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  1. Journal of Optimization Theory and Applications
  2. Journal of Optimization Theory and Applications : Volume 146
  3. Journal of Optimization Theory and Applications : Volume 146, Issue 1, July 2010
  4. Discrete-Time Linear-Quadratic Dynamic Games
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Journal of Optimization Theory and Applications : Volume 173
Journal of Optimization Theory and Applications : Volume 172
Journal of Optimization Theory and Applications : Volume 171
Journal of Optimization Theory and Applications : Volume 170
Journal of Optimization Theory and Applications : Volume 169
Journal of Optimization Theory and Applications : Volume 168
Journal of Optimization Theory and Applications : Volume 167
Journal of Optimization Theory and Applications : Volume 166
Journal of Optimization Theory and Applications : Volume 165
Journal of Optimization Theory and Applications : Volume 164
Journal of Optimization Theory and Applications : Volume 163
Journal of Optimization Theory and Applications : Volume 162
Journal of Optimization Theory and Applications : Volume 161
Journal of Optimization Theory and Applications : Volume 160
Journal of Optimization Theory and Applications : Volume 159
Journal of Optimization Theory and Applications : Volume 158
Journal of Optimization Theory and Applications : Volume 157
Journal of Optimization Theory and Applications : Volume 156
Journal of Optimization Theory and Applications : Volume 155
Journal of Optimization Theory and Applications : Volume 154
Journal of Optimization Theory and Applications : Volume 153
Journal of Optimization Theory and Applications : Volume 152
Journal of Optimization Theory and Applications : Volume 151
Journal of Optimization Theory and Applications : Volume 150
Journal of Optimization Theory and Applications : Volume 149
Journal of Optimization Theory and Applications : Volume 148
Journal of Optimization Theory and Applications : Volume 147
Journal of Optimization Theory and Applications : Volume 146
Journal of Optimization Theory and Applications : Volume 146, Issue 3, September 2010
Journal of Optimization Theory and Applications : Volume 146, Issue 2, August 2010
Journal of Optimization Theory and Applications : Volume 146, Issue 1, July 2010
Branch-and-Bound Outer Approximation Algorithm for Sum-of-Ratios Fractional Programs
Weak Convergence of an Iterative Method for Pseudomonotone Variational Inequalities and Fixed-Point Problems
An Inexact SQP Newton Method for Convex SC$^{1}$ Minimization Problems
On the Use of Outer Approximations as an External Active Set Strategy
Generalized Clarke Epiderivatives of Parametric Vector Optimization Problems
Existence of Solutions to Generalized Vector Variational-Like Inequalities
Multiple Solutions of Boundary-Value Problems for Fourth-Order Differential Equations with Deviating Arguments
Asymptotic Behavior for Retarded Parabolic Equations with Superlinear Perturbations
Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs
Discrete-Time Linear-Quadratic Dynamic Games
On the Application of the Perturbation Method in the Buckling Optimization of a Heavy Elastic Column of Constant Aspect Ratio
Multitime Dynamic Programming for Curvilinear Integral Actions
Recursive Algorithms for Trailing Stop: Stochastic Approximation Approach
Journal of Optimization Theory and Applications : Volume 145
Journal of Optimization Theory and Applications : Volume 144
Journal of Optimization Theory and Applications : Volume 143
Journal of Optimization Theory and Applications : Volume 142
Journal of Optimization Theory and Applications : Volume 141
Journal of Optimization Theory and Applications : Volume 140
Journal of Optimization Theory and Applications : Volume 139
Journal of Optimization Theory and Applications : Volume 138
Journal of Optimization Theory and Applications : Volume 137
Journal of Optimization Theory and Applications : Volume 136
Journal of Optimization Theory and Applications : Volume 135
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Journal of Optimization Theory and Applications : Volume 131
Journal of Optimization Theory and Applications : Volume 130
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Journal of Optimization Theory and Applications : Volume 127
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Journal of Optimization Theory and Applications : Volume 121
Journal of Optimization Theory and Applications : Volume 120
Journal of Optimization Theory and Applications : Volume 119
Journal of Optimization Theory and Applications : Volume 118
Journal of Optimization Theory and Applications : Volume 117
Journal of Optimization Theory and Applications : Volume 116
Journal of Optimization Theory and Applications : Volume 115
Journal of Optimization Theory and Applications : Volume 114
Journal of Optimization Theory and Applications : Volume 113
Journal of Optimization Theory and Applications : Volume 112
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Journal of Optimization Theory and Applications : Volume 109
Journal of Optimization Theory and Applications : Volume 108
Journal of Optimization Theory and Applications : Volume 107
Journal of Optimization Theory and Applications : Volume 106
Journal of Optimization Theory and Applications : Volume 105
Journal of Optimization Theory and Applications : Volume 104
Journal of Optimization Theory and Applications : Volume 103
Journal of Optimization Theory and Applications : Volume 102
Journal of Optimization Theory and Applications : Volume 101
Journal of Optimization Theory and Applications : Volume 100
Journal of Optimization Theory and Applications : Volume 99
Journal of Optimization Theory and Applications : Volume 98
Journal of Optimization Theory and Applications : Volume 97
Journal of Optimization Theory and Applications : Volume 96
Journal of Optimization Theory and Applications : Volume 95
Journal of Optimization Theory and Applications : Volume 94
Journal of Optimization Theory and Applications : Volume 93
Journal of Optimization Theory and Applications : Volume 92

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Discrete-Time Linear-Quadratic Dynamic Games

Content Provider Springer Nature Link
Author Pachter, M. Pham, K. D.
Copyright Year 2010
Abstract 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.
Starting Page 151
Ending Page 179
Page Count 29
File Format PDF
ISSN 00223239
Journal Journal of Optimization Theory and Applications
Volume Number 146
Issue Number 1
e-ISSN 15732878
Language English
Publisher Springer US
Publisher Date 2010-02-12
Publisher Place Boston
Access Restriction One Nation One Subscription (ONOS)
Subject Keyword Discrete-time linear-quadratic dynamic games Disturbance rejection Operations Research/Decision Theory Engineering Applications of Mathematics Theory of Computation Optimization Calculus of Variations and Optimal Control; Optimization
Content Type Text
Resource Type Article
Subject Applied Mathematics Control and Optimization Management Science and Operations Research
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