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12
A wellposed shooting algorithm for optimal control problems with singular arcs
, 2011
"... In this article we establish for the first time the wellposedness of the shooting algorithm applied to optimal control problems for which all control variables enter linearly in the Hamiltonian. We start by investigating the case having only initialfinal state constraints and free control variable ..."
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Cited by 10 (6 self)
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In this article we establish for the first time the wellposedness of the shooting algorithm applied to optimal control problems for which all control variables enter linearly in the Hamiltonian. We start by investigating the case having only initialfinal state constraints and free control variable, and afterwards we deal with control bounds. The shooting algorithm is wellposed if the derivative of its associated shooting function is injective at the optimal solution. The main result of this paper is to provide a sufficient condition for this injectivity, that is very close to the second order necessary condition. We prove that this sufficient condition guarantees the stability of the optimal solution under small perturbations and the wellposedness of the shooting algorithm for the perturbed problem. We present numerical tests that validate our method.
Numerical study of optimal trajectories with singular arcs for space launcher problems
 in "AIAA J. of Guidance, Control and Dynamics", To appear, 2009. International PeerReviewed Conference/Proceedings
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Continuous Time Optimal Hydrothermal Scheduling
"... We consider an optimal control problem of optimal hydrothermal scheduling. The model, already discussed in [1], is deterministic and takes into account the dependence of efficiency of hydroelectric energy with respect to the volume of water in dams. The thermal cost is a strongly convex and nondecre ..."
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Cited by 4 (3 self)
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We consider an optimal control problem of optimal hydrothermal scheduling. The model, already discussed in [1], is deterministic and takes into account the dependence of efficiency of hydroelectric energy with respect to the volume of water in dams. The thermal cost is a strongly convex and nondecreasing function of the thermal power. We study the possible occurrence of a singular arc, for which necessary conditions due to Goh are known. We are able to give conditions under which these conditions either automatically satisfied or excluded. 2. Keywords: Optimal control, singular arcs, hydrothermal scheduling. On a weekly basis, optimal hydrothermal scheduling is usually performed using linear programming techniques, see [2] and the references therein. In such a case limitations due to switch onoff of engines as well as the variable efficiency as function of height of water are neglected. Our proposal is to study the hydrothermal scheduling by taking into account this variable efficiency. Our model is deterministic and
Initialization of the shooting method via the hamiltonjacobibellman approach
 Journal of Optimization Theory and Applications
, 2010
"... The aim of this paper is to investigate from the numerical point of view the possibility of coupling the HamiltonJacobiBellman (HJB) equation and Pontryagin’s Minimum Principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to o ..."
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Cited by 3 (1 self)
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The aim of this paper is to investigate from the numerical point of view the possibility of coupling the HamiltonJacobiBellman (HJB) equation and Pontryagin’s Minimum Principle (PMP) to solve some control problems. A rough approximation of the value function computed by the HJB method is used to obtain an initial guess for the PMP method. The advantage of our approach over other initialization techniques (such as continuation or direct methods) is to provide an initial guess close to the global minimum. Numerical tests involving multiple minima, discontinuous control, singular arcs and state constraints are considered. The CPU time for the proposed method is less than four minutes up to dimension four, without code parallelization. Keywords. Optimal control problems, minimum time problem, HamiltonJacobiBellman equations, Pontryagin’s minimum principle, shooting method. MSC. 49Lxx, 49M05, 49N90. 1
The shooting approach to optimal control problems
, 2013
"... Abstract: We give an overview of the shooting technique for solving deterministic optimal control problems. This approach allows to reduce locally these problems to a finite dimensional equation. We first recall the basic idea, in the case of unconstrained or control constrained problems, and show t ..."
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Abstract: We give an overview of the shooting technique for solving deterministic optimal control problems. This approach allows to reduce locally these problems to a finite dimensional equation. We first recall the basic idea, in the case of unconstrained or control constrained problems, and show the link with secondorder optimality conditions and the analysis or discretization errors. Then we focus on two cases that are now better undestood: state constrained problems, and affine control systems. We end by discussing extensions to the optimal control of a parabolic equation.
An LQ suboptimal stabilizing feedback law for switched linear systems
, 2013
"... The aim of this paper is the design of a stabilizing feedback law for continuous time linear switched system based on the optimization of a quadratic criterion. The main result provides a control Lyapunov function and a feedback switching law leading to sub optimal solutions. As the Lyapunov functio ..."
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The aim of this paper is the design of a stabilizing feedback law for continuous time linear switched system based on the optimization of a quadratic criterion. The main result provides a control Lyapunov function and a feedback switching law leading to sub optimal solutions. As the Lyapunov function defines a tight upper bound on the value function of the optimization problem, the sub optimality is guaranteed. Practically, the switching law is easy to apply and the design procedure is effective if there exists at least a controllable convex combination of the subsystems. 1
Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
, 2007
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Control, Optimization, Models, Methods and Applications for Nonlinear Dynamical Systems
, 2008
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