Closed-loop optimal control of discrete systems

2011 ◽  
pp. 209-248
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Discrete Systems

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

Discrete Time-Delay Optimal Control Method for Experimental Active Chatter Suppression and Its Closed-Loop Stability Analysis

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Xingwu Zhang ◽  
Ziyu Yin ◽  
Jiawei Gao ◽  
Jinxin Liu ◽  
Robert X. Gao ◽  
...  
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Control Method ◽  
Trial And Error ◽  
Stability Lobe Diagram ◽  
Weighting Matrix ◽  
Chatter Suppression ◽  
Stability Lobe ◽  
Optimal Control Method ◽  
Discrete Time Delay

Chatter is a self-excited and unstable vibration phenomenon during machining operations, which affects the workpiece surface quality and the production efficiency. Active chatter control has been intensively studied to mitigate chatter and expand the boundary of machining stability. This paper presents a discrete time-delay optimal control method for chatter suppression. A dynamical model incorporating the time-periodic and time-delayed characteristic of active chatter suppression during the milling process is first formulated. Next, the milling system is represented as a discrete linear time-invariant (LTI) system with state-space description through averaging and discretization. An optimal control strategy is then formulated to stabilize unstable cutting states, where the balanced realization method is applied to determine the weighting matrix without trial and error. Finally, a closed-loop stability lobe diagram (CLSLD) is proposed to evaluate the performance of the designed controller based on the proposed method. The CLSLD can provide the stability lobe diagram with control and evaluate the performance and robustness of the controller cross the tested spindle speeds. Through many numerical simulations and experimental studies, it demonstrates that the proposed control method can make the unstable cutting parameters stable with control on, reduce the control force to 21% of traditional weighting matrix selection method by trial and error in simulation, and reduce the amplitude of chatter frequency up to 78.6% in experiment. Hence, the designed controller reduces the performance requirements of actuators during active chatter suppression.

Passive optimal feedback control of an articulated flexible arm

2020 ◽  
pp. 107754632095676
Author(s):  
Raja Tebbikh ◽  
Hicham Tebbikh ◽  
Sihem Kechida
Keyword(s):  
Optimal Control ◽  
Feedback Control ◽  
Closed Loop ◽  
Open Loop ◽  
Optimal Feedback Control ◽  
Convolution Operators ◽  
High Frequencies ◽  
Zero Initial Condition ◽  
Flexible Arm ◽  
Euler Bernoulli Beam

This article deals with stabilization and optimal control of an articulated flexible arm by a passive approach. This approach is based on the boundary control of the Euler–Bernoulli beam by means of wave-absorbing feedback. Due to the specific propagative properties of the beam, such controls involve long-memory, non-rational convolution operators. Diffusive realizations of these operators are introduced and used for elaborating an original and efficient wave-absorbing feedback control. The globally passive nature of the closed-loop system gives it the unconditional robustness property, even with the parameters uncertainties of the system. This is not the case in active control, where the system is unstable, because the energy of high frequencies is practically uncontrollable. Our contribution comes in the achievement of optimal control by the diffusion equation. The proposed approach is original in considering a non-zero initial condition of the diffusion as an optimization variable. The optimal arm evolution, in a closed loop, is fixed in an open loop by optimizing a criterion whose variable is the initial diffusion condition. The obtained simulation results clearly illustrate the effectiveness and robustness of the optimal diffusive control.

Efficient Human Motion Planning Using Recursive Dynamics and Optimal Control Techniques

1999 ◽  
Author(s):  
Janzen Lo ◽  
Dimitris Metaxas
Keyword(s):  
Optimal Control ◽  
Motion Planning ◽  
Closed Loop ◽  
High Efficiency ◽  
Human Motion ◽  
Lagrangian Formulation ◽  
Planning Problem ◽  
Tree Structures ◽  
Recursive Dynamics ◽  
Minimum Torque

Abstract We present an efficient optimal control based approach to simulate dynamically correct human movements. We model virtual humans as a kinematic chain consisting of serial, closed-loop, and tree-structures. To overcome the complexity limitations of the classical Lagrangian formulation and to include knowledge from biomechanical studies, we have developed a minimum-torque motion planning method. This new method is based on the use of optimal control theory within a recursive dynamics framework. Our dynamic motion planning methodology achieves high efficiency regardless of the figure topology. As opposed to a Lagrangian formulation, it obviates the need for the reformulation of the dynamic equations for different structured articulated figures. We use a quasi-Newton method based nonlinear programming technique to solve our minimum torque-based human motion planning problem. This method achieves superlinear convergence. We use the screw theoretical method to compute analytically the necessary gradient of the motion and force. This provides a better conditioned optimization computation and allows the robust and efficient implementation of our method. Cubic spline functions have been used to make the search space for an optimal solution finite. We demonstrate the efficacy of our proposed method based on a variety of human motion tasks involving open and closed loop kinematic chains. Our models are built using parameters chosen from an anthropomorphic database. The results demonstrate that our approach generates natural looking and physically correct human motions.

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