An adaptive tracking problem is considered for a linear stochastic SISO control plant. Several information bounds are obtained under a variety of conditions imposed on the disturbances and control strategies.
ISBN:
(纸本)0080417175
An adaptive tracking problem is considered for a linear stochastic SISO control plant. Several information bounds are obtained under a variety of conditions imposed on the disturbances and control strategies.
An indirect adaptive control algorithm for a MIMO plant is studied. It is shown that Polyak-Ruppert estimation algorithm along with the simple dead-beat control law constitutes an adaptive control strategy that achiev...
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ISBN:
(纸本)0080417175
An indirect adaptive control algorithm for a MIMO plant is studied. It is shown that Polyak-Ruppert estimation algorithm along with the simple dead-beat control law constitutes an adaptive control strategy that achieves the highest possible rate of convergence for the quadratic criterion.
Given a function F : N+ --> {X,Y} with the property that if F(n0) = Y then F(n) = Y for all n > n0, the unbounded search problem is to use tests of the form "is F(i) = X?" to determine the smallest n s...
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Given a function F : N+ --> {X,Y} with the property that if F(n0) = Y then F(n) = Y for all n > n0, the unbounded search problem is to use tests of the form "is F(i) = X?" to determine the smallest n such that F(n) = Y;the "cost" of a search algorithm is a function c(n), the number of such tests used when the location of the first Y is n. In Part I of this paper it is shown how to construct an infinite sequence of algorithms, each of which is much closer to optimality than its predecessor. Diagonalizing over this sequence yields a new algorithm that is far better than any of the algorithms in the sequence: this "omega-th" algorithm is within an additive factor of alpha-(n) + 2 of the corresponding lower bound, where alpha-(n) is a functional inverse of Ackermann's function-an extremely slowly growing function. In this paper the construction techiques are generalized to get dramatically better algorithms and lower bounds ad infinitum. Specifically, for each ordinal-iota less-than-or-equal-to epsilon-0, an algorithm is given that is dramatically closer to optimality than the algorithm corresponding to a smaller ordinal. All algorithms constructed for iota < epsilon-0 are proved to be optimal in a strong sense. Parallel results for the asymmetric case are also given.
Given a function F : N+ --> {X,Y} with the property that if F(n0) = Y then F(n) = Y for all n > n0, the unbounded search problem is to use tests of the form "is F(i) = X?" to determine the smallest n s...
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Given a function F : N+ --> {X,Y} with the property that if F(n0) = Y then F(n) = Y for all n > n0, the unbounded search problem is to use tests of the form "is F(i) = X?" to determine the smallest n such that F(n) = Y;the "cost" of a search algorithm is a function c(n), the number of such tests used when the location of the first Y is n. A solution to this search problem specifies a prefix-free, binary encoding of the positive integers in which the cost c(n) is the number of bits used to encode n. It is shown that the "ultimate algorithm," of Bentley and Yao [Inform. Process. Lett., 5 (1976), pp. 82-87], which is within an additive THETA-(lg* n) factor of a lower bound on the cost of this problem, is "far" from optimal in the sense that it is just the second in an infinite sequence of search algorithms, each of which is much closer to optimality than its predecessor. A corresponding sequence of lower bounds is also given, based on Kraft's inequality, each of which is much stronger than its predecessor. Diagonalizing over this sequence of search algorithms yields an algorithm, which is given explicitly in a Pascal-like notation, that is within an additive factor of alpha-(n) + 2 of the corresponding lower bound, where alpha-(n) is a functional inverse of Ackermann's function-an extremely slowly growing function. For each search algorithm, the corresponding prefix-free, binary encoding of the integers, is given, together with the decoding algorithm. Finally, algorithms/encodings are constructed that differ from the lower bounds by only negligible amounts even for the asymmetric case in which the cost of a Y answer and the cost of an X answer are not the same. In Part II it is shown how to continue the construction to get a transfinite sequence of dramatically better algorithms/encodings and lower bounds.
Linear arrays are characterized by a small communication bandwidth and a large communication diameter rendering them unsuited to the implementation of global computations. This paper presents efficient data movement a...
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Linear arrays are characterized by a small communication bandwidth and a large communication diameter rendering them unsuited to the implementation of global computations. This paper presents efficient data movement and partitioning techniques to overcome several shortcomings of linear arrays. These techniques are used to derive optimal parallel algorithms for several geometric problems on n x n images using a fixed-size linear array with p processors, where 1 less-than-or-equal-to p less-than-or-equal-to n. O(n2/p) time solutions are presented for labeling connected image regions, computing the convex hull of each region, and computing nearest neighbors. Consequently, a linear array with n processors can solve several image problems in O(n) time which is the same time taken by a two dimensional mesh-connected computer with n2 processors. Limitations of linear arrays are analyzed by presenting a class of image problems which can be solved sequentially in O(n2) time, but require OMEGA-(n2) time on a linear array, irrespective of the number of processors used and the partitioning of the input image among the processors. An alternate communication-efficient fixed-size organization with p processors is proposed to solve such problems in O(n2/p) time, for 1 less-than-or-equal-to p less-than-or-equal-to n.
Recently, Carlsson [3] proposed a variation of the heap data structure as an efficient implementation of a double-ended priority queue. This new data structure is referred to as thedeap. We show that constructing a de...
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Recently, Carlsson [3] proposed a variation of the heap data structure as an efficient implementation of a double-ended priority queue. This new data structure is referred to as thedeap. We show that constructing a deap with special properties can be done very easily, both sequentially and in parallel, by reducing the problem to selection and heap construction. Our parallel algorithm can be implemented to run inO(lognlog∗n) time using an optimal number of processors in the EREW-PRAM model or inO(logn) time using an optimal number of processors in the CRCW model.
A new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated. Convergence with probability one is proved for a variety of classical optimization and identification prob...
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A new recursive algorithm of stochastic approximation type with the averaging of trajectories is investigated. Convergence with probability one is proved for a variety of classical optimization and identification problems. It is also demonstrated for these problems that the proposed algorithm achieves the highest possible rate of convergence.
A graph G is P4-sparse if no set of five vertices in G induces more than one chordless path of length three. P4-sparse graphs generalize both the class of cographs and the class of P4-reducible graphs. One remarkable ...
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A graph G is P4-sparse if no set of five vertices in G induces more than one chordless path of length three. P4-sparse graphs generalize both the class of cographs and the class of P4-reducible graphs. One remarkable feature of P4-sparse graphs is that they admit a tree representation unique up to isomorphism. It has been shown that this tree representation can be obtained in polynomial time. This paper gives a linear time algorithm to recognize P4-sparse graphs and shows how the data structures returned by the recognition algorithm can be used to construct the corresponding tree representation in linear time.
A recursive stochastic optimization procedure under dependent disturbances is studied. It is based on the Polyak-Ruppert algorithm with trajectory averaging. Almost sure convergence of the algorithm is proved as well ...
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A recursive stochastic optimization procedure under dependent disturbances is studied. It is based on the Polyak-Ruppert algorithm with trajectory averaging. Almost sure convergence of the algorithm is proved as well as asymptotic normality of the delivered estimates. It is shown that the presented algorithm attains the highest possible asymptotic convergence rate for stochastic approximation algorithms
An adaptive tracking problem is considered for a linear stochastic SISO control plant. Several information bounds are obtained under a variety of conditions imposed on the disturbances and control strategies.
An adaptive tracking problem is considered for a linear stochastic SISO control plant. Several information bounds are obtained under a variety of conditions imposed on the disturbances and control strategies.
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