A nonlinear partially observed differential game with a finite-dimensional information state

1995 ◽  
Vol 26 (2) ◽  
pp. 137-145 ◽  
Author(s):  
M.R. James ◽  
S. Yuliar
Keyword(s):  
Differential Game ◽  
Information State ◽  
Finite Dimensional ◽  
Partially Observed

Minimax differential game with delay

2020 ◽  
pp. 359-369
Author(s):  
Arkadii V. Kim ◽  
Gennady A. Bocharov
Keyword(s):  
Dynamic Programming ◽  
Differential Games ◽  
Differential Game ◽  
Programming Method ◽  
Dynamic Programming Method ◽  
Mixed Strategies ◽  
Dimensional Theory ◽  
Analysis Methodology ◽  
Finite Dimensional ◽  
Finite Dimensional Case

The paper considers a minimax positional differential game with aftereffect based on the i-smooth analysis methodology. In the finite-dimensional (ODE) case for a minimax differential game, resolving mixed strategies can be constructed using the dynamic programming method. The report shows that the i-smooth analysis methodology allows one to construct counterstrategies in a completely similar way to the finite-dimensional case. Moreover as it is typical for the use of i-smooth analysis, in the absence of an aftereffect, all the results of the article pass to the corresponding results of the finite-dimensional theory of positional differential games.

General necessary conditions for partially observed optimal stochastic controls

1995 ◽  
Vol 32 (4) ◽  
pp. 1118-1137 ◽  
Author(s):  
Xunjing Li ◽  
Shanjian Tang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Problem ◽  
Necessary Conditions ◽  
Probabilistic Approach ◽  
The Maximum Principle ◽  
Finite Dimensional ◽  
Partially Observed ◽  
Stochastic Controls ◽  
Partially Observable

The partially observed control problem is considered for stochastic processes with control entering into the diffusion and the observation. The maximum principle is proved for the partially observable optimal control. A pure probabilistic approach is used, and the adjoint processes are characterized as solutions of related backward stochastic differential equations in finite-dimensional spaces. Most of the derivation is identified with that of the completely observable case.

General necessary conditions for partially observed optimal stochastic controls

1995 ◽  
Vol 32 (04) ◽  
pp. 1118-1137 ◽  
Author(s):  
Xunjing Li ◽  
Shanjian Tang
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Control Problem ◽  
Necessary Conditions ◽  
Probabilistic Approach ◽  
The Maximum Principle ◽  
Finite Dimensional ◽  
Partially Observed ◽  
Stochastic Controls ◽  
Partially Observable

The partially observed control problem is considered for stochastic processes with control entering into the diffusion and the observation. The maximum principle is proved for the partially observable optimal control. A pure probabilistic approach is used, and the adjoint processes are characterized as solutions of related backward stochastic differential equations in finite-dimensional spaces. Most of the derivation is identified with that of the completely observable case.

Non-Linear Dynamics of Cardiovascular Variability Signals

1994 ◽  
Vol 33 (01) ◽  
pp. 81-84 ◽  
Author(s):  
S. Cerutti ◽  
S. Guzzetti ◽  
R. Parola ◽  
M.G. Signorini
Keyword(s):  
Dimensional Space ◽  
Severe Heart Failure ◽  
Parametric Models ◽  
Deterministic Systems ◽  
Finite Dimensional ◽  
Return Maps ◽  
Pathological Conditions ◽  
Non Linear ◽  
Space State

Abstract:Long-term regulation of beat-to-beat variability involves several different kinds of controls. A linear approach performed by parametric models enhances the short-term regulation of the autonomic nervous system. Some non-linear long-term regulation can be assessed by the chaotic deterministic approach applied to the beat-to-beat variability of the discrete RR-interval series, extracted from the ECG. For chaotic deterministic systems, trajectories of the state vector describe a strange attractor characterized by a fractal of dimension D. Signals are supposed to be generated by a deterministic and finite dimensional but non-linear dynamic system with trajectories in a multi-dimensional space-state. We estimated the fractal dimension through the Grassberger and Procaccia algorithm and Self-Similarity approaches of the 24-h heart-rate variability (HRV) signal in different physiological and pathological conditions such as severe heart failure, or after heart transplantation. State-space representations through Return Maps are also obtained. Differences between physiological and pathological cases have been assessed and generally a decrease in the system complexity is correlated to pathological conditions.

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