the total number of samples that are used per state sampled in each stage. The worstcase runningtime complexity of the algorithm is O((AN) H), independent of the state space size, where A  is the size of the action space. The algorithm can be used to create an approximate receding horizon control to solve infinite horizon MDPs.
The Wireless Control Network: A New Approach for Control Over Networks
, 2011
"... We present a method to stabilize a plant with a network of resource constrained wireless nodes. As opposed to traditional networked control schemes where the nodes simply route information to and from a dedicated controller (perhaps performing some encoding along the way), our approach treats the ne ..."
Abstract

Cited by 29 (6 self)
 Add to MetaCart
We present a method to stabilize a plant with a network of resource constrained wireless nodes. As opposed to traditional networked control schemes where the nodes simply route information to and from a dedicated controller (perhaps performing some encoding along the way), our approach treats the network itself as the controller. Specifically, we formulate a strategy for each node in the network to follow, where at each timestep, each node updates its internal state to be a linear combination of the states of the nodes in its neighborhood. We show that this causes the entire network to behave as a linear dynamical system, with sparsity constraints imposed by the network topology. We provide a numerical design procedure to determine appropriate linear combinations to be applied by each node so that the transmissions of the nodes closest to the actuators will stabilize the plant. We also show how our design procedure can be modified to maintain mean square stability under packet drops in the network, and presen ta distributed scheme that can handle node failures while preserving stability. We call this architecture a Wireless Control Network, and show that it introduces very low computational and communication overhead to the nodes in the network, allows the use of simple transmission scheduling algorithms, and enables compositional design (where the existing wireless control infrastructure can be easily extended to handle new plants that are brought online in the vicinity of the network).
Deciding Stability and Mortality of Piecewise Affine Dynamical Systems
, 2001
"... In this paper we studyproblJ: such as: given a discrete timedynamical system of the form x(t +1)=f(x(t)) where f : R n #R n is a piecewise a#ne function, decide whetheral trajectories converge to 0. We show in our main theorem that this AttractivityProblc isundecidabl as soon as n2. The same is ..."
Abstract

Cited by 28 (0 self)
 Add to MetaCart
In this paper we studyproblJ: such as: given a discrete timedynamical system of the form x(t +1)=f(x(t)) where f : R n #R n is a piecewise a#ne function, decide whetheral trajectories converge to 0. We show in our main theorem that this AttractivityProblc isundecidabl as soon as n2. The same is true of tworelkMI problI+J Stabil+J (is thedynamical systemglJH #RI asymptotical# stablto andMortal#M (do al trajectories go through 0?). We then show that Attractivity andStabilI: becomedecidabl in dimension 1 for continuous functions. c # 2001El1/JkR Science B.V.Al rights reserved. Keywords: Discretedynamical systems; Piecewise a#ne systems; Piecewiselecew systems; Hybrid systems;Mortal/JM Stabil/JM Decidabilk: 1.IP141 In this paper we studyproblJ+ such as: given a discrete timedynamical system of the form x(t +1)=f(x(t)) where f : R n #R n is a(possibl discontinuous) piecewise # This research waspartl carried outwhil Bllkk was visitingTsitsiklJ at MIT (Cambridge) and Koiran at ENS (Lyon). This research was supported by the ARO under grant DAAL0392G0115, by the NATO under grant CRG961115 and by the European Commission under the TMR(AlMkI;/z network contract ERBFMRXCT960074. # Corresponding author. Email addresses: blmCppCpA/J#JM:/zRkJ; (V.D.BlD./kIH Ol./kIH:J/zRkJ;/lkJ;/l (O. Bournez), pascal),/;MJMI/zRkJ;/ll (P. Koiran), christos@cs.berkel/ll (C.H. Papadimitriou), jnt@mit.edu (J.N. TsitsiklM#/ 03043975/01/$  see front matter c # 2001El1/kRk Science B.V.Al rights reserved. PII: S03043975(00)003996 688 V.D. Blondel et al. / Theoretical Computer Science 255 (2001) 687696 a#ne function, decide whetheral trajectories converge to 0. We show in our main theorem (Theorem 2) that this AttractivityProblc isundecidabl as soon as n2. The same is true of t...
Random sampling of states in dynamic programming
 in Proc. NIPS Conf., 2007
"... Abstract—We combine three threads of research on approximate dynamic programming: sparse random sampling of states, value function and policy approximation using local models, and using local trajectory optimizers to globally optimize a policy and associated value function. Our focus is on finding s ..."
Abstract

Cited by 23 (4 self)
 Add to MetaCart
(Show Context)
Abstract—We combine three threads of research on approximate dynamic programming: sparse random sampling of states, value function and policy approximation using local models, and using local trajectory optimizers to globally optimize a policy and associated value function. Our focus is on finding steadystate policies for deterministic timeinvariant discrete time control problems with continuous states and actions often found in robotics. In this paper, we describe our approach and provide initial results on several simulated robotics problems. Index Terms—Dynamic programming, optimal control, random sampling. I.