Synthesis of Optimum Multivariable Control Systems by the Method of Steepest Descent

The optimum synthesis of multivariable control systems with generalized quadratic error criterion is solved by using time method of steepest descent in the Hilbert space. Apart from the conventional minimization techniques, this approach works directly on the functional of the error criterion itself so that the optimal solution can be determined through sucessive approximations. Since this solution can be obtained at high speed and with high accuracy by using a digital computer, this method is particularly useful in solving the actuation problem of adaptive control systems.