scholarly journals Risk-sensitive control of stochastic hybrid systems on infinite time horizon

2000 ◽  
Vol 5 (6) ◽  
pp. 459-478 ◽  
Author(s):  
Thordur Runolfsson
Keyword(s):  
Control Problem ◽  
Hybrid Systems ◽  
Risk Sensitivity ◽  
Optimal Controls ◽  
Stochastic Hybrid Systems ◽  
Risk Sensitive ◽  
Risk Sensitive Control ◽  
Equivalence Relationship ◽  
Noise Input ◽  
The Cost

A risk-sensitive optimal control problem is considered for a hybrid system that consists of continuous time diffusion process that depends on a discrete valued mode variable that is modeled as a Markov chain. Optimality conditions are presented and conditions for the existence of optimal controls are derived. It is shown that the optimal risk-sensitive control problem is equivalent to the upper value of an associated stochastic differential game, and insight into the contributions of the noise input and mode variable to the risk sensitivity of the cost functional is given. Furthermore, it is shown that due to the mode variable risk sensitivity, the equivalence relationship that has been observed between risk-sensitive andH∞control in the nonhybrid case does not hold for stochastic hybrid systems.

scholarly journals On the policy improvement algorithm for ergodic risk-sensitive control

2020 ◽  
pp. 1-26
Author(s):  
Ari Arapostathis ◽  
Anup Biswas ◽  
Somnath Pradhan
Keyword(s):  
Control Problem ◽  
General Result ◽  
Region Of Attraction ◽  
Policy Improvement ◽  
Improvement Algorithm ◽  
Risk Sensitive ◽  
Risk Sensitive Control ◽  
Whole Space ◽  
Controlled Diffusions ◽  
Running Cost

In this article we consider the ergodic risk-sensitive control problem for a large class of multidimensional controlled diffusions on the whole space. We study the minimization and maximization problems under either a blanket stability hypothesis, or a near-monotone assumption on the running cost. We establish the convergence of the policy improvement algorithm for these models. We also present a more general result concerning the region of attraction of the equilibrium of the algorithm.

Analysis of a risk-sensitive control problem for hidden Markov chains

1999 ◽  
Vol 44 (5) ◽  
pp. 1093-1100 ◽  
Author(s):  
D. Hernandez-Hernandez ◽  
S.I. Marcus ◽  
P.J. Fard
Keyword(s):  
Markov Chains ◽  
Control Problem ◽  
Hidden Markov ◽  
Hidden Markov Chains ◽  
Risk Sensitive ◽  
Risk Sensitive Control

Robust Variance-constrained Control of a Class of Stochastic Hybrid Systems

2010 ◽  
Vol 36 (2) ◽  
pp. 337-343
Author(s):  
You-Li WU ◽  
Yang-Wang FANG ◽  
Hong-Qiang WANG ◽  
Wen-Jie LIU
Keyword(s):  
Hybrid Systems ◽  
Constrained Control ◽  
Stochastic Hybrid Systems ◽  
Robust Variance

scholarly journals An Optimal Control Problem by a Hybrid System of Hyperbolic and Ordinary Differential Equations

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 23
Author(s):  
Alexander Arguchintsev ◽  
Vasilisa Poplevko
Keyword(s):  
Optimal Control ◽  
Differential Equations ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Ordinary Differential Equations ◽  
Hyperbolic Equations ◽  
Control Methods ◽  
The Right ◽  
The Cost ◽  
Optimal Control Methods

This paper deals with an optimal control problem for a linear system of first-order hyperbolic equations with a function on the right-hand side determined from controlled bilinear ordinary differential equations. These ordinary differential equations are linear with respect to state functions with controlled coefficients. Such problems arise in the simulation of some processes of chemical technology and population dynamics. Normally, general optimal control methods are used for these problems because of bilinear ordinary differential equations. In this paper, the problem is reduced to an optimal control problem for a system of ordinary differential equations. The reduction is based on non-classic exact increment formulas for the cost-functional. This treatment allows to use a number of efficient optimal control methods for the problem. An example illustrates the approach.

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