Optimal Static Output Feedback Research Articles

Density estimation based soft actor-critic: deep reinforcement learning for static output feedback control with measurement noise

ABSTRACT The state-of-the-art deep reinforcement learning (DRL) methods, including Deep Deterministic Policy Gradient (DDPG), Twin Delayed DDPG (TD3), Proximal Policy Optimization (PPO), Soft Actor-Critic (SAC), among others, demonstrate significant capability in solving the optimal static state feedback control (SSFC) problem. This problem can be modeled as a fully observed Markov decision process (MDP). However, the optimal static output feedback control (SOFC) problem with measurement noise is a typical partially observable MDP (POMDP), which is difficult to solve, especially for the continuous state-action-observation space with high dimensions. This paper proposes a two-stage framework to address this challenge. In the laboratory stage, both the states and the noisy outputs are observable; the SOFC policy is converted to a constrained stochastic SSFC policy, of which the probability density function is generally not analytical. To this end, a density estimation based SAC algorithm is proposed to explore the optimal SOFC policy by learning the optimal constrained stochastic SSFC. Consequently, in the real-world stage, only the noisy outputs and the learned SOFC policy are required to solve the optimal SOFC problem. Numerical simulations and the corresponding experiments with robotic arms are provided to illustrate the effectiveness of our method. The code is available at https://github.com/RanKyoto/DE-SAC.

Optimal Static Output Feedback Stabilization of Fractional-Order Systems With Caputo Derivative Order 1 ≤ α < 2

Optimal Static Output Feedback Stabilization of Fractional-Order Systems With Caputo Derivative Order 1 ≤ α < 2

Control of drill string torsional vibrations using optimal static output feedback

Failures during oil extraction can have impacts on exploration costs and time, especially those caused by vibrations during the drilling phase. A proper way to reduce these detrimental failures is to design an active controller that efficiently mitigates vibrations with the constraint of using the limited amount of real time data available in field operations. In this context, a technique that might be suitable for the controller design is the optimal static output feedback (OSOF), that considers only the measured signals for feedback. Recently, the authors proposed some modifications to this technique, involving the addition of sensors locations and a new way of dealing with the dependence of the controller parameters on the system initial condition. The aim of this contribution is to apply this novel control technique to suppress drill string torsional vibrations and address all the particular aspects regarding the application of the proposed controller for the drill string problem, i.e., reformulation of the equations of motion as a stabilization problem, determination of the output matrix and linearization. Analyses and comparison of the proposed controller with proportional–integral (PI) and linear quadratic regulator (LQR) controllers are performed considering numerical simulations of a finite element model with a non-regularized dry friction function. Results indicate that the proposed controller has a performance similar to the LQR with a significantly reduced number of sensors, and also exhibits superior performance and robustness with an equivalent control effort over the PI controller. • Simulations with FEM and discontinuous friction for typical drilling conditions. • Theoretical basis for application of OSOF control for nonlinear drilling system. • Analyses showing proposed controller superiority over the one usually employed. • Analyses showing controller robustness for large friction parameter variations.

Enhanced attenuation band in active 2D mass-in-mass metamaterial using static output feedback

Active feedback control is implemented between the inner and outer masses of a 2D mass-in-mass metamaterial to widen the attenuation bandwidth by reducing the displacement of the outer mass of each unit cell. The optimal static output feedback control is applied to a single representative unit. The gain is computed from the analysis of a single unit cell and further used along with the Bloch–Floquet theorem for obtaining the dispersion relationship for an infinite 2D discrete square lattice metamaterial. The proposed model is validated by comparing the results against the finite element simulation in ANSYS. The control gain couples the displacements and velocities, which generates the damping phenomenon even in an undamped system. The controller design requires feedback of only a few measured output instead of all the state variables, and offline computation of the feedback gains reduces the time delay. Effective mass analysis and energy dissipation mechanism are performed which sheds light on the physics underlying the attenuation phenomena. An ultra-wide uninterrupted attenuation band can be perceived as the negative effective mass region significantly extends beyond the standard limit by employing the active feedback control. Additionally, the attenuation bandwidth exists in the low frequency due to the damping induced from the active control.

Design of Optimal Static Output Feedback Controllers for Linear Control Systems Subject to General Structural Constraints

This work considers the design of optimal static output feedback controllers with priori structural constraints for linear systems. The structural constraints impose individual elements of the feedback matrix to satisfy certain equality or inequality constraints. The barrier method is used to address an auxiliary minimization problem to attain an approximate solution to the original nonconvex constrained optimization problem. The Lagrange multiplier method is applied to derive necessary conditions for the optimal solution. An easy-to-implement algorithm based on the gradient descent method is developed to solve the auxiliary minimization problem, and the convergence of the algorithm is proven. The effectiveness of the proposed methodology is validated using two numerical examples.

Discrete-time multivariable PID controller design with application to an overhead crane

This paper considers the problems of designing multivariable proportional-integral-derivative (PID) controllers for discrete-time systems with D-stability and/or performance constraints. First, the PID control problem is cast into a static output feedback (SOF) control problem, and linear matrix inequality (LMI) conditions are presented. Then, a cone complementarity linearisation (CCL) method is used to solve the SOF-stabilisation problem, and a coordinate transformation matrix (CTM) optimisation approach is extended to solve the optimal SOF control problem. Finally, a numerical example is provided to show the effectiveness and advantage of the CTM optimisation approach, and application to the anti-sway and positioning control of an overhead crane demonstrates the validity of the approach.

A New Compensator Design for Optimal Static Output Feedback Control Across a Communication Channel Subject to Random Packet Dropouts

This paper studies compensation of networked control across an unreliable communication channel subject to random packet dropouts. By posing it as a two decision-variable optimization problem, the control and compensation for static output feedback LQR are unified by the proposed design. New governing equations are derived for the controller and the compensator satisfying optimality conditions concurrently. Also presented is a convergent algorithm that solves these equations for the optimal gains. Finally, to validate the design and verify its effectiveness, a numerical example is given on which a computer simulation is conducted to compare its performance against that of three other existing schemes. The simulation results demonstrate its saliency among the four methods.

On the noncollocated control of structures with optimal static output feedback: Initial conditions dependence, sensors placement, and sensitivity analysis

Structural Control and Health MonitoringVolume 27, Issue 1 e2469 ERRATUM On the noncollocated control of structures with optimal static output feedback: Initial conditions dependence, sensors placement, and sensitivity analysis Hélio Jacinto Cruz Neto, Hélio Jacinto Cruz NetoSearch for more papers by this authorMarcelo Areias Trindade, Marcelo Areias TrindadeSearch for more papers by this author Hélio Jacinto Cruz Neto, Hélio Jacinto Cruz NetoSearch for more papers by this authorMarcelo Areias Trindade, Marcelo Areias TrindadeSearch for more papers by this author First published: 18 November 2019 https://doi.org/10.1002/stc.2469Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume27, Issue1January 2020e2469 RelatedInformation

On the noncollocated control of structures with optimal static output feedback: Initial conditions dependence, sensors placement, and sensitivity analysis

It is well known that the linear quadratic regulator (LQR) exhibits significant frequency margins and reduced sensitivity properties. However, its application in real problems is restricted because it requires availability of all state variables of the controlled system to be measured. This problem is not satisfactorily overcome by state observers, because they are sensitive to spillover and their more complex structure can entail time delay. Another alternative to solve this problem is to use only linear combinations of measured signals for feedback, a technique known as optimal static output feedback (OSOF) or partial state feedback. In this paper, this method is studied considering additionally sensors locations as optimization variables. Necessary conditions of optimality are presented in order to highlight the dependence of the optimal solution on system initial conditions. A new approach to deal with this dependence, which is based on approaching the performances of OSOF and LQR for any initial condition, is developed and compared with the existing one. The method developed is tested on a simply supported plate modeled using the finite element method. The analyses of the results show that with a significantly reduced number of sensors, the OSOF controller has a performance equivalent to LQR. The developed methodology also provided the controlled system a relevant behavior to major problems of noncollocated control, such that it maintained stability and performance considering parameters variations and a large increase in frequency bandwidth.

On positive realness, negative imaginariness, and [formula omitted] control of state-space symmetric systems

This paper studies positive realness and negative imaginariness of state-space symmetric systems. First, a necessary and sufficient condition is provided for a state-space symmetric system to be, respectively, positive real and negative imaginary. Then an explicit formulation for the infimum of H∞ norm under a mixed H∞ and negative imaginary performance and an explicit solution for the associated optimal static output feedback control gain are developed based on symmetric negative imaginary theorem. Finally, three examples are provided to illustrate the main results of the paper.

Performance optimization over positive [formula omitted] cones

Abstract In this paper we study linear systems with positivity type of constraints. First, we consider the case where the input to a system is restricted to be in the positive cone of l ∞ , denoted by l ∞ + , and seek to characterize the system’s induced norm from l ∞ + to l ∞ . We obtain an exact characterization of this norm which is particularly easy to calculate in the case of LTI systems. Furthermore, we consider and solve the model matching problem, and show that time-varying linear or nonlinear control/filtering does not improve the performance with respect to this norm for LTI systems. In the second part of the paper, we consider the case when the output is forced to be in the positive l ∞ cone when the input is in this cone. We show if internal positivity is sought, a dynamic optimal controller offers no advantage over a static one. Also, if the measurement matrix satisfies certain conditions, synthesizing an optimal static output feedback controller reduces to a linear program.

Semiactive Control of Earthquake/Wind Excited Buildings Using Output Feedback

Abstract Output feedback control using Magnetorheological dampers and Variable Stiffness Tuned Mass Dampers is considered. Firstly, seismic response control of a building with MR dampers is considered. Optimal Static Output Feedback (OSOF) control yields the desired control force. Two laws are proposed to obtain voltage that achieves the desired force. OSOF yields a reduction in responses and CPU time vis-a-vis LQG and Passive-on controllers. Instantaneous Optimal Control is also considered. Next, a stiff and a flexible building are connected by a MR damper. Input voltage is predicted by a Recurrent Neural Network using desired control force from LQG/OSOF. Both output feedback controllers yield significant reduction in response and base shear and require much less control effort compared to passive-on control. Lateral-torsional seismic response control of plan asymmetric buildings connected by MR dampers is also studied. Finally, control of a wind excited benchmark building using a Variable Stiffness TMD is considered. The nominal stiffness corresponds to the fundamental frequency, resulting in an LTI system for which the desired control force is computed using OSOF/LQG control. A simple control law yields the device configuration. The present control is comparable with active-TMD and better than Short-time-Fourier-Transform control. A variable length pendulum TMD is proposed.

Control of MR Damper Connected Buildings by Output Feedback

The control of seismic response of buildings connected by a magnetorheological (MR) damper is studied. The desired control force is obtained using Linear Quadratic Gaussian (LQG) control based on the feedback of states estimated via measured outputs or Optimal Static Output Feedback (OSOF) control using the direct feedback of measured outputs. The damper input voltage is predicted using a Recurrent Neural Network (RNN), which proves more effective than the Clipped Voltage Law (CVL). Various sensor configurations and state weightings are considered to obtain effective control. LQG-RNN/OSOF-RNN yield significant reduction in response and base shear and require much less control effort compared to passive-on control with saturation voltage. Compared to passive-off control, they are very effective in attenuating maximum-peak/RMS responses and storeywise responses of the flexible building, except for max-peak accelerations that increase slightly. However, passive-off control is unable to transfer base shear to the stiffer building. LQG-RNN/OSOF-RNN also yield control at least as effective as LQR-RNN by deploying much fewer sensors but using a somewhat higher damper force. They are mostly comparable to each other, but OSOF-RNN requires an order-of-magnitude less CPU time for the control loop. Effective control is possible using few sensors.

線形時変力学系のLMIを用いた静的出力フィードバック制御の<i>L</i><sub>2</sub>ゲイン性能最適設計

線形時変力学系のLMIを用いた静的出力フィードバック制御の<i>L</i><sub>2</sub>ゲイン性能最適設計

Semi-Active Control Using Magnetorhelogical Dampers with Output Feedback and Distributed Sensing

Control of seismic response of a building fitted with magnetorheological dampers is considered using Optimal Static Output Feedback (OSOF) for desired damper forces. The Modified Bouc-Wen damper model is used and two control voltage laws based on the MR constraint filter, i.e., Semi-inverse Quadratic Voltage Law and Semi-inverse On-Off Voltage Law, are proposed. These appear to perform at least as well as an existing Clipped Voltage Law. Comparisons with available results from a robust reliability-based controller show OSOF control to be quite effective. Controlled response using OSOF is compared with Linear Quadratic Guassian (LQG) and passive-on controllers. Moderate to substantial reduction in maximum peak/RMS responses is mostly obtained with base configuration of sensors when using OSOF control, and controller CPU time reduces by two orders of magnitude. Parametric studies regarding sensor configuration and state/control weighting matrices are performed in order to obtain effective control. Effective OSOF control requires drift feedback with drift sensor preferably collocated with damper.

Semi-Active Control Using Magnetorhelogical Dampers with Output Feedback and Distributed Sensing

Control of seismic response of a building fitted with magnetorheological dampers is considered using Optimal Static Output Feedback (OSOF) for desired damper forces. The Modified Bouc-Wen damper model is used and two control voltage laws based on the MR constraint filter, i.e., Semi-inverse Quadratic Voltage Law and Semi-inverse On-Off Voltage Law, are proposed. These appear to perform at least as well as an existing Clipped Voltage Law. Comparisons with available results from a robust reliability-based controller show OSOF control to be quite effective. Controlled response using OSOF is compared with Linear Quadratic Guassian (LQG) and passive-on controllers. Moderate to substantial reduction in maximum peak/RMS responses is mostly obtained with base configuration of sensors when using OSOF control, and controller CPU time reduces by two orders of magnitude. Parametric studies regarding sensor configuration and state/control weighting matrices are performed in order to obtain effective control. Effective OSOF control requires drift feedback with drift sensor preferably collocated with damper.

An analysis of static output feedback control for tendon driven master-slave manipulator — Simulation study

In this work, a bilateral control for a master-slave manipulator system which will be used for handling objects contaminated by radioactivity has been addressed. The links of manipulators are driven independently by individual motors installed on the base and the driving torque is transmitted through pre-tensioned tendons. The measurable variables are the positions and rates of master/slave motors. In the consideration of the flexibility of the power transmission tendon and available measurements for control, we proposed an optimal static output feedback control for possible bilateral control architecture. The system model is reduced to guarantee the controllability and observability which are necessity for the static output feedback control by using modal analysis. Based on the reduced model, the control gains are determined to attenuate vibration in the sense of optimality. The feasibility of the proposed control design was verified along with some simulation results.

Wing box transonic-flutter suppression using piezoelectric self-sensing diagonal-link actuators

The main objective of this research is to study the capability of Piezoelectric (PE) self-sensing actuators to suppress the transonic wing-box flutter, which is a flow-structure interaction phenomenon. The unsteady general frequency modified Transonic Small Disturbance (TSD) equation is used to model the transonic flow about the wing. The wing-box structure and the piezoelectric actuators are modeled using the equivalent plate method, which is based on the first-order shear deformation plate theory (FSDPT). The piezoelectric actuators are used as diagonal-links. The optimal electromechanical-coupling conditions between the piezoelectric actuators and the wing are collected from previous work. Three main different control strategies; Linear Quadratic Gaussian (LQG) which combines the Linear Quadratic Regulator (LQR) with the Kalman Filter Estimator (KFE), Optimal Static Output Feedback (SOF), and Classic Feedback Controller (CFC); are studied and compared. The optimum actuators and sensors locations are determined using the Norm of Feedback Control Gains (NFCG) and Norm of Kalman Filter Estimator Gains (NKFEG), respectively. A genetic algorithm (GA) optimization technique is used to calculate the controller and estimator parameters to achieve a target response.

Optimal static output feedback control of a building using an MR damper

Optimal static output feedback (OSOF) control is used to obtain the control force desired from a magnetorheological (MR) damper fitted between ground and first storey of a three-storey building model. The modified Bouc–Wen model is considered for obtaining damper response. This exhibits a non-linear relationship between damper force and input-voltage/states, and hence obtaining the input voltage to realize a desired control force is a non-trivial task. Two voltage control laws are proposed, i.e. inverse quadratic voltage law (IQVL) and inverse On–off voltage law (IOOVL), both based on the MR constraint filter. These are implemented in addition to the existing clipped voltage law (CVL). Results for controlled response of the building are obtained in terms of peak and RMS values of response quantities (Interstorey Drift, Displacement, Acceleration). These are compared with existing results obtained via linear quadratic Gaussian (LQG) control using CVL, and via passive-on control with constant (saturation) voltage applied. A reduction in the maximum peak interstorey drift, maximum RMS interstorey drift, and performance index is obtained when using OSOF-IOOVL/CVL control as compared with passive-on control. These quantities as well as RMS storey displacements are attenuated when comparing OSOF-IOOVL/CVL control with LQG-CVL control, with the exception of maximum peak interstorey drift for which the attenuation occurs for IOOVL only. The peak and RMS values of accelerations are reduced via OSOF compared with passive-on/LQG-CVL control, except when considering first-storey accelerations using passive-on control. The peak value of the applied damper force is least when using OSOF control. Copyright © 2010 John Wiley & Sons, Ltd.

Optimal periodic output feedback control: a continuous-time approach and a case study

This article deals with the problem of optimal static output feedback control of linear periodic systems in continuous time, for which a continuous-time approach, which allows to deal with both stable and unstable open loop systems, is presented. The proposed approach is tested on the problem of designing attitude control laws for a Low-Earth Orbit (LEO) satellite on the basis of feedback from a triaxial magnetometer and a set of high-precision gyros. Simulation results are used to demonstrate the feasibility of the proposed strategy and to evaluate its performance.