## A novel iterative algorithm for solving coupled Riccati equations.(English)Zbl 1433.93156

Summary: In this paper, a novel iterative algorithm is developed for solving the coupled algebraic Riccati equation arising from the quadratic optimal control problem for continuous-time Markovian jump linear systems. First, two existing iterative algorithms to solve the coupled Riccati matrix equation are reviewed. Next, based on analysis for these two algorithms, a new iterative algorithm that combines both the information in the current iterative step and the information in the last iterative step is proposed. It is shown that the proposed algorithm with proper initial conditions can monotonically converge to the unique positive definite solution of the coupled Riccati matrix equation if the associated Markovian jump system is stochastically stabilizable. Also, numerical examples show that the presented algorithm is faster than some previous algorithms when the weighted parameter is appropriately selected.

### MSC:

 93E20 Optimal stochastic control 49K45 Optimality conditions for problems involving randomness 49N10 Linear-quadratic optimal control problems 60J28 Applications of continuous-time Markov processes on discrete state spaces 65H10 Numerical computation of solutions to systems of equations 93D15 Stabilization of systems by feedback 93E03 Stochastic systems in control theory (general)
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### References:

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