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The combination of the time-scaling transformation and control parameterization has proven to be an effective approach in addressing optimal control problems involving switching systems with predefined subsystem sequences. However, this approach has certain limitations. First, the number of control switchings is required to be no less than the number of subsystem switchings. Second, the switching of the subsystem must be accompanied by the switching of the control. Third, this scheme introduces many hyperparameters, leading to combinatorial explosion. To address these drawbacks, we introduce a novel computational approach such that the control switching can be independent of subsystem switching. The superiority of this novel approach can be clearly observed from the solutions obtained using the proposed method for solving two illustrative examples. [ABSTRACT FROM AUTHOR]

In this paper, we consider a class of control theoretic spline model, which can be formulated as a linear quadratic optimal control problem. The unknown initial condition and the control are to be chosen optimally such that the output best fits a set of measurement data which are corrupted by noise with crucial knowledge of its distribution. We first transform the uncertain objective function into a deterministic objective function. The solution method is based on the control parameterization technique. We show that the approximate optimal controls obtained from the approximate finite dimensional problems converge to the optimal control of the original control problem in the weak ⋆ topology of L ∞ ( [ 0 , T ] , R r ) . Numerical results show that the proposed method is effective. [ABSTRACT FROM AUTHOR]

Efficient and reliable integrators are indispensable for the design of sequential solvers for optimal control problems involving continuous dynamics, especially for real-time applications. In this paper, optimal control problems for systems represented by index-1 differential-algebraic equations are investigated. On the basis of a time-scaling transformation, the control is parameterized as a piecewise constant function with variable heights and switching time instants. Compared with control parameterization with fixed time grids, the flexibility of adjusting switching time instants increases the chance of finding the optimal solution. Furthermore, error constraints are introduced in the optimization procedure such that the optimal control obtained has a guarantee of integration accuracy. For the derived approximate nonlinear programming problem, a function evaluation and forward sensitivity propagation algorithm is proposed with an embedded implicit Runge–Kutta integrator, which executes one Newton iteration in the limit by employing a predictor-corrector strategy. This algorithm is combined with a nonlinear programming solver Ipopt to construct the optimal control solver. Numerical experiments for the solution of the optimal control problem for a Delta robot demonstrate that the computational speed of this solver is increased by a factor of 0.5–2 when compared with the same solver without the predictor-corrector strategy, and increased by a factor of 20–40 when compared with solver embedding IDAS , the Implicit Differential-Algebraic solver with Sensitivity capabilities developed by Lawrence Livermore National Laboratory. Meanwhile, the accuracy loss compared with the one using IDAS is small and admissible. [ABSTRACT FROM AUTHOR]