A method is presented for direct trajectory optimization and costate estimation using global collocation at Legendre-Gauss-Radau (LGR) points. The method is formulated first by casting the dynamics in integral form and computing the integral from the initial point to the interior LGR points and the terminal point. The resulting integration matrix is nonsingular and thus can be inverted so as to express the dynamics in inverse integral form. Then, by appropriate choice of the approximation for the state, a pseudospectral (i.e., differential) form that is equivalent to the inverse integral form is derived. As a result, the method presented in this paper can be thought of as either a global implicit integration method or a pseudospectral method. Moreover, the formulation derived in this paper enables solving general finite-horizon problems using global collocation at the LGR points. A key feature of the method is that it provides an accurate way to map the KKT multipliers of the nonlinear programming problem (NLP) to the costates of the optimal control problem. Finally, * M.S. Student, Dept. it is shown that a previously developed Radau collocation method, which is restricted to infinite-horizon problems, is subsumed by the method presented in this paper. The results of this paper show that the use of LGR collocation as described in this paper leads to the ability to determine accurate primal and dual solutions to general finite-horizon optimal control problems.
A method is presented for direct trajectory optimization and costate estimation using global collocation at Legendre-Gauss-Radau (LGR) points. The method is formulated first by casting the dynamics in integral form and computing the integral from the initial point to the interior LGR points and the terminal point. The resulting integration matrix is nonsin-gular and thus can be inverted so as to express the dynamics in inverse integral form. Then, by appropriate choice of the approximation for the state, a pseudospectral (i.e., differential) form that is equivalent to the inverse integral form is derived. As a result, the method presented in this paper can be thought of as either a global implicit integration method or a pseudospectral method. Moreover, the formulation derived in this paper enables solving general finite-horizon problems using global collocation at the LGR points. A key feature of the method is that it provides an accurate way to map the KKT multipliers of the non-linear programming problem (NLP) to the costates of the optimal control problem. Finally, * M.S. Student, it is shown that a previously developed Radau collocation method, which is restricted to infinite-horizon problems, is subsumed by the method presented in this paper. The results of this paper show that the use of LGR collocation as described in this paper leads to the ability to determine accurate primal and dual solutions to general finite-horizon optimal control problems.
Local anesthetics are used very often in medicine and dentistry. They have few adverse effects, but the increased use of these drugs has resulted in a higher incidence of local and systemic anesthetic toxicity (LAST). From the initial symptoms to the deleterious effects on cardiac and the central nervous system, LAST is an important consequence of which we should be aware. LAST is known since the introduction and use of local anesthetics; it was originally associated with seizures and respiratory failure. However, in the 1970s, side effects on the heart were also identified, as the fatal cardiac toxicity associated with bupivacaine was discovered in healthy patients. Prevention and safe administration of regional anesthesia remains primary factors in the avoidance of the toxicity of these drugs. When a patient has LAST, treatment should be started immediately to reduce seizures. If there is cardiac arrest, follow ACLS guidelines. Intravenous lipids improve cardiac conduction, contractility and coronary perfusion by removing liposoluble local anesthetic from cardiac tissue.
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