An Optimal Feedback Control-Strategy Pair For Zero-Sum Linear-Quadratic Stochastic Differential Game: the Riccati Equation Approach

2015 ◽  
Vol 53 (4) ◽  
pp. 2141-2167 ◽  
Author(s):  
Zhiyong Yu
Keyword(s):  
Feedback Control ◽  
Riccati Equation ◽  
Differential Game ◽  
Control Strategy ◽  
Optimal Feedback Control ◽  
Stochastic Differential Game ◽  
Equation Approach ◽  
Linear Quadratic ◽  
Feedback Control Strategy ◽  
Zero Sum

scholarly journals An Analytic and Numerical Investigation of a Differential Game

Axioms ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 66
Author(s):  
Aviv Gibali ◽  
Oleg Kelis
Keyword(s):  
Differential Game ◽  
Equation Approach ◽  
Linear Quadratic ◽  
Control Cost ◽  
Dual Representation ◽  
Cost Functional ◽  
Variational Derivatives ◽  
Zero Sum ◽  
The Cost ◽  
Derivatives Of

In this paper we present an appropriate singular, zero-sum, linear-quadratic differential game. One of the main features of this game is that the weight matrix of the minimizer’s control cost in the cost functional is singular. Due to this singularity, the game cannot be solved either by applying the Isaacs MinMax principle, or the Bellman–Isaacs equation approach. As an application, we introduced an interception differential game with an appropriate regularized cost functional and developed an appropriate dual representation. By developing the variational derivatives of this regularized cost functional, we apply Popov’s approximation method and show how the numerical results coincide with the dual representation.

scholarly journals An Optimal Feedback Control Strategy for Nonlinear, Distributed-Parameter Processes

Processes ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 758 ◽  
Author(s):  
Debaprasad Dutta ◽  
Simant Ranjan Upreti
Keyword(s):  
Feedback Control ◽  
Oil Recovery ◽  
Control Strategy ◽  
Moving Boundary ◽  
State Feedback Control ◽  
Optimal Feedback Control ◽  
Distributed Parameter ◽  
Optimal State ◽  
Non Linear ◽  
Feedback Control Strategy

In this work, an optimal state feedback control strategy is proposed for non-linear, distributed-parameter processes. For different values of a given parameter susceptible to upsets, the strategy involves off-line computation of a repository of optimal open-loop states and gains needed for the feedback adjustment of control. A gain is determined by minimizing the perturbation of the objective functional about the new optimal state and control corresponding to a process upset. When an upset is encountered in a running process, the repository is utilized to obtain the control adjustment required to steer the process to the new optimal state. The strategy is successfully applied to a highly non-linear, gas-based heavy oil recovery process controlled by the gas temperature with the state depending non-linearly on time and two spatial directions inside a moving boundary, and subject to pressure upsets. The results demonstrate that when the process has a pressure upset, the proposed strategy is able to determine control adjustments with negligible time delays and to navigate the process to the new optimal state.

scholarly journals Partial Information Stochastic Differential Games for Backward Stochastic Systems Driven by Lévy Processes

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Fu Zhang ◽  
QingXin Meng ◽  
MaoNing Tang
Keyword(s):  
Differential Game ◽  
Stochastic Systems ◽  
Partial Information ◽  
Backward Stochastic Differential Equation ◽  
Game Problem ◽  
Stochastic Differential Game ◽  
Linear Quadratic ◽  
Independent Brownian Motion ◽  
Teugels Martingales ◽  
Zero Sum

In this paper, we consider a partial information two-person zero-sum stochastic differential game problem, where the system is governed by a backward stochastic differential equation driven by Teugels martingales and an independent Brownian motion. A sufficient condition and a necessary one for the existence of the saddle point for the game are proved. As an application, a linear quadratic stochastic differential game problem is discussed.

CONTINUOUS FEEDBACK CONTROL STRATEGY WITH MAXIMAL CAPTURE ZONE IN A CLASS OF PURSUIT GAMES

2005 ◽  
Vol 07 (01) ◽  
pp. 1-24 ◽  
Author(s):  
VLADIMIR TURETSKY ◽  
VALERY Y. GLIZER
Keyword(s):  
Feedback Control ◽  
Differential Game ◽  
Linear Feedback ◽  
Capture Zone ◽  
State Variables ◽  
Linear Quadratic ◽  
Kinematical Model ◽  
Continuous Feedback ◽  
Feedback Control Strategy ◽  
Noisy Measurements

An interception problem of a highly maneuverable target is considered using a linearized kinematical model with first order acceleration dynamics of the interceptor and the target. The problem is interpreted as a differential game of pursuit. An admissible pursuer (interceptor) feedback strategy, continuous with respect to the state variables and having a maximal capture zone, is constructed. This strategy is the saturated version of a linear feedback control, obtained from the solution of an auxiliary linear-quadratic differential game with cheap controls. This strategy is evaluated by Monte-Carlo simulation of the interception with noisy measurements.

scholarly journals Nash Equilibrium Sequence in a Singular Two-Person Linear-Quadratic Differential Game

Axioms ◽  
2021 ◽  
Vol 10 (3) ◽  
pp. 132
Author(s):  
Valery Y. Glizer
Keyword(s):  
Nash Equilibrium ◽  
Differential Game ◽  
Quadratic Functional ◽  
Linear Quadratic ◽  
Feedback Controls ◽  
Cheap Control ◽  
Optimal Values ◽  
Definition Of ◽  
Zero Sum ◽  
Equilibrium Sequence

A finite-horizon two-person non-zero-sum differential game is considered. The dynamics of the game is linear. Each of the players has a quadratic functional on its own disposal, which should be minimized. The case where weight matrices in control costs of one player are singular in both functionals is studied. Hence, the game under the consideration is singular. A novel definition of the Nash equilibrium in this game (a Nash equilibrium sequence) is proposed. The game is solved by application of the regularization method. This method yields a new differential game, which is a regular Nash equilibrium game. Moreover, the new game is a partial cheap control game. An asymptotic analysis of this game is carried out. Based on this analysis, the Nash equilibrium sequence of the pairs of the players’ state-feedback controls in the singular game is constructed. The expressions for the optimal values of the functionals in the singular game are obtained. Illustrative examples are presented.

Sign in / Sign up

Export Citation Format

Share Document