Conference Paper

A sequential linear quadratic approach for constrained nonlinear optimal control

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Conference Paper

A sequential linear quadratic approach for constrained nonlinear optimal control

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Abstract

A sequential quadratic programming method is proposed for solving nonlinear optimal control problems subject to general path constraints including mixed state-control and state-only constraints. The proposed algorithm formulates linear quadratic optimal control subproblems with a solution that provides a descent direction for a non-differentiable exact penalty function. A set of conditions is given under which the minimization of the merit function produces a sequence of controls with limit points that satisfy the first order necessary conditions of the optimal control problem. The subproblems solved at each step of the algorithm inherit the structure of the nonlinear optimal control problem and can be solved efficiently via Riccati methods.

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... Recent research proposes the use of Sequential Quadratic Programs (SQPs) employing sequential linearizations of the constraints in the NL-OCP in order to efficiently solve it [27]. However, this approach converges to a local optimum of the NL-OCP defined in (3), if and only if the system is locally N-step controllable [27]. ...
... Recent research proposes the use of Sequential Quadratic Programs (SQPs) employing sequential linearizations of the constraints in the NL-OCP in order to efficiently solve it [27]. However, this approach converges to a local optimum of the NL-OCP defined in (3), if and only if the system is locally N-step controllable [27]. Additionally, the terminal equality constraint is only satisfied as the number of 1 Although x x x r and u u u r may be obtained by any approach, an auxiliary optimization problem to obtain these is provided in Appendix A. ...
... Algorithm 1 Dual-mode model predictive / linear control 1: OFFLINE 2: Select µ and compute K k , P k using Lemma 1 3: Compute γ k using Lemma 2 4: Select δ and compute ε 1 k using Proposition 1 Utilize an SQP procedure [27] to produce a feasible virtual control sequenceũ u u * k . ...
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