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Under appropriate conditions, the dynamics of a control system governed by ordinary differential equations can be formulated in several ways: differential inclusion, control parametrization, flatness parametrization, higher-order inclusions and so on. A plethora of techniques have been proposed for each of these formulations but they are typically not(More)
Recent convergence results with pseudospectral methods are exploited to design a robust, multigrid, spectral algorithm for computing optimal controls. The design of the algorithm is based on using the pseudospectral differentiation matrix to locate switches, kinks, corners, and other discontinuities that are typical when solving practical optimal control(More)
We consider nonlinear optimal control problems with mixed state-control constraints. A discretization of the Bolza problem by a Legendre pseudospec-tral method is considered. It is shown that the operations of discretization and dual-ization are not commutative. A set of Closure Conditions are introduced to commute these operations. An immediate consequence(More)
Proof: The solution for the x2 component of the system with additive impulses can be written explicitly as x2 (t) = e (k+1)h02t x2 (0) 8t 2 (kh; (k + 1)h] : (31) Indeed, for this signal we have _ x2 = 02x2 on the intervals (kh; (k + 1)h], k 0; and at times kh, k 0 we have that x2 (kh) + d k = e kh02kh x2(0) + (1 0 e 0h)e 0(k01)h x2(0) = e 0(k01)h x 2 (0) =(More)