Generalized differential Riccati equation and indefinite stochastic LQ control with cross term

Cheng-xin, Luo; Feng, Enmin

doi:10.1016/s0096-3003(03)00766-5

Cited by 8 publications

(8 citation statements)

References 11 publications

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“…Hence also makes Hurwitz. Since is the unique stabilizing solution to (18) and since satisfies the same equation and is also stabilizing, we conclude that (see [10]), thereby in turn giving . Since the optimal control law that minimizes cost function (32) subject to constraint (33) is , we now set (according to our game plan) and proceed in this manner as outlined in the chart in Fig.…”

Section: Game Theoretic Interpretation Of the Algorithmmentioning

confidence: 72%

“…2) Set . 3) Construct (for example using the Kleinman algorithm in [2], though this is not necessary) the unique real symmetric stabilizing solution which satisfies (18) where is defined in (3). 4) Set .…”

Section: Algorithmmentioning

confidence: 99%

“…But when this stabilizability condition is satisfied , construction of the series and is always possible and either converges to (which is captured by step 5) or just diverges to infinity, which again means that there does not exist a stabilizing solution to . Remark 1: It is worth pointing out that when the Kleinman algorithm is used to solve (18), how to stop the Kleinman iteration can be an important issue (see Example 2 in the Appendix for a demonstration of this). In fact, a simple criterion to stop the Kleinman iteration is to compute the residue of (18).…”

Section: ) Ifmentioning

confidence: 99%

“…Remark 1: It is worth pointing out that when the Kleinman algorithm is used to solve (18), how to stop the Kleinman iteration can be an important issue (see Example 2 in the Appendix for a demonstration of this). In fact, a simple criterion to stop the Kleinman iteration is to compute the residue of (18). When the residue of the right hand side terms of (18) is small enough, the Kleinman iteration should be stopped.…”

Section: ) Ifmentioning

confidence: 99%

“…Consequently, if one were to use the Kleinman algorithm to solve (18), the Kleinman algorithm cannot always be initialized with the simple choice (for Hurwitz). Also, we point out that while is guaranteed to be monotonically increasing, is not guaranteed to be monotonically decreasing.…”

Section: Technical Remarksmentioning

confidence: 99%

See 4 more Smart Citations

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

Lanzon

Feng

Anderson

et al. 2008

IEEE Trans. Automat. Contr.

105

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Abstract-An iterative algorithm to solve Algebraic RiccatiEquations 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. Index Terms-Algebraic Riccati equation (ARE),Riccati equations, indefinite quadratic term, iterative algorithms.

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Section: Game Theoretic Interpretation Of the Algorithmmentioning

confidence: 72%

Section: Algorithmmentioning

confidence: 99%

Section: ) Ifmentioning

confidence: 99%

Section: ) Ifmentioning

confidence: 99%

Section: Technical Remarksmentioning

confidence: 99%

See 3 more Smart Citations

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

Lanzon

Feng

Anderson

et al. 2008

IEEE Trans. Automat. Contr.

105

View full text Add to dashboard Cite

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Solution of generalized matrix Riccati differential equation for indefinite stochastic linear quadratic singular fuzzy system with cross-term using neural networks

Kumaresan

2010

Neural Comput & Applic

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In this paper, solution of generalized matrix Riccati differential equation (GMRDE) for indefinite stochastic linear quadratic singular fuzzy system with crossterm is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of GMRDE obtained from wellknown traditional Runge Kutta (RK) method and nontraditional neural network method. To obtain the optimal control, the solution of GMRDE is computed by feed forward neural network (FFNN). Accuracy of the solution of the neural network approach to this problem is qualitatively better. The advantage of the proposed approach is that, once the network is trained, it allows instantaneous evaluation of solution at any desired number of points spending negligible computing time and memory. The computation time of the proposed method is shorter than the traditional RK method. An illustrative numerical example is presented for the proposed method.

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Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems

Costa

Paulo

2007

Automatica

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Generalized differential Riccati equation and indefinite stochastic LQ control with cross term

Cited by 8 publications

References 11 publications

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

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

Solution of generalized matrix Riccati differential equation for indefinite stochastic linear quadratic singular fuzzy system with cross-term using neural networks

Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems

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