Static Output Feedback Control Research Articles

Design of Static Output Feedback Suspension Controllers for Ride Comfort Improvement and Motion Sickness Reduction

This paper presents a method to design a static output feedback active suspension controller for ride comfort improvement and motion sickness reduction in a real vehicle system. Full-state feedback controller has shown good performance for active suspension control. However, it requires a lot of states to be measured, which is very difficult in real vehicles. To avoid this problem, a static output feedback (SOF) controller is adopted in this paper. This controller requires only three sensor outputs, vertical velocity, roll and pitch rates, which are relatively easy to measure in real vehicles. Three types of SOF controller are proposed and optimized with linear quadratic optimal control and the simulation optimization method. Two of these controllers have only three gains to be tuned, which are much smaller than those of full-state feedback. To validate the performance of the proposed SOF controllers, a simulation is carried out on a vehicle simulation package. From the results, the proposed SOF controllers are quite good at improving ride comfort and reducing motion sickness.

Finite frequency H ∞ control for singular systems with application to a 2-machine 6-bus power network

This paper is concerned with the H ∞ control problem for singular systems over finite frequency ranges. The disturbance is assumed to be within low-/middle-/high-frequency ranges. Both the state feedback and static output feedback controllers are designed. First, by combining the Lyapunov function method and the generalized Kalman–Yakubovich–Popov lemma, a new finite frequency bounded real lemma (BRL) is proposed, which ensures the resulting closed-loop system to be regular, impulse free and stable with given finite frequency H ∞ performance bound. It is shown by theoretical analysis and numerical simulation that the proposed BRL has less conservatism than the existing ones in the literature. With the aid of the Finsler's Lemma, two improved finite frequency BRLs are further presented for the design of controllers. Then, by utilizing convexification techniques, sufficient conditions for solving the desired state feedback and static output feedback gains are presented in terms of linear matrix inequalities, respectively. Finally, the applicability and effectiveness of the proposed control methods are verified by a 6-bus power network system.

Robust H∞ adaptive model following control for fractional-order systems with polytopic and bounded uncertainties subject to input saturation

This paper investigates a type of robust observer-based tracking control for the well-known inverted pendulum as an uncertain fractional-order system with two-norm bounded uncertainties subject to input saturation along with external disturbance that focuses on the case of a fractional-order α such that [Formula: see text]. The main goal is to design a robust model following tracking control servomechanism by the side of stability analysis. This paper addresses the well-known quadratic Lyapunov function in addition to the Gronwall–Bellman lemma and the sector condition of the saturation function stability synthesis. This paper proposes an outstanding strategy to achieve the best model following robust observer in the cast of output-feedback control subject to input saturation in the framework of an uncertain fractional-order system based on the linear matrix inequality (LMI) solution. The LMI procedure can be used to achieve static output-feedback tracking control and observer gain. Several valuable theorems support this approach, and various simulation scenarios are available to showcase its effectiveness.

Design of Active Suspension Controller for Ride Comfort Enhancement and Motion Sickness Mitigation

This paper presents a method for designing an active suspension controller for ride comfort enhancement and motion sickness mitigation. For this, it is necessary to design an active suspension controller, which aims to reduce the vertical acceleration and pitch rate of a sprung mass in a vehicle. A half-car vehicle model was selected. For the controller design, a static output feedback (SOF) control was selected instead of a full-state feedback control because it is hard to measure all state variables in real vehicles. With the available signals, three types of SOF controller were proposed. To determine the gains of the SOF controllers, a linear quadratic optimal control methodology and a simulation-based optimization method were adopted. To validate the proposed method, a simulation was carried out using vehicle simulation software. The simulation results show that the proposed method is quite effective for ride comfort enhancement and motion sickness mitigation.

FEM-based eigenstructure recovery of a space truss with active members

Abstract Large truss structures have many potential applications in space, such as antennas, telescopes and space solar power plants. In this scenario, a natural concern is the susceptibility of these lightweight structures to be damaged during their operational life, due to impacts, transient thermal states and fatigue phenomena. The inclusion of active elements, equipped with sensor/actuator systems capable of modulating their shape and strength, makes it possible to transform the truss into a smart structure capable of remedying the damage, once it is detected. In this paper, a procedure is described that is capable of restoring at least the basic functionality of a composite truss for space applications, starting with the observation that damage has occurred, regardless of its specific location. The system eigenstructure is used as a benchmark for damage detection, as well as a target characteristic for the subsequent restoration activity. The observer/Kalman filter identification algorithm (OKID), in cascade with the eigensystem realization algorithm (ERA), is adopted to reconstruct, from sensor recordings, the dynamic response of the truss in terms of system state-space representation and eigen-characteristics. Finally, a static output feedback control is developed to recover the low-frequency dynamic behaviour of the truss. The entire procedure is tested using finite element analysis. All activities are coordinated in an innovative procedure that, within a unique Python language code, automatically generates finite element (FE) models, launches finite element analysis (FEA), extracts output data, implements OKID-ERA, processes the control law and applies it to the final FE simulation.

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.

Inverse Q-Learning Using Input-Output Data.

This article addresses the problem of learning the objective function of linear discrete-time systems that use static output-feedback (OPFB) control by designing inverse reinforcement learning (RL) algorithms. Most of the existing inverse RL methods require the availability of states and state-feedback control from the expert or demonstrated system. In contrast, this article considers inverse RL in a more general case where the demonstrated system uses static OPFB control with only input-output measurements available. We first develop a model-based inverse RL algorithm to reconstruct an input-output objective function of a demonstrated discrete-time system using its system dynamics and the OPFB gain. This objective function infers the demonstrations and OPFB gain of the demonstrated system. Then, an input-output Q -function is built for the inverse RL problem upon the state reconstruction technique. Given demonstrated inputs and outputs, a data-driven inverse Q -learning algorithm reconstructs the objective function without the knowledge of the demonstrated system dynamics or the OPFB gain. This algorithm yields unbiased solutions even though exploration noises exist. Convergence properties and the nonunique solution nature of the proposed algorithms are studied. Numerical simulation examples verify the effectiveness of the proposed methods.

Synthesizing Negative-Imaginary Systems With Closed-Loop H∞-Performance Via Static Output Feedback Control

Abstract This paper develops an algorithm for synthesizing negative imaginary (NI) systems with a specified H∞-norm bound by exploiting the convex relaxation technique in the static output-feedback (SOF) control design framework. This scheme improves the robustness objective since the present framework can handle both NI and H∞-norm-bounded unstructured uncertainty of the system. The non-strict inequality involved in the NI system description that creates a major difficulty in the SOF control design, can efficiently be tackled by the developed convex relaxation-based iterative algorithm. The advantages of the algorithm are shown using several examples and the results are compared with the existing works.

A novel semi-active control of an integrated chassis and seat quasi-zero stiffness suspension system for off-road vehicles

This article introduces an innovative semi-active suspension system for off-road vehicles, incorporating a quasi-zero stiffness suspension to enhance driver comfort. The system includes a central pneumatic spring, double-acting pneumatic linear actuators for adjustable stiffness, and magnetorheological dampers for controlled damping. Using Lyapunov stability theory, a static output feedback control law is designed to address uncertainties in road profiles, driver body parameters, and actuator saturation, relying on measured variables as feedback. Performance constraints focus on driver head acceleration, suspension displacement, and dynamic tire load. The control law problem is converted into a convex optimization problem with linear matrix inequalities. The new semi-active QZSS system is theoretically tested via Matlab simulations and validated through hardware-in-the-loop testing. Comparative analysis between passive QZSS and the new semi-active QZSS on different roads, and vehicle speeds closely aligns with simulation results, with minor disparities attributable to network discrepancies and signal interruptions. Impressively, the semi-active QZSS system reduces driver head vertical acceleration between 26.53 and 35.0% compared to passive air QZSS, showing potential for significantly improving ride comfort, reducing vibration transfer, and enhancing driver wellbeing with minimal energy requirement.

Optimization Landscape of Policy Gradient Methods for Discrete-Time Static Output Feedback.

In recent times, significant advancements have been made in delving into the optimization landscape of policy gradient methods for achieving optimal control in linear time-invariant (LTI) systems. Compared with state-feedback control, output-feedback control is more prevalent since the underlying state of the system may not be fully observed in many practical settings. This article analyzes the optimization landscape inherent to policy gradient methods when applied to static output feedback (SOF) control in discrete-time LTI systems subject to quadratic cost. We begin by establishing crucial properties of the SOF cost, encompassing coercivity, L -smoothness, and M -Lipschitz continuous Hessian. Despite the absence of convexity, we leverage these properties to derive novel findings regarding convergence (and nearly dimension-free rate) to stationary points for three policy gradient methods, including the vanilla policy gradient method, the natural policy gradient method, and the Gauss-Newton method. Moreover, we provide proof that the vanilla policy gradient method exhibits linear convergence toward local minima when initialized near such minima. This article concludes by presenting numerical examples that validate our theoretical findings. These results not only characterize the performance of gradient descent for optimizing the SOF problem but also provide insights into the effectiveness of general policy gradient methods within the realm of reinforcement learning.

Structured Output Feedback Control for Linear Quadratic Regulator Using Policy Gradient Method

We consider the static output feedback control for Linear Quadratic Regulator problems with structured constraints under the assumption that system parameters are unknown. To solve the problem in the model free setting, we propose the policy gradient algorithm based on the gradient projection method and show its global convergence to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\varepsilon$</tex-math></inline-formula> -stationary points. In addition, we introduce a variance reduction technique and show both theoretically and numerically that it significantly reduces the variance in the gradient estimation. We also show in the numerical experiments that the model free approach efficiently solves the problem.

Finite Horizon Memory Control of Networked Systems Using Chain-like Lyapunov Function

Abstract: This paper proposes a novel finite horizon memory control (FHMC) design framework for networked systems by using input delay approach. A chain-like input delay model is established to characterize the networked control system (NCS) under memory control architecture in order to make full use of historic sampled-data. Based on the proposed chain-like delay model, the corresponding chain-like Lyapunov-Krasovskii function, which records the historic sampling information of NCS, is well constructed for facilitating further analysis and synthesis of the proposed FHMC scheme. Both state feedback controllers and static output feedback controllers are derived by solving LMIs (Linear matrix inequalities). The proposed FHMC scheme is skilled in improving control performance of networked systems. Simulations show the effectiveness of the presented FHMC scheme.

Probabilistic Event-Triggered Policy for Extended Dissipative Finite-Time Control of MJSs under Cyber-Attacks and Actuator Failures

This technical note investigates the problem of extended dissipative finite-time control for Markov jump systems (MJSs) with cyber-attacks and actuator failures. A probabilistic event-triggered mechanism (PETM) is proposed to relieve the communication burden by exploiting both the pattern variation of triggering thresholds and the time-varying characteristic of transmission delays. To characterize the actual control inputs, a stochastic actuator failure model (SAFM) is established using a random variable of any discrete-time distribution over [0,1]. Firstly, based on the PETM and SAFM, static output feedback controllers are devised which may not switch with the system synchronously. Then, novel sufficient conditions with less conservatism are obtained to achieve the extended dissipative finite-time control performance of the closed-loop system under admissible cyber-attacks and actuator failures. Furthermore, controller gains with non-convex constraints are calculated with the aid of a newly proposed lemma. Finally, an application oriented example is provided to verify the effectiveness and superiority of the proposed results.

A PARAMETER ADJUSTMENT LAW FOR MULTIVARIABLE PID CONTROL SYSTEMS WITH DISTURBANCE ATTENUATION PERFORMANCE

This paper shows a new parameter adjustment law of PID controllers for MIMO linear system with guaranteed disturbance attenuation performance. In the proposed design approach, the design problem of PID parameters is reduced to the problem of static output feedback controllers for MIMO linear systems. In this paper, we show that sufficient conditions for the existence of the proposed PID control system can be reduced to solvability of linear matrix inequalities (LMIs). Finally, a simple numerical example is shown to effectiveness of the proposed PID control system.

Intermittent Static Output Feedback Control for Stochastic Delayed-Switched Positive Systems With Only Partially Measurable Information

Intermittent Static Output Feedback Control for Stochastic Delayed-Switched Positive Systems With Only Partially Measurable Information

On the convexity of static output feedback control synthesis for systems with lossless nonlinearities

Computing a stabilizing static output-feedback (SOF) controller is an NP-hard problem, in general. Yet, these controllers have amassed popularity in recent years because of their practical use in feedback control applications, such as fluid flow control and sensor/actuator selection. The inherent difficulty of synthesizing SOF controllers is rooted in solving a series of non-convex problems that make the solution computationally intractable. In this note, we show that SOF synthesis is a convex problem for the specific case of systems with a lossless (i.e., energy-conserving) nonlinearity. Our proposed method ensures asymptotic stability of an SOF controller by enforcing the lossless behavior of the nonlinearity using a quadratic constraint approach. In particular, we formulate a bilinear matrix inequality (BMI) using the approach, then show that the resulting BMI can be recast as a linear matrix inequality (LMI). The resulting LMI is a convex problem whose feasible solution, if one exists, yields an asymptotically stabilizing SOF controller.

Lyapunov-based stabilization mobile control design of linear parabolic PDE systems

This article considers the exponential mobile stabilization control of linear parabolic partial differential equation (PDE) systems. Firstly, a stabilization scheme based on static output feedback (SOF) control and mobile actuator/sensor guidance is proposed. Next, the operator theory is used to discuss the well-posedness of closed-loop PDE systems. Thus, the SOF control and mobile guidance design approach is simultaneously proposed to guarantee that the closed-loop PDE system is exponentially stable. In final, the effectiveness of the design method is verified by numerical simulation.

A Novel relaxation of the static output feedback problem for a class of plants

The static output feedback control problem is important, as it is concerned with the case when one cannot measure all state variables. It seeks to obtain a stabilising control under these conditions and is, often, difficult to solve. For a certain class of linear dynamical systems, we provide a novel approach to obtain a stabilising control gain matrix. The class of plants considered is of those, for which we can measure at least half of all state variables and where those measurements affect at least half of all state variables. Moreover, when we write the (linearly transformed) system matrix in block form, we require that either the two lower block matrices are nonsingular, or, if the inputs affect the measured state variables directly, at least the lower left one is nonsingular. We then show that we can determine the stabilising control gain matrix from the solution of a linear matrix inequality. Finally, we apply the approach to different benchmark problems, where it performs well, and confirm its good performance through additional numerical experiments.

Criteria for Stability and Stabilization of Variable Fractional-Order Uncertain Neutral Systems With Time-Varying Delay: Delay-Dependent Analysis

This work focuses on the stability and stabilization of variable fractional-order neutral systems (VFONS) with time-varying delays and time-varying structured uncertainties. Via the FO Lyapunov function, a new set of delay-and order-dependent criterion is proposed for both nominal and uncertain VFONS. The resultant criteria are formulated by designing a linear matrix inequality-based static output feedback control strategy in a set of linear matrix inequalities. The numerical simulations verify the theoretical formulation.

Performance analysis of distributed power systems using error dynamics passive output feedback control

This paper presents a novel control approach for integrated converters using Exact Tracking Error Dynamics Passive Output Feedback control and Exact Static Error Dynamics Passive Output Feedback control. By continuously injecting active distributed power systems (DPS) power sources into the utility grid and loads, the approach reduces harmonic current distortion and maintains unity for the grid’s power factor. The paper compares existing control methods, such as P, PI, proportional–integral–derivative (PID), energy structuring and damping infusion and interconnection and damping assignment—passivity-based control and considers the impacts of instantaneous fluctuations in reference current elements on the AC side and oscillations in DC voltage generated by the DC-link voltage. Relevant switching state functions are designed, and if the maximum power can be fed exceeds the required power from grid-connected loads, the true, reactive, and harmonic current elements of loads are adjusted dynamically, resulting in in-phase sinewave grid currents. The performance analysis is performed using MATLAB/Simulink, and a smaller research prototype is built and discussed.