Stochastic Optimal Control of Partially Observable Nonlinear Systems
| Authors: | Çimen Tayfun, Turkish Naval Forces, Turkish Naval Research Center Command, Turkey
Banks Stephen P., The University of Sheffield, United Kingdom |
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| Topic: | 2.3 Non-Linear Control Systems |
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| Session: | Nonlinear Stability and Structural Analysis |
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| Keywords: | Nonlinear non-affine systems, Stochastic systems, Optimal control, Optimal filtering, Kalman filter, LQG control, Separation principle, Approximation theory, Iterative methods, Continuous-time systems, Time-varying systems. |
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Abstract
This paper presents a new theory for solving the continuous-time stochastic optimal control problem for a very general class of nonlinear (nonautonomous and nonaffine controlled) systems with partial state information. The proposed theory transforms the nonlinear problem into a a sequence of linear-quadratic Gaussian (LQG) problems, which uniformly converge under very mild conditions of local Lipschitz continuity. The proposed method introduces an "approximating sequence of Riccati equations" (ASRE) to explicitly find the error covariance matrix and nonlinear time-varying optimal feedback controllers for such nonlinear systems, using the framework of Kalman-Bucy filtering, separation principle and LQR theory. The paper shows a practical way of designing optimal feedback control systems for complex nonlinear stochastic problems using a combination of modern LQG and LQR methodologies.
