Optimal control in Ito-Volterra systems (Q2769553)

The paper deals with optimal linear-quadratic control problems for stochastic integral Ito-Volterra systems of type NEWLINE\[NEWLINEx(t)= x(t_0)+\int^t_{t_0} \bigl[a_0(t,s) +a(t,s)x(s)+ b(t,s)u(t,s) \bigr]ds+ \int^t_{ t_0} g(s)dW_1(s),NEWLINE\]NEWLINE where the Wiener process \(W_1(t)\) represents a random disturbance. The cost functional is the expectation of a quadratic function in the state and the control. The control \(u(t,s)\) depends on two variables. The optimal control problem is to find a control \(u^*(t)\) of one variable that minimizes the cost functional along the trajectory \(x^*(t)\) corresponding to \(u^* (t)\). The states may be continuous or discontinuous. The obtained solutions are based on applying the duality principle for Volterra systems to the solutions of the dual filtering problems for Ito-Volterra states. The optimal control laws and the gain matrix equations are derived in the general case and then simplified to processes with differential equations whose optimal control for a dynamic plant is considered.NEWLINENEWLINENEWLINEAs an example the optimal control problem for the motion of a missile with two motors is considered. The task is to reach the maximal possible altitude with a minimal possible fuel consumption.