Discrete-time controller for stochastic nonlinear polynomial systems with Poisson noises

ABSTRACT

This paper presents a solution to the optimal control problem for discrete-time stochastic nonlinear polynomial systems confused with white Poisson noises subject to a quadratic criterion. The solution is obtained in the following way: a nonlinear optimal controller is first developed for polynomial systems, considering the state vector completely available for control design. Then, based on the solution of the state estimation problem for polynomial systems with white Poisson noises, the state estimate vector is used in the control law to obtain a closed-form solution. Performance of this controller is compared to that of the controller employing the extended Kalman filter and the linear-quadratic regulator and the controller designed for polynomial systems confused with white Gaussian noises.

KEYWORDS:

• Discrete-time systems
• polynomial systems
• Poisson noise
• optimal control
• state estimation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors thank the Mexican National Council of Science and Tech-nology (CONACyT) for financial support [Grant Number 250611].