Minimax control of a multivariate time-continuous linear stochastic system

Stochastic Control in Continuous Time

A Linear Time Algorithm for Near Minimax Continuous Piecewise Linear Representations of Discrete Data

An algorithm that constructs a continuous piecewise linear representation, subject to a certain slope/segment length constraint, of a given set of data is described. The algorithm yields an optimal or near optimal representation, subject to this constraint, in the L∞ norm and does so in at worst O(nK) time, where n is the number of data points and K the number of segments. The constraint is det...

Minimax Trees in Linear Time

A minimax tree is similar to a Huffman tree except that, instead of minimizing the weighted average of the leaves’ depths, it minimizes the maximum of any leaf’s weight plus its depth. Golumbic (1976) introduced minimax trees and gave a Huffman-like, O(n log n)-time algorithm for building them. Drmota and Szpankowski (2002) gave another O(n log n)-time algorithm, which checks the Kraft Inequali...

Idempotent Expansions for Continuous-Time Stochastic Control

It is now well-known that many classes of deterministic control problems may be solved by max-plus or minplus (more generally, idempotent) numerical methods. These methods include max-plus basis-expansion approaches [1], [2], [6], [9], as well as the more recently developed curseof-dimensionality-free methods [9], [14]. It has recently been discovered that idempotent methods are applicable to s...

Optimal Finite-time Control of Positive Linear Discrete-time Systems

This paper considers solving optimization problem for linear discrete time systems such that closed-loop discrete-time system is positive (i.e., all of its state variables have non-negative values) and also finite-time stable. For this purpose, by considering a quadratic cost function, an optimal controller is designed such that in addition to minimizing the cost function, the positivity proper...