Cost Distribution Shaping: The Relations Between Bode Integral, Entropy, Risk-Sensitivity, and Cost Cumulant Control
نویسنده
چکیده
The cost function in stochastic optimal control is viewed as a random variable. Then the classical linearquadratic-Gaussian control, entropy control, risk-sensitive control, and cost cumulant control can be viewed as the cost distribution shaping methods. In this paper, we will survey the existing relations between entropy, Bode integral, and risk-sensitive cost function. Furthermore, we will relate the cost cumulants with information theoretic entropy, and Bode integral. The interpretation of cost cumulant control is given in terms of the control entropy minimization. The paper also relates information theoretic entropy with exponential-ofintegral cost function using a Lagrange multiplier and calculus of variations. Finally, the logarithmic-exponential-of-integral cost function is related to the information theoretic entropy using large deviation theory.
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