A computer aided design method for linear multirate digital control systems is presented in this paper. The design problem is formulated on the infinity norm of signals and the induced l(1)-system norm. An upper bound...
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ISBN:
(纸本)9780780397972
A computer aided design method for linear multirate digital control systems is presented in this paper. The design problem is formulated on the infinity norm of signals and the induced l(1)-system norm. An upper bound for the l(1)-system norm leading to niatrix inequalities is the basis of the design procedure. It is a characteristic feature of the method that the controller is attained by repeatedly solving small size convex optimization problems. Considering an example it turns out, that multirate digital controllers can help to overcome the well known problem of inflating controller order in l(1)-control.
We investigate solution of the maximum cut problem using a polyhedral cut and price approach. The dual of the well-known SDP relaxation of maxcut is formulated as a semi-infinite linear programming problem, which is s...
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We investigate solution of the maximum cut problem using a polyhedral cut and price approach. The dual of the well-known SDP relaxation of maxcut is formulated as a semi-infinite linear programming problem, which is solved within an interior point cutting plane algorithm in a dual setting;this constitutes the pricing (column generation) phase of the algorithm. Cutting planes based on the polyhedral theory of the maxcut problem are then added to the primal problem in order to improve the SDP relaxation;this is the cutting phase of the algorithm. We provide computational results, and compare these results with a standard SDP cutting plane scheme.
Let C be a n x n symmetric matrix. For each integer 1 = m(epsilon) >= Sigma(n)(i=1)lambda(i)(C) + epsilon(f) over bar - 2kL(2)/lambda(k+1)(C) - lambda(k)(C) epsilon(2) where (f) over bar is the minimum value of f o...
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Let C be a n x n symmetric matrix. For each integer 1 <= k < n we consider the minimization problem m(epsilon) := min(X) {Tr{CX} + epsilon(f)(X)}. Here the variable X is an n x n symmetric matrix, whose eigenvalues satisfy 0 <= lambda(i)(X) <= 1 and Sigma(n)(i=1)lambda(i)(X) = k, the number e is a positive (perturbation) parameter and f is a Lipchitz-continuous function (in general nonlinear). It is well known that when epsilon = 0 the minimum value, m(0), is the sum of the smallest k eigenvalues of C. Assuming that the eigenvalues of C satisfy lambda(1)(C) <= ... <= lambda(k)(C) < lambda(k+ 1)(C) <= ... <= lambda(n)(C), we establish the following upper and lower bounds for the minimum value m(epsilon): Sigma(n)(i=1)lambda(i)(C) + epsilon(f) over bar >= m(epsilon) >= Sigma(n)(i=1)lambda(i)(C) + epsilon(f) over bar - 2kL(2)/lambda(k+1)(C) - lambda(k)(C) epsilon(2) where (f) over bar is the minimum value of f over the solution set of unperturbed problem and L is the Lipschitz-constant of f. The above inequality shows that the error by replacing the upper bound (or the lower bound) by the exact value is at least quadratic in the perturbation parameter. We also treat the case that lambda(k+ 1)(C) = lambda(k)(C). We compare the exact solution with the upper and lower bounds for some examples.
This paper studies a stochastic linear-quadratic (LQ) control problem over an infinite time horizon with Markovian jumps in parameter values, allowing the weighting matrices in the cost to be indefinite. Coupled gener...
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ISBN:
(纸本)1424403316
This paper studies a stochastic linear-quadratic (LQ) control problem over an infinite time horizon with Markovian jumps in parameter values, allowing the weighting matrices in the cost to be indefinite. Coupled generalized algebraic Riccati equations (CGAREs) involving pesudo inverse of a matrix are introduced. It is shown that the solvability of the LQ problem boils down to that of the CGAREs. However, the system of the CGAREs is hard to treat. To overcome this difficulty, the corresponding semidefinite programming (SDP) and related duality are utilized. Several implication relations among the SDP complementary duality, the existence of the solution to the CGAREs and the optimality of LQ problem are established. A numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is presented: it identifies a stabilizing optimal feedback control or determines that the LQ problem has no optimal solution.
We consider a recently proposed optimization formulation of multi-task learning based on trace norm regularized least squares. While this problem may be formulated as a semidefinite program (SDP), its size is beyond g...
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We consider a recently proposed optimization formulation of multi-task learning based on trace norm regularized least squares. While this problem may be formulated as a semidefinite program (SDP), its size is beyond general SDP solvers. Previous solution approaches apply proximal gradient methods to solve the primal problem. We derive new primal and dual reformulations of this problem, including a reduced dual formulation that involves minimizing a convex quadratic function over an operator-norm ball in matrix space. This reduced dual problem may be solved by gradient-projection methods, with each projection involving a singular value decomposition. The dual approach is compared with existing approaches and its practical effectiveness is illustrated on simulations and an application to gene expression pattern analysis.
semidefinite programs are a class of optimization problems that have been studied extensively during the past 15 years. semidefinite programs are naturally related to linear programs, and both are defined using determ...
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semidefinite programs are a class of optimization problems that have been studied extensively during the past 15 years. semidefinite programs are naturally related to linear programs, and both are defined using deterministic data. Stochastic programs were introduced in the 1950s as a paradigm for dealing with uncertainty in data defining linear programs. In this paper, we introduce stochastic semidefinite programs as a paradigm for dealing with uncertainty in data defining semidefinite programs.
Abstract We consider the safety of a V-bar hopping manoeuvre which forms part of the final stage in autonomous space rendezvous. This manoeuvre is controlled by thrusters: we assume these inputs are perfect impulses a...
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Abstract We consider the safety of a V-bar hopping manoeuvre which forms part of the final stage in autonomous space rendezvous. This manoeuvre is controlled by thrusters: we assume these inputs are perfect impulses and model the system in a hybrid automaton framework. We consider the operation of the system under bounded parametric uncertainties, e.g. thruster misalignment, and use the concept of Barrier function certificates to assess system safety. This methodology provides an efficient tool for the systematic investigation of the safety property and does not rely on Monte-Carlo simulations. In particular, the existence of a Barrier function certificate guarantees that all trajectories of the system starting from a given initial set do not enter a predefined unsafe region under any possible combination of parameter deviations. Such a Barrier function certificate can be constructed efficiently using the Sum of Squares (SOS) decomposition and semi-definite programming (SDP).
This paper considers the problem of reducing the computational complexity associated with the Sum-of-Squares approach to stability analysis of time-delay systems. Specifically, this paper considers systems with a larg...
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ISBN:
(纸本)9781424474264
This paper considers the problem of reducing the computational complexity associated with the Sum-of-Squares approach to stability analysis of time-delay systems. Specifically, this paper considers systems with a large state-space but with relatively few delays-- the most common situation in practice. The paper uses the general framework of coupled differential-difference equations with delays in low-dimensional feedback channels. This framework includes both the standard delayed and neutral-type systems. The approach is based on recent results which introduced a new type of Lyapunov-Krasovskii form which was shown to be necessary and sufficient for stability of this class of systems. This paper shows how exploiting the structure of the new functional can yield dramatic improvements in computational complexity. Numerical examples are given to illustrate this improvement.
We derive an upper bound on the tail distribution of the transient waiting time for the GI/GI/1 queue from a formulation of semidefinite programming (SDP). Our upper bounds are expressed in closed forms using the firs...
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ISBN:
(纸本)9781450300384
We derive an upper bound on the tail distribution of the transient waiting time for the GI/GI/1 queue from a formulation of semidefinite programming (SDP). Our upper bounds are expressed in closed forms using the first two moments of the service time and the interarrival time. The upper bounds on the tail distributions are integrated to obtain the upper bounds on the corresponding expectations. We also extend the formulation of the SDP, using the higher moments of the service time and the interarrival time, and calculate upper bounds and lower bounds numerically.
This paper addresses the problem of locating a single source from noisy range measurements in wireless sensor networks. An approximate solution to the maximum likelihood location estimation problem is proposed, by red...
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ISBN:
(纸本)9781424442959
This paper addresses the problem of locating a single source from noisy range measurements in wireless sensor networks. An approximate solution to the maximum likelihood location estimation problem is proposed, by redefining the problem in the complex plane and relaxing the minimization problem into semidefinite programming form. Existing methods solve the source localization problem either by minimizing the maximum likelihood function iteratively or exploiting other semidefinite programming relaxations. In addition, using squared range measurements, exact and approximate least squares solutions can be calculated. Our relaxation for source localization in the complex plane (SLCP) is motivated by the near-convexity of the objective function and constraints in the complex formulation of the original (non-relaxed) problem. Simulation results indicate that the SLCP algorithm outperforms existing methods in terms of accuracy, particularly in the presence of outliers and when the number of anchors is larger than three.
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