Discrete-time Indefinite LQ Control with State and Control Dependent Noises
Journal of Global Optimization
Indefinite Stochastic Linear Quadratic Control with Markovian Jumps in Infinite Time Horizon
Journal of Global Optimization
Idenfinite stochastic optimal LQR control with cross term under IQ constraints
The Korean Journal of Computational & Applied Mathematics
Computer-aided on-line development and derivation of the motion equation of space module
Automation and Remote Control
Stabilization and destabilization of hybrid systems of stochastic differential equations
Automatica (Journal of IFAC)
Automatica (Journal of IFAC)
Tracking a Financial Benchmark Using a Few Assets
Operations Research
Brief paper: Gradient dynamic optimization with Legendre chaos
Automatica (Journal of IFAC)
Optimal control for stochastic nonlinear singular system using neural networks
Computers & Mathematics with Applications
A generalized multi-period mean-variance portfolio optimization with Markov switching parameters
Automatica (Journal of IFAC)
Neural, Parallel & Scientific Computations
Neural, Parallel & Scientific Computations
Automatica (Journal of IFAC)
Brief Multiple-objective risk-sensitive control and its small noise limit
Automatica (Journal of IFAC)
Near-optimal controls of random-switching LQ problems with indefinite control weight costs
Automatica (Journal of IFAC)
Journal of Computational Neuroscience
LQ control for Itô-type stochastic systems with input delays
Automatica (Journal of IFAC)
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This paper considers optimal (minimizing) control of stochastic linear quadratic regulators (LQRs). The assumption that the control weight costs must be positive definite, inherited from the deterministic case, has been taken for granted in the literature. It is, however, shown in this paper that some stochastic LQR problems with indefinite (in particular, negative) control weight costs may still be sensible and well-posed due to the deep nature of stochastic systems. New stochastic Riccati equations, which are backward stochastic differential equations involving complicated nonlinear terms, are presented and their solvability is proved to be sufficient for the well-posedness and the solutions of the optimal LQR problems. Existence and uniqueness of solutions to the Riccati equation for a special case are obtained. Finally, it is argued that, quite contrary to the deterministic systems, the stochastic maximum principle cannot fully characterize the optimality of the stochastic LQR problems.