Abstract
Cost-cumulant control, also known as statistical control, is an optimal control method that minimizes a linear combination of quadratic cost cumulants. Risk-sensitive control is an optimal control method that minimizes the exponential of the quadratic cost criterion. This is equivalent to optimizing adenumerable sum of all the cost cumulants. This chapter describes linear-quadratic-Gaussian (LQG), minimal cost variance (MCV), and risk-sensitive (RS) controls in terms of the cost cumulants. Cost cumulant control, which is also called statistical control, views the optimization criterion as a random variable and minimizes any cumulant of the optimization criterion. Then LQG, MCV, and RS are all special cases of cost cumulant control where in LQG the mean, in MCV the variance, and in RS all cumulants of the cost function are optimized. This chapter provides the optimal controllers for the LQG, MCV, and RS methods. Finally, satellite attitude control application using RS controller and building control application using MCV controller are also described.
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