This paper proposes a novel adaptive pseudospectral (NAP) method for solving the time-energy optimal control model to minimize the parking time and the energy output of the vehicle. The time-energy optimal control model is first discretized into a nonlinear programming problem at Gauss collocations by the NAP method. Subsequently, we prove the equivalence between the nonlinear programming problem derived from the NAP method and the time-energy optimal control model problem. Compared to those of the interior point method and the piecewise gauss pseudospectal method, simulation results show that the NAP method has higher computational efficiency and accuracy in solving the time-energy optimal control model problem.

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The theoretical properties of a novel time-optimal L 1 /L 2 norms optimal control for linear time-invariant systems are investigated. The L 0 -optimal control (or sparsest control) is converted to the time-optimal L 1 /L 2 norms optimal control which can be solved efficiently. The proposed control is obtained via minimization of the time-optimal L 1 /L 2 norms optimal control input along with the constraints on the state variable. Subsequently, by using the nonsmooth maximum principle, the uniqueness and continuity of the optimal solution of the time-optimal L 1 /L 2 norms optimal control are proved. The superiority of the time-optimal L 1 /L 2 norms optimal control is illustrated by numerical examples.