A Suboptimal Dual Control Method for the Stochastic Systems with Parameters Drifting

Yang, Hengzhan; Gao, Song; Qian, Fucai; Huang, Jiaoru

doi:10.1002/asjc.1750

Cited by 3 publications

(4 citation statements)

References 23 publications

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“…where (11) is the new information about the system parameters contained in z(t + 1), i.e., the innovation sequence. Equation (10) shows the estimation and tracking of drift parameters at the current sanpling isntant.…”

Section: Parameter Predictionmentioning

confidence: 99%

“…For the deterministic drift phenomena, a double exponentially weighted moving average feedback controller is designed to compensate the slow drift of the system in the literature [ 10 ]. In addition, Yang et al [ 11 ] proposed a suboptimal dual control method for the systems with parameter drifting. However, these above methods are only for SISO cases.…”

Section: Introductionmentioning

confidence: 99%

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Optimal Control Algorithm for Stochastic Systems with Parameter Drift

Zhang

Gao

Chen

et al. 2023

Sensors

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A novel optimal control problem is considered for multiple input multiple output (MIMO) stochastic systems with mixed parameter drift, external disturbance and observation noise. The proposed controller can not only track and identify the drift parameters in finite time but, furthermore, drive the system to move towards the desired trajectory. However, there is a conflict between control and estimation, which makes the analytic solution unattainable in most situations. A dual control algorithm based on weight factor and innovation is, therefore, proposed. First, the innovation is added to the control goal by the appropriate weight and the Kalman filter is introduced to estimate and track the transformed drift parameters. The weight factor is used to adjust the degree of drift parameter estimation in order to achieve a balance between control and estimation. Then, the optimal control is derived by solving the modified optimization problem. In this strategy, the analytic solution of the control law can be obtained. The control law obtained in this paper is optimal because the estimation of drift parameters is integrated into the objective function rather than the suboptimal control law, which includes two parts of control and estimation in other studies. The proposed algorithm can achieve the best compromise between optimization and estatimation. Finally, the effectiveness of the algorithm is verified by numerical experiments in two different cases.

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Section: Parameter Predictionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal Control Algorithm for Stochastic Systems with Parameter Drift

Zhang

Gao

Chen

et al. 2023

Sensors

Self Cite

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“…When p ( t )=1, system () reduces to the well‐known normal form, controller design and stability analysis problems arise, which have been investigated in many works [1–11]. Specifically, [1]–[2] give the basic definitions and stability results for stochastic systems.…”

Section: Introductionmentioning

confidence: 99%

“…Specifically, [1]–[2] give the basic definitions and stability results for stochastic systems. For the Lyapunov‐based controller design, there are mainly two methods: quartic Lyapunov functions [3]‐[4] and quadratic Lyapunov functions multiplied by different weighting functions [5], which are further developed by [6–11]. When the power p ( t )>1, system () is called stochastic high‐order nonlinear system.…”

Section: Introductionmentioning

confidence: 99%

State‐feedback stabilization and inverse optimal control for stochastic high‐order nonlinear systems with time‐varying powers

Liu

Yao

2019

Asian Journal of Control

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This paper considers the stability and optimality problems associated with stochastic high‐order nonlinear systems with time‐varying powers. This research extends previous studies on the plant with constant powers. In this paper, we firstly construct a state‐feedback controller to ensure that the equilibrium at the origin of the closed‐loop system is globally asymptotically stable (GAS) in probability. Then we redesign a new optimal controller with infinite gain margin to solve the inverse optimal stabilization (IOS) problem. Specifically, the optimal controller is not only optimal with respect to a meaningful cost functional but also globally asymptotically stabilizes the closed‐loop system. The efficiency of the designed controllers is demonstrated by a simulation example.

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A Numerical Algorithm for Self-Learning Model Predictive Control in Servo Systems

Yang

Weng

et al. 2022

Mathematics

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Model predictive control (MPC) is one of the most effective methods of dealing with constrained control problems. Nevertheless, the uncertainty of the control system poses many problems in its performance optimization. For high-precision servo systems, friction is typically the main factor in uncertainty affecting the accuracy of the system. Our work focuses on stochastic systems with unknown parameters and proposes a model predictive control strategy with machine learning characteristics that utilizes pre-estimated information to reduce uncertainty. Within this model, the parameters are obtained using the estimator. The uncertainty caused by the parameter estimation error in the system is parameterized, serving as a learning control component to reduce future uncertainty. Then, the estimated parameters and the current state of the system are used to predict the future p-step state. The control sequence is calculated under the MPC’s rolling optimization mechanism. After the system output is obtained, the new parameter value at the next moment is re-estimated. Finally, MPC is carried out to realize the dual rolling optimization mechanism. In general, the proposed strategy optimizes the control objective while reducing the system uncertainty of the future parameter and achieving better system performance. Simulation results demonstrate the effectiveness of the algorithm.

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A Suboptimal Dual Control Method for the Stochastic Systems with Parameters Drifting

Cited by 3 publications

References 23 publications

Optimal Control Algorithm for Stochastic Systems with Parameter Drift

Optimal Control Algorithm for Stochastic Systems with Parameter Drift

State‐feedback stabilization and inverse optimal control for stochastic high‐order nonlinear systems with time‐varying powers

A Numerical Algorithm for Self-Learning Model Predictive Control in Servo Systems

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