Optimal growth for linear processes with affine control
نویسندگان
چکیده
We analyse an optimal control with the following features: the dynamical system is linear, and the dependence upon the control parameter is affine. More precisely we consider ẋα(t) = (G+α(t)F )xα(t), where G and F are 3×3 matrices with some prescribed structure. In the case of constant control α(t) ≡ α, we show the existence of an optimal Perron eigenvalue with respect to varying α under some assumptions. Next we investigate the Floquet eigenvalue problem associated to time-periodic controls α(t). Finally we prove the existence of an eigenvalue (in the generalized sense) for the optimal control problem. The proof is based on the results by [Arisawa 1998, Ann. Institut Henri Poincaré] concerning the ergodic problem for Hamilton-Jacobi equations. We discuss the relations between the three eigenvalues. Surprisingly enough, the three eigenvalues appear to be numerically the same.
منابع مشابه
Hybrid model predictive control of a nonlinear three-tank system based on the proposed compact form of piecewise affine model
In this paper, a predictive control based on the proposed hybrid model is designed to control the fluid height in a three-tank system with nonlinear dynamics whose operating mode depends on the instantaneous amount of system states. The use of nonlinear hybrid model in predictive control leads to a problem of mixed integer nonlinear programming (MINLP) which is very complex and time consuming t...
متن کاملA New Near Optimal High Gain Controller For The Non-Minimum Phase Affine Nonlinear Systems
In this paper, a new analytical method to find a near-optimal high gain controller for the non-minimum phase affine nonlinear systems is introduced. This controller is derived based on the closed form solution of the Hamilton-Jacobi-Bellman (HJB) equation associated with the cheap control problem. This methodology employs an algebraic equation with parametric coefficients for the systems with s...
متن کاملMathematical Cybernetics: Hybrid, Stochastic and Decentralized Systems
We consider partially observed stochastic dynamical systems whose state equations are of McKean-Vlasov type SDE and hence contain a measure term where the measure term is also random. Such SDEs are used to model the state dynamics of the agents in Mean Field Games framework with Major and Minor agents. We present nonlinear filtering equations in both normalized and unnormalized forms and, for s...
متن کاملOn Analytical Study of Self-Affine Maps
Self-affine maps were successfully used for edge detection, image segmentation, and contour extraction. They belong to the general category of patch-based methods. Particularly, each self-affine map is defined by one pair of patches in the image domain. By minimizing the difference between these patches, the optimal translation vector of the self-affine map is obtained. Almost all image process...
متن کامل