Discrete-Time Linear-Quadratic Dynamic Games

Finite-dimensional, time invariant, linear quadratic dynamic games are perhaps the best understood and researched class of dynamic games. This is particularly true for continuous-time linear quadratic differential games. In this paper, the application of the theory of dynamic games to signal process...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2010-07, Vol.146 (1), p.151-179
Main Authors: Pachter, M., Pham, K. D.
Format: Article
Language:English
Subjects:
Algorithms
Applications of Mathematics
Applied sciences
Calculus of Variations and Optimal Control
Optimization
Controllers
Digital signal processing
Disturbances
Dynamical systems
Dynamics
Engineering
Exact sciences and technology
Exact solutions
Game theory
Games
Inertia
Linear quadratic
Mathematical analysis
Mathematical programming
Mathematics
Mathematics and Statistics
Noise
Operational research and scientific management
Operational research. Management science
Operations Research/Decision Theory
Optimization
Rejection
Signal processing
Studies
Theory of Computation
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Summary:Finite-dimensional, time invariant, linear quadratic dynamic games are perhaps the best understood and researched class of dynamic games. This is particularly true for continuous-time linear quadratic differential games. In this paper, the application of the theory of dynamic games to signal processing is considered. We are interested in digital signal processing and therefore we confine our attention to discrete-time linear-quadratic dynamic games (LQDG). In discrete-time the cost function contains product terms between the decision variables which complicates the analysis compared to its continuous-time analogue. With a view to facilitate the application of the theory of dynamic games to digital signal processing, and in particular, disturbance rejection, the complete solution of the discrete-time LQDG is worked out and explicit results are obtained. Thus,discrete-time LQDGs have the distinct advantage of being amenable to analysis, closed-form solutions are possible, and one is in tune with modern digital signal processing techniques. In this paper, minimal necessary and sufficient conditions for the existence of a solution to the discrete-time LQDG are provided and its explicit, closed-form, solution is worked out. This opens the way to designing novel digital signal processing algorithms for disturbance rejection. Information plays a critical role in game theory and in particular in dynamic games. Using our explicit solution of the deterministic LQDG, a hierarchy of three zero-sum stochastic LQDGs characterized by a sequence of information patterns which increase in complexity is analyzed.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-010-9661-x