Linear Quadratic Control Research Articles

Extended linear quadratic regulator control and its application in trajectory following control of autonomous vehicles

Extended linear quadratic regulator control and its application in trajectory following control of autonomous vehicles

Input-Output Feedback Linearization Associates with Linear Quadratic Regulator for Stabilization Control of Furuta Pendulum System

Manuscript provides a key technology, namely Input-Output Feedback Linearization Associates with Linear Quadratic Regulator (for short, IOFLALQR). The objective of this research is to study the possibility of integrating two control strategies, which includes input-output feedback linearization technique (for short, IOFL) and linear quadratic regulator controller (for short, LQR), for stabilization control of Furuta pendulum system. Furuta pendulum system belongs to the group of under-actuated robot systems. In this work, structure of IOFLALQR, control implementation, comparison of IOFLALQR and conventional LQR are adequately studied and discussed. Simulation is completed in MATLAB/Simulink environment and experiment is done on real-time experimental setup. Numerical simulation and experimental results show that the IOFLALQR are implemented on Furuta pendulum successfully. Besides, results have been drawn for demonstrating IOFLALQR better than another classical method.

Extended linear quadratic regulator control and its application in trajectory following control of autonomous vehicles

Extended linear quadratic regulator control and its application in trajectory following control of autonomous vehicles

Challenges for Control Engineering Curricula: Motivating 800 Students via Current Trends in Industry and Research

This paper presents new teaching curricula developments for Control engineering based on current challenges in industry and research. A major change has been proposed for the core module on Control Theory taught at CentraleSupélec for 800 students. The new syllabus is based on the state-space representation of multivariable systems, thus including state-feedback control based on pole placement, Linear Quadratic (LQ) control, together with observers (i.e. Luenberger observer, Kalman filter). Performance and robustness analysis tools are proposed both for monovariable and multivariable systems. A balance between theoretical and practical training, together with the current issues and open problems in Control are the main key points of this new Control course. Feedback and lessons learned are provided in this paper.

Rotary Inverted Pendulum Control using Robust Generalized Dynamic Inversion with Adaptive Neural Estimation

A novel robust generalized dynamic inversion control system with adaptive neural estimation (RGDI-ANE) is designed for trajectory tracking of the under actuated rotary inverted pendulum (RIP). The RGDI control design begins by prescribing a virtual differential constraint dynamics (VCD) that imitates the desired tracking control objectives. The baseline RGDI control law is derived by inverting the VCD using dynamically scaled Generalized Inversion, and then augmenting a sliding mode control (SMC) element to provide robustness against performance deterioration due to dynamic scaling of the Moore-Penrose generalized inverse. Furthermore, an adaptive estimator that is based on radial basis function neural networks (RBF-NN) is adopted to limit the dependency of RGDI control on the RIP mathematical model. The weighting matrices of the RBF-NN are updated using a Lyapunov control function. The closed loop RGDI-ANE control system is shown to guarantee semi-global asymptotic stability. Computer simulations along with experimental tests have been conducted on Quanser's RIP system to validate the performance of RGDI-ANE control, and the results are compared with the results obtained by using the SMC and the linear quadratic control methodologies.

Closed-form and robust expressions for data-driven LQ control

This article provides an overview of certain direct data-driven control results, where control sequences are computed from (noisy) data collected during offline control experiments without an explicit identification of the system dynamics. For the case of noiseless datasets, we derive several closed-form data-driven expressions that solve a variety of optimal control problems for linear systems with quadratic cost functions of the state and input (including the linear quadratic regulator problem, the minimum energy control problem, and the linear quadratic control problem with terminal constraints), discuss their advantages and drawbacks with respect to alternative data-driven and model-based approaches, and showcase their effectiveness through a number of numerical studies. Interestingly, these results provide an alternative and explicit way of solving classic control problems that, for instance, does not require the solution of an implicit and recursive Riccati equation as in the model-based setting. For the case of noisy datasets, we show how the closed-form expressions derived in the noiseless setting can be modified to compensate for the bias induced by noise, and perform a sensitivity analysis to reveal favorable asymptotic robustness properties of the derived data-driven controls. We conclude the paper with some considerations and a discussion of outstanding questions and directions of future investigation.

Optimal exploration strategies for finite horizon regret minimization in some adaptive control problems

In this work, we consider the problem of regret minimization in adaptive minimum variance and linear quadratic control problems. Regret minimization has been extensively studied in the literature for both types of adaptive control problems. Most of these works give results of the optimal rate of the regret in the asymptotic regime. In the minimum variance case, the optimal asymptotic rate for the regret is log(T) which can be reached without any additional external excitation. On the contrary, for most adaptive linear quadratic problems, it is necessary to add an external excitation in order to get the optimal asymptotic rate of √T. In this paper, we will actually show from a theoretical study, as well as, in simulations that when the control horizon is pre-specified a lower regret can be obtained with either no external excitation or a new exploration type termed immediate.

Globally Convergent Policy Gradient Methods for Linear Quadratic Control of Partially Observed Systems

While the optimization landscape of policy gradient methods has been recently investigated for partially observed linear systems in terms of both static output feedback and dynamical controllers, they only provide convergence guarantees to stationary points. In this paper, we propose a new policy parameterization for partially observed linear systems, using a past input-output trajectory of finite length as feedback. We show that the solution set to the parameterized optimization problem is a matrix space, which is invariant to similarity transformation. By proving a gradient dominance property, we show the global convergence of policy gradient methods. Moreover, we observe that the gradient is orthogonal to the solution set, revealing an explicit relation between the resulting solution and the initial policy. Finally, we perform simulations to validate our theoretical results.

Risk-Aware Linear Quadratic Control Using Conditional Value-at-Risk

Stochastic linear quadratic control problems are considered from the viewpoint of risks. In particular, a worst-case conditional value-at-risk (CVaR) of quadratic objective function is minimized subject to additive disturbances whose first two moments of the distribution are known. The study focuses on three problems of finding the optimal feedback gain that minimizes the quadratic cost of: stationary distribution, one-step, and infinite time horizon. For the stationary distribution problem, it is proved that the optimal control gain that minimizes the worst-case CVaR of the quadratic cost is equivalent to that of the standard (stochastic) linear quadratic regulator. For the one-step problem, an approach to an optimal solution as well as analytical suboptimal solutions are presented. For the infinite time horizon problem, two suboptimal solutions that bound the optimal solution and an approach to an optimal solution for a special case are discussed. The presented theorems are illustrated with numerical examples.

LiDAR-Based Obstacle Detection and Avoidance for Navigation and Control of an Unmanned Ground Robot Using Model Predictive Control

Unmanned Ground Vehicles (UGVs) have, as of late, been utilized in a wide assortment of utilizations because of their flexibility, diminished expense, and quick response, among other benefits. Search and Rescue (SAR) is quite possibly the most conspicuous zones for the work of UGVs instead of a monitored mission, mainly due to its impediments on the expenses, human resources, and view of the human administrators. An ongoing way of arranging to utilize numerous helpful UGVs for the SAR mission is proposed in this study. This study aims to introduce the initial moves towards a Model Predictive Control (MPC) based peril evasion calculation for UGVs representing the vehicle elements through high constancy models and uses just surrounding data about the environment as given by the available onboard sensors. In particular, the paper presents the MPC definition for peril evasion utilizing a Light Detection and Ranging (LiDAR) sensor and applies it to a contextual of the effect of model constancy on the calculation's presentation, where execution is estimated principally when to arrive at the objective point. The Robot Operating System (ROS) is used to drive the sensors and visualize the data in RVIZ. This study presents MPC development for navigating Husky A200 by adjusting the longitudinal, lateral, and yaw motion command behaviors. The proposed algorithm for Husky A200 is tested indoors and compared the results with the simulation results plotted using MATLAB and GAZEBO. A novel simulator package is developed for the Husky using RVIZ and GAZEBO. The efficiency of the proposed MPC design is tested through simulation and compared with real world experiments, the real-time longitudinal movement follows the simulation results closely. For MPC's short-term optimization, an optimized control signal from a linear framework is utilized for a linear quadratic controller. According to the Husky position and orientation, applying a transformation to convert the map coordinate system to the Husky coordinate system. Transforming the map coordinate system helped in computing the errors because the initial vector considers position and orientation as zero.

Decentralized Robust Control of a Coupled Wind Turbine and Diesel Engine Generator System

This paper presents the design of a robust decentralized controller for the frequency and active power control of a single stand-alone (off-grid) mechanically-coupled generator system including wind turbine and diesel engine generator subsystems. Two robust decentralized controllers are designed and optimized for the two subsystems by using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mu$</tex-math></inline-formula> -synthesis technique. The decentralized controllers address the mechanical coupling between the two subsystems without communicating with each other. In addition, both controllers are designed in such a way that they are robust against the concurrent variations of all the system parameters, which in turn improves the frequency and power control performances significantly. Simulation results indicate that the proposed decentralized controllers have a better performance as compared to the benchmark decentralized model predictive controllers and decentralized linear-quadratic Gaussian controllers. It is also demonstrated that the proposed control scheme is able to damp out mild and large disturbances originating from the load and wind power changes, and has an acceptable robust performance against the concurrent variations in all parameters of the system.

Learning to Control Under Communication Constraints

How to effectively communicate over wireless networks characterized by link failures is central to understanding the fundamental limits in the performance of a networked control system. In this paper, we study the online remote control of linear-quadratic Gaussian systems over unreliable wireless channels (with random packet drops), where the controller is a priori oblivious to the cost parameters. We first reformulate the problem using a semi-definite program and consequently compute a stabilizing policy from its solution. We then derive a O(T) regret bound (against a best offline policy in hindsight) for a projected online gradient algorithm, where T is the length of the horizon of interest. In the process, we introduce finite-time notions of the classical mean-square stability, which may be of independent interest. Finally, we provide a numerical example to validate the theoretical results, demonstrating the limitations induced by lossy communication on the control performance.

Optimal control on investment and reinsurance strategies with delay and common shock dependence in a jump-diffusion financial market

&lt;p style='text-indent:20px;'&gt;In this paper, we consider an optimal mean-variance investment and reinsurance problem with delay and Common Shock Dependence. An insurer can control the claim risk by purchasing proportional reinsurance. He/she invests his/her wealth on a risk-free asset and a risky asset, which follows the jump-diffusion process. By introducing a capital flow related to the historical performance of the insurer, the wealth process described by a stochastic differential equation with delay is obtained. By stochastic linear-quadratic control theory and stochastic control theory with delay, we achieve the explicit expression of the optimal strategy and value function in the framework of the viscosity solution. Furthermore, an efficient strategy and its efficient frontier are derived by Lagrange dual method. Finally, we analyze the influence of the parameters of our model on the efficient frontier by a numerical example.&lt;/p&gt;

A Jump Ornstein–Uhlenbeck Bridge Based on Energy-Optimal Control and Its Self-Exciting Extension

We study a version of the Ornstein-Uhlenbeck bridge driven by a spectrally-positive subordinator. Our formulation is based on a Linear-Quadratic control subject to a singular terminal condition. The Ornstein-Uhlenbeck bridge, we develop, is written as a limit of the obtained optimally controlled processes, and is shown to admit an explicit expression. Its extension with self-excitement is also considered. The terminal condition is confirmed to be satisfied by the obtained process both analytically and numerically. The methods are also applied to a streamflow regulation problem using a real-life dataset.

Stochastic linear-quadratic control with a jump and regime switching on a random horizon

In this paper, we study a stochastic linear-quadratic control problem with random coefficients and regime switching on a random horizon $ [0,T\wedge\tau] $, where $ \tau $ is a given random jump time for the underlying state process and $ T $ a constant. We obtain the explicit optimal feedback control and explicit optimal value of the problem by solving a system of stochastic Riccati equations (SREs) with jumps on the random horizon $ [0,T\wedge\tau] $. By the decomposition approach stemming from filtration enlargement theory, we express the solution to the system of SREs with jumps in terms of another system of SREs involving only Brownian filtration on the deterministic horizon $ [0,T] $. Solving the latter system is the key theoretical contribution of this paper and we accomplish this under three different conditions, one of which seems to be new in the literature. The above results are then applied to study a mean-variance hedging problem with random parameters that depend on both Brownian motion and Markov chain. The optimal portfolio and optimal value are presented in closed forms with the aid of a system of linear backward stochastic differential equations with jumps and unbounded coefficients in addition to the SREs with jumps.

Development of modified LQG controller for mitigation of seismic vibrations using swarm intelligence

Development of modified LQG controller for mitigation of seismic vibrations using swarm intelligence

Development of modified LQG controller for mitigation of seismic vibrations using swarm intelligence

Development of modified LQG controller for mitigation of seismic vibrations using swarm intelligence

Robust LQG Controller Design by LMI Approach of a Doubly-Fed Induction Generator for Aero-Generator

Robust LQG Controller Design by LMI Approach of a Doubly-Fed Induction Generator for Aero-Generator

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.

Active Vibration Control of Timoshenko Sigmoid Functionally Graded Porous Composite Beam with Distributed Piezoelectric Sensor/Actuator in a Thermal Environment

This work presents the study of the dynamics and active control of a cantilever sigmoid FGM beam with porosities in a thermal environment. During this study, we considered the Timoshenko beam’s theory combined with the finite element method (FEM). This work also presents a comparative study with an experimental study for the vibration of a functionally graded piezoelectric beam (FGPM) to validate the numerical model. Linear quadratic Gaussian (LQG) optimal control with a Kalman filter was used for the vibration control using piezoelectric sensors and actuators as symmetrical layers to eliminate membrane effects. The controlled and uncontrolled responses are presented, considering the influence of thermal effect, the porosity of the FGM material, and the location of the sensor pair on the smart structure. The results indicate that the porosity effect of the FGM material, as well as the application of the thermal effect, involves an increase in vibration frequencies, in contrast to the increase in the power law index. The study also shows that the thermal and porosity effects result in an increase in vibration amplitudes.