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A methodology is described for solving optimal pointwise control of a coupled system of Burgers' equations. It is aimed to determine the optimal pointwise control that minimizes a given performance measure. The performance measure is specified as a quadratic functional of the distance between a final state function and a predefined target function along with the energy due to the control effort. The modal expansion method is used to reduce the optimal control of distributed parameter systems into the control of the invariant lumped parameter systems. A system of non-linear algebraic equations are derived as necessary conditions of optimality and solved by Runge–Kutta method to obtain the optimal Fourier coefficients and frequencies. The feasibility of the proposed methodology is demonstrated by numerical simulations. [ABSTRACT FROM PUBLISHER]

A mathematical theory for a class of optimal control problems for a damped distributed-parameter system represented by N serially connnected flexible structures coupled through boundary conditions is formulated. The control is to be implemented by applying a finite number of actuators to a discrete number of points within the structure. A maximum principle is proved for a system of N partial differential equations of second order in time and forth order in space, coercive in space variables, with variable coefficients. Under additional convexity assumptions on the state variables and their derivatives, the optimal control is shown to be unique. The proposed theory is demonstrated by applying it to problem of controlling the vibrations of the two strings that are coupled at the connecting point. Numerical results are given for various parameters, and the efficiency of the control is investigated. [ABSTRACT FROM PUBLISHER]