Optimal Estimation for Continuous-Time Nonlinear Systems Using State-Dependent Riccati Equation (SDRE)
This paper introduces a unified approach for state estimation and control of nonlinear dynamic systems, employing the State-Dependent Riccati Equation (SDRE) framework. The proposed approach naturally extends classical linear quadratic Gaussian (LQG) methods into nonlinear scenarios, avoiding linearization by using state-dependent coefficient (SDC) matrices. An SDRE-based Kalman filter (SDRE-KF) is integrated within an SDRE-based control structure, providing a coherent and intuitive strategy for nonlinear system analysis and control design. To evaluate the effectiveness and robustness of the proposed methodology, comparative simulations are conducted on two benchmark nonlinear systems: a simple pendulum and a Van der Pol oscillator. Results demonstrate that the SDRE-KF achieves comparable or superior estimation accuracy compared to traditional methods, including the Extended Kalman Filter (EKF) and Particle Filter (PF). These findings underline the potential of the unified SDRE-based approach as a viable alternative for nonlinear state estimation and control, providing valuable insights for both educational purposes and practical engineering applications.
Code (0)
등록된 구현이 없습니다.
Tasks
State EstimationSimilar Papers 제목 키워드 기반
Ensemble Kalman-Bucy filtering for nonlinear model predictive control
We consider the problem of optimal control for partially observed dynamical systems. Despite its prevalence in practical applications, there are still very few algorithms available, which take uncertainties in the curren…
Model Predictive ControlState EstimationRelaxed Actor-Critic with Convergence Guarantees for Continuous-Time Optimal Control of Nonlinear Systems
This paper presents the Relaxed Continuous-Time Actor-critic (RCTAC) algorithm, a method for finding the nearly optimal policy for nonlinear continuous-time (CT) systems with known dynamics and infinite horizon, such as …
Neural Stochastic Contraction Metrics for Learning-based Control and Estimation
We present Neural Stochastic Contraction Metrics (NSCM), a new design framework for provably-stable robust control and estimation for a class of stochastic nonlinear systems. It uses a spectrally-normalized deep neural n…
Estimation Sample Complexity of a Class of Nonlinear Continuous-time Systems
We present a method of parameter estimation for large class of nonlinear systems, namely those in which the state consists of output derivatives and the flow is linear in the parameter. The method, which solves for the u…
parameter estimationregressionSafe reinforcement learning control for continuous-time nonlinear systems without a backup controller
This paper proposes an on-policy reinforcement learning (RL) control algorithm that solves the optimal regulation problem for a class of uncertain continuous-time nonlinear systems under user-defined state constraints. W…
reinforcement-learningReinforcement Learning (RL)Safe Reinforcement Learning