A Minimax Formulation of theIn nite - Dimensional
نویسنده
چکیده
We formulate a minimax game which is equivalent to the Nehari problem in the sense that this minimax game is well-posed if and only if the Hankel norm of a given operator is less than a prescribed constant. This game and the dual game provide us with physical interpretations of the Riccati operators that are commonly used in the solution of the Nehari problem.
منابع مشابه
On the Minimax Optimality of Block Thresholded Wavelets Estimators for ?-Mixing Process
We propose a wavelet based regression function estimator for the estimation of the regression function for a sequence of ?-missing random variables with a common one-dimensional probability density function. Some asymptotic properties of the proposed estimator based on block thresholding are investigated. It is found that the estimators achieve optimal minimax convergence rates over large class...
متن کاملInformation States in Optimal Control and Filtering: A Lie Algebraic Theoretic Approach
The purpose of this paper is twofold; (i) to introduce the suucient statistic algebra which is responsible for propagating the suucient statistic, or information state, in the optimal control of stochastic systems, and (ii) to apply certain Lie algebraic methods widely used in nonlinear control theory, to derive new results concerning nite-dimensional controllers. This, enhances our understandi...
متن کاملFinite-dimensional nonlinear output feedback dynamic games and bounds for sector nonlinearities
In general, nonlinear output feedback dynamic games are innnite-dimensional. This paper treats a class of minimax games when the nonlinearities enter the dynamics of the unobservable states. An information state approach is introduced to re-cast these games as one of full information in innnite-dimensions. Explicit solutions of the rst-order partial diieren-tial information state equation are d...
متن کاملMixed Risk-Neutral/Minimax Control of Markov Decision Processes
This paper introduces a formulation of the mixed risk-neutral/minimax control problem for Markov Decision Processes (MDPs). Drawing on results from risk-neutral control and minimax control, we derive an information state process and dynamic programming equations for the value function. Furthermore, we develop a methodology to synthesize an optimal control law on the nite horizon, and a near-opt...
متن کاملFrameness bound for frame of subspaces
In this paper, we show that in each nite dimensional Hilbert space, a frame of subspaces is an ultra Bessel sequence of subspaces. We also show that every frame of subspaces in a nite dimensional Hilbert space has frameness bound.
متن کامل