This paper is concerned with a linear-quadratic (LQ, for short) optimal control problem backward stochastic differential equations (BSDEs, short), where the coefficients of system and weighting matrices in cost functional are allowed to be random. By variational method, optimality system, which coupled linear forward-backward equation (FBSDE, derived, by Hilbert space unique solvability obtaine...

This paper studies the finite-horizon H∞-optimal control problem for linear hyperbolic systems when only time-sampled values of the state are available, with control acting on the boundary. The problem is formulated in a differential game framework by associating a zero-sum differential game with the original disturbance attenuation problem. The minimizing player’s minimax strategy in this game...

A linear quadratic optimal stochastic control problem with random coefficients and indefinite state/control weight costs is usually linked to an indefinite stochastic Riccati equation (SRE), which is a matrix-valued quadratic backward stochastic differential equation along with an algebraic constraint involving the unknown. Either the optimal control problem or the SRE is solvable only if the g...

This contribution addresses the development of a Linear Quadratic Regulator (LQR) for a set of time-varying hyperbolic PDEs coupled with a set of time-varying ODEs through the boundary. The approach is based on an infinitedimensional Hilbert state-space realization of the system and operator Riccati equation (ORE). In order to solve the optimal control problem, the ORE is converted to a set of ...

This paper derives linear quadratic regulator (LQR) results for boundary controlled parabolic partial differential equations (PDEs) via weak-variations. Research on optimal control of PDEs has a rich 40-year history. This body of knowledge relies heavily on operator and semigroup theory. Our research distinguishes itself by deriving existing LQR results from a more accessible set of mathematics...

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It has been proven by Rosu and Cornejo-Pérez [1, 2] that for some nonlinear second-order ODEs it is a very simple task to find one particular solution once the nonlinear equation is factorized with the use of two first-order differential operators. Here, it is shown that an interesting class of parametric solutions are easy to obtain if the proposed factorization has a particular form, which ha...

Abstract—In this article an evolutionary technique has been used for the solution of nonlinear Riccati differential equations of fractional order. In this method, genetic algorithm is used as a tool for the competent global search method hybridized with active-set algorithm for efficient local search. The proposed method has been successfully applied to solve the different forms of Riccati diff...