Optimal control of multi-delay systems via shifted Legendre polynomials

Based on using shifted Legendre polynomials (SLPs) a new approach for computing optimal control law of linear time-invariant/time-varying, time-delay free/time-delay dynamic systems with quadratic performance index is discussed in this paper. The governing delay-differential equations of dynamic systems are converted into linear algebraic equations by using the operational matrices of differentiation, integration, delay and product of SLPs. Thus, the problem of finding optimal control law is reduced to the problem of solving algebraic equations obtained via the operational matrices. Numerical examples are included to demonstrate the applicability of the proposed approach.