Game-theoretic linear quadratic method for air mission control

Mukai, H.; Tanikawa, Akio; Tunay, I.; Özcan, İsmail; Katz, Irving; Schättler, Heinz; Rinaldi, Paolo; Wang, G.J.; Yang, Lixia; Sawada, Yuichi

doi:10.1109/cdc.2000.914191

Cited by 13 publications

(9 citation statements)

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“…However, the proof for its convergence was missing. We also observed much faster convergence of the SQQM than the iterative methods based on lower order approximations such as the SLQM reported in [6,7]. This faster convergence in numerical experiments seems to verify that the subproblem of SQQM, although implemented as a linearly-constrained quadratic problem, retains the intrinsic characteristic of a quadratic approximation around the solution estimate to the original game problem.…”

Section: Introductionsupporting

confidence: 62%

“…However, each approximated subproblem cannot be solved easily since the subproblem does not have a linear (or affine) dynamics. Thus, in order to avoid this difficulty, the linear (or affine) approximation to the system dynamics was actually proposed in the Sequential Linear-Quadratic Method (SLQM) in [6,7]. Later in [8], this drawback was overcome as follows: we proposed a new subproblem by removing the quadratic terms in the system dynamics and adding them to the payoff function after multiplied by a suitable multiplier function.…”

Section: Introductionmentioning

confidence: 99%

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Local Convergence of the Sequential Quadratic Method for Differential Games

Tanikawa

Mukai²,

Xu³

2012

Stochastic Systems Theory and its Applications (SSS)

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For computing a Nash (saddle point) solution to a zero-sum differential game for a general nonlinear system, Mukai et al. presented an iterative Sequential Quadratic-Quadratic Method (SQQM) as follows. Given a solution estimate, they defined a subproblem which approximates the original problem up to the second order around the solution estimate. They proposed to replace the subproblem with another subproblem in order to obtain a game problem with only a linear dynamics by removing the quadratic terms in the system dynamics and adding them to the payoff function as in Lagrangian function. We can now solve this subproblem conveniently by a Riccati equation method. We then update the solution estimate by adding its Nash solution to the current solution estimate for the original game. Through our extensive experiments, we observed not only local convergence of the SQQM but also much faster convergence of the SQQM than the iterative methods based on lower order approximations such as the Sequential Linear-Quadratic Method (SLQM). In this paper we will establish local convergence of the SQQM.

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Section: Introductionsupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Local Convergence of the Sequential Quadratic Method for Differential Games

Tanikawa

Mukai²,

Xu³

2012

Stochastic Systems Theory and its Applications (SSS)

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“…We new improved solution estimate to the original game also observed much faster convergence of the SQQM problem. However, each approximated subproblem than the iterative methods based on lower order apcannot be solved easily since the subproblem does not proximations such as the SLQM reported in [6,7]. have a linear (or affine) dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…have a linear (or affine) dynamics. Thus, in order to This faster convergence in numerical experiments avoid this difficulty, the linear (or affine) approximaseems to verify that the subproblem of SQQM, altion to the system dynamics was actually proposed though implemented as a linearly-constrained in the Sequential Linear-Quadratic Method (SLQM) quadratic problem, retains the intrinsic characterisin [6,7]. Later in [8], this drawback was overcome as stronger conditions in Theorem 10.…”

Section: Introductionmentioning

confidence: 99%

Local Convergence of the Sequential Quadratic Method for Differential Games

Tanikawa

Mukai²,

Xu³

2012

Transactions of ISCIE

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“…Many of these efforts emphasized a control-system based mathematical framework. Mukai et al (2000) provides a differential game formulation for opposing air and ground units. Unit movement (on a 2-D grid) and attrition are governed by differential equations.…”

Section: Previous Researchmentioning

confidence: 99%

<title>Model identification and optimization for operational simulation</title>

Popken¹,

Cox²

2003

SPIE Proceedings

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REPORT DOCUMENTATION PAGEForm Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503 AGENCY USE ONLY (Leave blank)2. REPORT DATE Aug 04 REPORT TYPE AND DATES COVEREDFinal Mar 03 -Feb 04 TITLE AND SUBTITLE MODEL IDENTIFICATION AND OPTIMIZATION FOR OPERATIONAL SIMULATION AUTHOR(S)Douglas A. Popken and Louis A. Cox FUNDING NUMBERSC -F30602-03-C-0167 PE -62702F PR -459S TA -MA WU -02 PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)Systems View 9139 Roadrunner St. Highlands Ranch, CO 80129 The purpose of this research effort was to develop and test frameworks and algorithms for use in air warfare planning systems. Developing planning systems for this problem domain is particularly challenging due to their great complexity and uncertainty. The effort focused on predictive simulation models for generating potential outcomes of proposed operational plans. The planning process was organized as a hierarchy of decisions, with those at the top being broadest and longest term. The algorithms at the highest level of planning use a hill-climbing approach, wherein proposed "Blue" plans are evaluated, and the average marginal benefits of alternative force reallocations are computed. Evaluation and measurement of each proposed Blue plan is accomplished via a "Stochastic Evaluator" that draws multiple samples of potential outcomes and "Red" force levels for a given Blue force structure and a combined target composition. The evaluation metric is the net discounted value from enemy targets hit. Within the evaluator, linear programming and simulation generate optimized Red responses, assumed outcomes, and relative marginal force values. This project successfully demonstrated automated plan optimization, practical embedding of optimization algorithms into an operational planning cycle operating over a multi-period conflict, and use of hierarchical decisionmaking to decomposed planning and on-line optimization problems into computationally practical tasks. PERFORMING ORGANIZATION REPORT NUMBER SPONSORING / MONITORING AGENCY NAME(S) AND ADDRESS(ES)AFRL SummaryThis research effort developed and tested frameworks and algorithms for use in air warfare planning systems. It focused on the use of simulation models as predictive tools for generating potential outcomes of proposed plans, and incorporating realistically high degrees of complexity and uncertainty into optimization of plans.In this effort, the p...

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Game-theoretic linear quadratic method for air mission control

Cited by 13 publications

References 0 publications

Local Convergence of the Sequential Quadratic Method for Differential Games

Local Convergence of the Sequential Quadratic Method for Differential Games

Local Convergence of the Sequential Quadratic Method for Differential Games

<title>Model identification and optimization for operational simulation</title>

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