Improved precise integration method for differential Riccati equation

An improved precise integration method （IPIM） for solving the differential Riccati equation （DRE） is presented. The solution to the DRE is connected with the exponential of a Hamiltonian matrix, and the precise integration method （PIM） for solving the DRE is connected with the scaling and squaring method for computing the exponential of a matrix. The error analysis of the scaling and squaring method for the exponential of a matrix is applied to the PIM of the DRE. Based ,on the error analysis, the criterion for choosing two parameters of the PIM is given. Three kinds of IPIMs for solving the DRE are proposed. The numerical examples machine accuracy solutions. show that the IPIM is stable and gives the

PRECISE INTEGRATION METHOD FOR LQG OPTIMAL MEASUREMENT FEEDBACK CONTROL PROBLEM

By using the precise integration method, the numerical solution of linear quadratic Gaussian (LQG) optimal control problem was discussed. Based on the separation principle, the LQG central problem decomposes, or separates, into an optimal state-feedback control problem and an optimal state estimation problem. That is the off-line solution of two sets of Riccati differential equations and the on-line integration solution of the state vector from a set of time-variant differential equations. The present algorithms are not only appropriate to solve the two-point boundary-value problem and the corresponding Riccati differential equation, but also can be used to solve the estimated state from the time-variant differential equations. The high precision of precise integration is of advantage for the control and estimation. Numerical examples demonstrate the high precision and effectiveness of the algorithm.

Infinite horizon LQR for systems with multiple delays in a single input channel

This paper is concerned with the linear quadratic regulation （LQR） problem for both linear discrete-time systems and linear continuous-time systems with multiple delays in a single input channel. Our solution is given in terms of the solution to a two-dimensional Riccati difference equation for the discrete-time case and a Riccati partial differential equation for the continuous-time case. The conditions for convergence and stability are provided.

Mixed deterministic and random optimal control of linear stochastic systems with quadratic costs

In this paper,we consider the mixed optimal control of a linear stochastic system with a quadratic cost functional,with two controllers—one can choose only deterministic time functions,called the deterministic controller,while the other can choose adapted random processes,called the random controller.The optimal control is shown to exist under suitable assumptions.The optimal control is characterized via a system of fully coupled forward-backward stochastic differential equations(FBSDEs)of mean-field type.We solve the FBSDEs via solutions of two(but decoupled)Riccati equations,and give the respective optimal feedback law for both deterministic and random controllers,using solutions of both Riccati equations.The optimal state satisfies a linear stochastic differential equation(SDE)of mean-field type.Both the singular and infinite time-horizonal cases are also addressed.

H_(2)/H_(∞) Control for Stochastic Jump-Diffusion Systems with Markovian Switching

In this paper, a stochastic H2/H∞ control problem is investigated for Poisson jumpdiffusion systems with Markovian switching, which are driven by a Brownian motion and a Poisson random measure with the system parameters modulated by a continuous-time finite-state Markov chain.A stochastic jump bounded real lemma is proved, which reveals that the norm of the perturbation operator below a given threshold is equivalent to the existence of a global solution to a parameterized system of Riccati type differential equations. This result enables the authors to obtain sufficient and necessary conditions for the existence of H2/H∞ control in terms of two sets of interconnected systems of Riccati type differential equations.