Abstract
This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example.
Highlights
This paper presents a global optimization approach to solving linear non-quadratic optimal control problems
The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space
With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem
Summary
Associated with the optimal control problem ( ), let’s introduce the Hamiltonian function. Associated with the state variable x (.) and the adjoint variable λ (.) , we have ( ) x = Hλ x,u, λ = Ax + Bu, x (0) = a,. Since in (2.6) the global optimization is processed on the variable u over Rm for a given t, it is equivalent to deal with the optimization (for obtaining a global minimizer):. We turn to consider the following optimization with respect to a given parameter vector λ ∈ Rn min u∈Rm λ. For a given adjoint variable, we solve the optimization (2.8) to create a function u = h (λ ). In Hamiltonian boundary problem (2.2), (2.3) we replace the variable u with the function h (λ ) and solve the following equation.
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