Infinite Horizon Discrete Time Control Problems for Bounded Processes
نویسنده
چکیده
We establish Pontryagin Maximum Principles in the strong form for infinite horizon optimal control problems for bounded processes, for systems governed by difference equations. Results due to Ioffe and Tihomirov are among the tools used to prove our theorems. We write necessary conditions with weakened hypotheses of concavity and without invertibility, and we provide new results on the adjoint variable. We show links between bounded problems and nonbounded ones. We also give sufficient conditions of optimality.
منابع مشابه
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...
متن کاملSolving infinite horizon optimal control problems of nonlinear interconnected large-scale dynamic systems via a Haar wavelet collocation scheme
We consider an approximation scheme using Haar wavelets for solving a class of infinite horizon optimal control problems (OCP's) of nonlinear interconnected large-scale dynamic systems. A computational method based on Haar wavelets in the time-domain is proposed for solving the optimal control problem. Haar wavelets integral operational matrix and direct collocation method are utilized to find ...
متن کاملInfinite horizon H2/H∞ control for discrete-time time-varying Markov jump systems with multiplicative noise
In this paper we consider the infinite horizon H2/H∞ control problem for discrete-time timevarying linear systems subject to Markov jump parameters and state-multiplicative noises. A stochastic bounded real lemma is firstly developed for a class of discrete-time time-varying Markov jump systems with stateand disturbance-multiplicative noises. Based on which, a necessary and sufficient condition...
متن کاملDynamic Monetary Risk Measures for Bounded Discrete-Time Processes
We study time-consistency questions for processes of monetary risk measures that depend on bounded discrete-time processes describing the evolution of financial values. The time horizon can be finite or infinite. We call a process of monetary risk measures time-consistent if it assigns to a process of financial values the same risk irrespective of whether it is calculated directly or in two ste...
متن کاملAn Abelian Limit Approach to a Singular Ergodic Control Problem
We consider an ergodic stochastic control problem for a class of one-dimensional Itô processes where the available control is an added bounded variation process. The corresponding infinite horizon discounted control problem is solved in [28]. Here, we show that, as the discount factor approaches zero, the optimal strategies derived in [28] “converge” to an optimal strategy for the ergodic contr...
متن کامل