Yantao Feng

A game theoretic algorithm to compute local stabilizing solutions to HJBI equations in nonlinear H∞ control

In this paper, an iterative algorithm to solve Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations for a broad class of nonlinear control systems is proposed. By constructing two series of nonnegative functions, we replace the problem of solving an HJBI equation by the problem of solving a sequence of Hamilton-Jacobi-Bellman (HJB) equations whose solutions can be approximated recursively by existing methods. The local convergence of the algorithm and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the effectiveness of the proposed algorithm. A game theoretical interpretation of the algorithm is given.

Computing the Positive Stabilizing Solution to Algebraic Riccati Equations With an Indefinite Quadratic Term via a Recursive Method

An iterative algorithm to solve algebraic riccati equations with an indefinite quadratic term is proposed. The global convergence and local quadratic rate of convergence of the algorithm are guaranteed and a proof is given. Numerical examples are also provided to demonstrate the superior effectiveness of the proposed algorithm when compared with methods based on finding stable invariant subspaces of Hamiltonian matrices. A game theoretic interpretation of the algorithm is also provided.

An iterative algorithm to solve state-perturbed stochastic algebraic Riccati equations in LQ zero-sum games

An iterative algorithm to solve a kind of state-perturbed stochastic algebraic Riccati equation (SARE) in LQ zero-sum game problems is proposed. In our algorithm, we replace the problem of solving a SARE with an indefinite quadratic term by the problem of solving a sequence of SAREs with a negative semidefinite quadratic term, which can be solved by existing methods. Under some appropriate conditions, we prove that our algorithm is globally convergent. We give a numerical example to show the effectiveness of our algorithm. Our algorithm also has a natural game theoretic interpretation.

A New Iterative Algorithm to Solve Periodic Riccati Differential Equations With Sign Indefinite Quadratic Terms

An iterative algorithm to solve periodic Riccati differential equations (PRDE) with an indefinite quadratic term is proposed. In our algorithm, we replace the problem of solving a PRDE with an indefinite quadratic term by the problem of solving a sequence of PRDEs with a negative semidefinite quadratic term which can be solved by existing methods. The global convergence and the local quadratic rate of convergence are both established. A numerical example is given to illustrate our algorithm.

An iterative procedure to solve HJBI equations in nonlinear H∞ control

Abstract In this paper, an iterative algorithm to solve a special class of Hamilton-Jacobi-Bellman-Isaacs (HJBI) equations is proposed. By constructing two series of nonnegative functions, we replace the problem of solving an HJBI equation by the problem of solving a sequence of Hamilton-Jacobi-Bellman (HJB) equations whose solutions can be approximated recursively by existing methods. The local convergence of the algorithm is guaranteed. A numerical example is provided to demonstrate the accuracy of the proposed algorithm.

Solving discrete algebraic Riccati equations: A new recursive method

In this paper, an iterative algorithm is proposed to solve discrete time algebraic Riccati equations (DARE) with a sign indefinite quadratic term, which arise from linear discrete time H∞ control. By constructing two positive semidefinite matrix sequences, we obtain the stabilizing solution of the given DARE. The algorithm has a global convergence property.

On an iterative algorithm to compute the positive stabilizing solution of generalized algebraic Riccati equations

An iterative algorithm to solve a kind of generalized algebraic Riccati equations (GARE) in LQ stochastic zero-sum game problems is proposed. In our algorithm, we replace the problem of solving a GARE with an indefinite quadratic term by the problem of solving a sequence of GARE with a negative semidefinite quadratic term which can be solved by existing methods. Under some appropriate conditions, we prove that our algorithm is globally convergent.