Optimal Output Feedback Control Research Articles

Data‐driven based optimal output feedback control with low computation cost

SummaryA partial model‐free, data‐driven adaptive optimal output feedback (OPFB) control scheme with low computational cost continuous‐time is proposed in this paper. The design objective is to obtain the optimal control law by using measurable input and output data, without some knowledge of system model information. Firstly, the system states are decoupled into measurable and unmeasurable parts, and a new state‐space equation is built to estimate the unmeasurable states by using a reduced‐order observer. Based on this, a parametrization method is utilized to reconstruct the system states. Subsequently, by using the reconstructed states, the adaptive dynamic programming (ADP) Bellman equations based on policy‐iteration (PI) and value‐iteration (VI) are presented to solve the control problems with initially stable and unstable conditions, respectively. Then, the convergence of the system is proved. Compared with the early proposed OPFB algorithms, only the unknown internal state needs to be reconstructed. Therefore, the computation cost and design complexity are reduced for the proposed scheme. The effectiveness of the proposed scheme is verified through two numerical simulations. In addition, a practical inverted pendulum experiment is carried out to demonstrate the performance of the proposed scheme.

Optimal Output-Feedback Control Over Markov Wireless Communication Channels

Optimal Output-Feedback Control Over Markov Wireless Communication Channels

Inverse Optimal Adaptive Fuzzy Output Feedback Control for Nonlinear Systems With Output Quantization

Inverse Optimal Adaptive Fuzzy Output Feedback Control for Nonlinear Systems With Output Quantization

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.

Online Policy Learning-Based Output-Feedback Optimal Control of Continuous-Time Systems

Online Policy Learning-Based Output-Feedback Optimal Control of Continuous-Time Systems

Spectral-based optimal output-feedback boundary control of a cracking catalytic reactor PDE model

This research paper focuses on the design of a boundary optimal controller with output feedback for a tubular catalytic cracking reactor. The process is represented by a set of non-linear parabolic partial differential equations (PDEs). The approach involves utilising the linearised infinite-dimensional version of the model, taking advantage of the system generator being a Riesz spectral operator. A stabilising compensator is designed by leveraging the eigenvalues and eigenvectors of the system generator. This paper also includes numerical simulations to demonstrate the performance of the developed algorithm.

Inverse optimally adaptive neural output‐feedback control of stochastic nonlinear systems

SummaryIn this article, for a class of stochastic nonlinear systems with non‐strict feedback, a neural adaptive inverse optimal output feedback control design scheme is presented. First, according to the existing inverse optimal criterion, an auxiliary system is established. On this basis, a novel observer is built to evaluate the unpredictable states. Second, in the control process, neural networks (NNs) are applied to estimate the unknown functions. Based on NNs and the backstepping technology, an adaptive neural inverse optimal output feedback controller is established. It is indicated that the proposed scheme could ensure the semi‐globally uniformly ultimately bounded of the closed‐loop system and also achieve the objective of inverse optimality. Eventually, an example is applied to testify the feasibility of this scheme.

Direct integral pseudospectral and integral spectral methods for solving a class of infinite horizon optimal output feedback control problems using rational and exponential Gegenbauer polynomials

This study is concerned with the numerical solution of a class of infinite-horizon linear regulation problems with state equality constraints and output feedback control. We propose two numerical methods to convert the optimal control problem into nonlinear programming problems (NLPs) using collocations in a semi-infinite domain based on rational Gegenbauer (RG) and exponential Gegenbauer (EG) basis functions. We introduce new properties of these basis functions and derive their quadratures and associated truncation errors. A rigorous stability analysis of the RG and EG interpolations is also presented. The effects of various parameters on the accuracy and efficiency of the proposed methods are investigated. The performance of the developed integral spectral method is demonstrated using two benchmark test problems related to a simple model of a divert control system and the lateral dynamics of an F-16 aircraft. Comparisons of the results of the current study with available numerical solutions show that the developed numerical scheme is efficient and exhibits faster convergence rates and higher accuracy.

Novel extended Kalman filter + H∞$$ {\mathbf{H}}_{\infty } $$ optimal output feedback control configuration for small satellites with high pointing stability requirements

SummaryOne of the most challenging subsystems for the CubeSats is the attitude determination and control system (ADCS) because it involves hardware and software integration, advanced strategies and algorithms to determine and control the attitude that impacts on space maneuvering and well working of a large set of payload (e.g., the optical payload). Although ADCS is largely studied, it still requires further investigations and analysis in order to achieve high‐performance and a reduced efforts. This paper presents an effective and reliable solution for the ADCS of CubeSats involved in Earth observation missions. The solution is based on an innovative framework that leverages the strengths of two distinct methodologies—H‐infinity optimal output feedback control and the extended Kalman filter (EKF)‐to significantly enhance the pointing stability of satellite systems. While H‐infinity optimal output feedback control is traditionally associated with partial state knowledge, we intentionally extend its application to scenarios with complete state information. The study includes a comparative performance analysis involving three algorithm configurations: the classic combination of EKF and model predictive control (MPC), the utilization of H‐infinity optimal output feedback control without EKF, and our proposed integrated approach. Performance evaluations are based on extrinsic indicators, demonstrating the advantages of our method in terms of pointing stability and overall control system performance. This research underscore the significance of combining innovative thinking with well‐established methodologies, unlocking new possibilities for stability enhancement in a range of engineering applications.

Event‐triggered‐based integral reinforcement learning output feedback optimal control for partially unknown constrained‐input nonlinear systems

AbstractIn this paper, an adaptive output feedback event‐triggered optimal control algorithm is proposed for partially unknown constrained‐input continuous‐time nonlinear systems. First, a neural network observer is constructed to estimate unmeasurable state. Next, an event‐triggered condition is established, and only when the event‐triggered condition is violated will the event be triggered and the state be sampled. Then, an event‐triggered‐based synchronous integral reinforcement learning (ET‐SIRL) control algorithm with critic‐actor neural networks (NNs) architecture is proposed to solve the event‐triggered Hamilton–Jacobi–Bellman equation under the established event‐triggered condition. The critic and actor NNs are used to approximate cost function and optimal event‐triggered optimal control law, respectively. Meanwhile, the event‐triggered‐based closed‐loop system state and all the neural network weight estimation errors are uniformly ultimately bounded proved by Lyapunov stability theory, and there is no Zeno behavior. Finally, two numerical examples are presented to show the effectiveness of the proposed ET‐SIRL control algorithm.

Data-driven Optimal Output Feedback Control of Linear Systems from Input-Output Data

We design optimal output feedback controllers for linear systems where only outputs are available for measurement and control actuation. The goal is to render the closed-loop system stable while minimizing a quadratic cost function balancing performance and control effort. We first provide a model-based solution to this problem, where an optimal dynamic output feedback controller is computed by solving a semidefinite program. Then, we shift our attention to data-based solutions, bypassing the system identification step. We derive semidefinite programs that are explicitly stated in terms of input-output data. The effectiveness of the method is illustrated via a power system case study.

Adaptive constrained output feedback optimal consensus tracking for uncertain nonlinear multi-agent systems and its application

This paper addresses the output feedback optimal consensus tracking control problem for a class of nonlinear multi-agent systems (MASs) with unknown internal dynamics and input saturation. Firstly, an adaptive observer is designed to reconstruct the unmeasurable states using neural networks (NNs) based on the augmented dynamic model. Subsequently, a novel distributed feedforward controller is proposed using the backstepping method, where an auxiliary state is introduced to deal with the input saturation problem. Unlike the traditional recursive design technique, the procedures we take can reduce the consensus tracking control problem into the optimal regulation issue, which is then solved by the adaptive dynamic programming (ADP) method. Therefore, the designed consensus control protocol consists of a distributed feedforward controller and a distributed optimal feedback controller. Moreover, the stability of the MASs is guaranteed by the Lyapunov theory. Numerical simulation on multi-missile guidance problem demonstrates the effectiveness of the proposed control scheme.

Adaptive inverse optimal backstepping control strategy for longitudinal vibration of high-speed elevator system based on fuzzy observer

To effectively suppress the longitudinal vibration of the car under the conditions of high-speed operation and emergency braking, and improve the ride comfort of the car system, this paper proposes an adaptive fuzzy inverse optimal output feedback control strategy. Firstly, the dynamic model of the high-speed elevator system is established and the nonlinear dynamic model is approximated by the fuzzy logic system, and the auxiliary system model is established. Fuzzy state observer is designed to estimate the unmeasurable state. Furthermore, an adaptive inverse optimal output feedback controller based on fuzzy observer is designed by using adaptive backstepping technology and inverse optimal control principle. The stability analysis shows that the proposed adaptive fuzzy inverse optimal output feedback control strategy not only ensures the stability of the car attitude of high-speed elevator but also realizes the inverse optimization of the target cost function. Finally, the acceleration time–frequency response analysis of the two typical stages of high-speed elevator uniform running and emergency braking is carried out, and the numerical results are compared with the linear quadratic controller optimized by stepping quantum genetic algorithm (GA-LQR) and controller based on the state-dependent Ricatti equation (SDRE). The analysis verifies the effectiveness of the controller.

Robust output feedback-based neuro-fuzzy controller for seismically excited tall buildings with ATMD accounting for variations in the type of supporting soil

Recently, developing the control algorithms for tuning the voltage/force command of smart control devices for application in seismic-excited buildings and bridges has been well addressed considering soil-structure interaction (SSI) effects. A controller is often designed for a soil pre-set condition. Moreover, considering an exact model of soil in the controller design process is a tedious task due to high computational costs. Consequently, the seismic performance and robustness of the adopted controller are questionable against the variations in soil conditions. The motivation of the present paper is to propose a robust controller for seismic-excited tall buildings against the variations of soil conditions than the pre-set condition. Taking advantage of the optimal output feedback controller (OOFC), a simple and practical controller based on OOFC is proposed for application in tall buildings equipped with an active tuned mass damper (ATMD) accounting for SSI effects. Considering different soil types, a dataset is generated from the proposed OOFC and an adaptive neuro-fuzzy inference system (ANFIS) is trained to fit them in a robust dataset. Then, a robust output feedback-based ANFIS controller, namely ROFBANFISC, is proposed. The robustness of the OOFC and ROFBANFISC are validated for different soil types. Considering six performance criteria, the numerical studies are conducted on a 40-story structure subjected to five real ground motions. The simulation results carried out for different soil conditions show that the proposed ROFBANFISC is more robust than the OOFC. Also, it can maintain its appropriate seismic performance in different soil types.

Observer-Based Finite-Time Inverse Optimal Output Regulation for Uncertain Nonlinear Systems

This paper deals with the finite-time inverse optimal output regulation problem for a class of uncertain nonlinear systems that are subjected to an exosystem. The nonlinear systems not only contain external disturbances in the exosystem but also take the unknown nonlinear functions and unmeasured states into account. The output regulation problem is first converted into a stabilization problem through the internal model. Then, fuzzy logic systems (FLSs) are employed to approximate the unknown nonlinear functions. An auxiliary system is constructed and, based on the auxiliary system, a fuzzy state observer is designed to estimate the unmeasured states. Furthermore, a novel adaptive fuzzy finite-time inverse optimal output feedback controller and adaptive law are designed by combining backstepping technology, adaptive control technology, finite-time stability theory, and the inverse optimal control method. The control algorithm ensures that all the signals of the closed-loop system are semiglobally practical finite-time stable (SGPFS), so the newly well-defined cost function that is connected with the auxiliary system can be minimized. Finally, the validity of the approach is confirmed by virtue of the simulation results.

Model‐free distributed optimal control for continuous‐time linear systems

This paper studies the distributed optimal consensus problem for a group of continuous-time linear systems in the scenario that the dynamics of linear systems are completely unknown. Both an optimal state feedback control law and an optimal output feedback control law are constructed by solving the Algebraic Riccati Equation (ARE) that contains no global information, which guarantees the consensus of linear systems and the global optimality. Adaptive Dynamic Programming (ADP) method is presented to solve the ARE, thus the control algorithms are not relying on the dynamics of linear systems any more. Finally, numerical simulation results are presented to demonstrate the efficiency of proposed approach.

Scheduling and control of high throughput screening systems with uncertainties and disturbances

ABSTRACT Based on the existing research work on the modeling and control of cyclically operated high-throughput screening systems, this paper presents the scheduling and control of high-throughput screening systems with uncertainties and disturbances. Different definitions of disturbance decoupling problems are considered in order to achieve the optimal scheduling of high-throughput screening systems. Online scheduling was achieved by computing optimal prefilters and output feedback controllers, which can be computed using residuation theory. The control strategies achieved by the controllers are optimal in the sense of the just-in-time criterion commonly used in industrial schedule practice.

Neural Network Adaptive Output-Feedback Optimal Control for Active Suspension Systems

The adaptive neural network (NN) output-feedback optimal control issue has been investigated for a quarter-car active electric suspension systems, where the suspension stiffness is unknown and partial state variables are unavailable for measurement. NNs are utilized to identify unknown nonlinearities, and an NN state observer is devised to estimate the unmeasurable states. For each backstepping step, via reinforcement learning (RL), a critic–actor architecture is designed to get the approximation solution of Hamilton–Jacobi–Bellman (HJB) equations and actual and virtual optimization controllers are designed, in which the input saturation constraint and road interference are considered. It is analytically proved that all controlled system signals remain bounded, while the power of the control input signal, as well as the amplitude of the vertical displacement, has been minimized. A comparative simulation is eventually given to elaborate the feasibility of the developed control algorithm.

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.

Optimal output feedback control of a class of linear systems with quasi-colored control-dependent multiplicative noise

This paper addresses the mean-square optimal control problem for a class of discrete-time linear systems with a quasi-colored control-dependent multiplicative noise via output feedback. The noise under study is novel and shown to have advantage on modeling a class of network phenomena such as random transmission delays. The optimal output feedback controller is designed using an optimal mean-square state feedback gain and two observer gains, which are determined by the mean-square stabilizing solution to a modified algebraic Riccati equation (MARE), provided that the plant is minimum-phase and left-invertible. A necessary and sufficient condition for the existence of the stabilizing solution to the MARE is explicitly presented. It shows that the separation principle holds in a certain sense for the optimal control design of the work. The result is also applied to the optimal control problems in networked systems with random transmission delays and analog erasure channels, respectively.