Monotone Approximations of Minimum and Maximum Functions and Multi-objective Problems |
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Authors: | Du?an M Stipanovi? Claire J Tomlin George Leitmann |
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Institution: | 1. Coordinated Science Laboratory, Department of Industrial and Enterprise Systems Engineering, University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA 2. Department of Electrical Engineering and Computer Science, University of California at Berkeley, Berkeley, USA 3. College of Engineering, University of California at Berkeley, Berkeley, USA
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Abstract: | In this paper the problem of accomplishing multiple objectives by a number of agents represented as dynamic systems is considered. Each agent is assumed to have a goal which is to accomplish one or more objectives where each objective is mathematically formulated using an appropriate objective function. Sufficient conditions for accomplishing objectives are derived using particular convergent approximations of minimum and maximum functions depending on the formulation of the goals and objectives. These approximations are differentiable functions and they monotonically converge to the corresponding minimum or maximum function. Finally, an illustrative pursuit-evasion game example with two evaders and two pursuers is provided. |
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