LQ Control Research Articles

Stochastic LQ Control with Extra Measurability Restriction

Stochastic LQ Control with Extra Measurability Restriction

LQG - Based Robust Tracking for the Magnetic Levitation Laboratory Plant

The paper deals with the design of robust LQG-based control for a maglev laboratory plant to ensure tracking of selected types of the levitating ball position reference and rejection of measurable input disturbance. The reference position tracking and the disturbance rejection are provided by the command generator tracker (CGT) – the LQ control designed for the modified state-space model augmented by the reference and disturbance state variable models. Robustness to model uncertainty guarantees that the linear CGT is applicable over the full range of the levitating ball distances from the upper coil and is achieved through adjusting the process- and measurement noise covariances in the Kalman filter design. The proposed CGT – LQG design for the real maglev system proceeds in several steps using simulations and experiments providing the insight into specific control problems.

A Control-Recoverable Added-Noise-Based Privacy Scheme for LQ Control in Networked Control Systems

A Control-Recoverable Added-Noise-Based Privacy Scheme for LQ Control in Networked Control Systems

Non-homogeneous stochastic LQ control with regime switching and random coefficients

Non-homogeneous stochastic LQ control with regime switching and random coefficients

Solving Infinite-Dimensional Harmonic Lyapunov and Riccati Equations

In this paper, we address the problem of solving infinite-dimensional harmonic algebraic Lyapunov and Riccati equations up to an arbitrary small error. This question is of major practical importance for analysis and stabilization of periodic systems including tracking of periodic trajectories. We first give a closed form of a Floquet factorization in the general setting of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L^{2}$</tex-math></inline-formula> matrix functions and study the spectral properties of infinite-dimensional harmonic matrices and their truncated version. This spectral study allows us to propose a generic and numerically efficient algorithm to solve infinite-dimensional harmonic algebraic Lyapunov equations up to an arbitrary small error. We combine this algorithm with the Kleinman algorithm to solve infinite-dimensional harmonic Riccati equations and we apply the proposed results to the design of a harmonic LQ control with periodic trajectory tracking.

Equilibrium Control of Robot Arm Tip Mounted on a Transfer Coaxial Two-Wheel Robot

Japan has continued to experience population decline which adversely affect working-age group (15-64 years). As a remedy to this social issue, advancements in robotics and human-machine cooperation is proposed to make up for the declining labor force. To this end, design of robots which can work in constrained (indoor) workspace is desirable. A coaxial two-wheeled robot with an appended robot arm aimed at transporting objects is proposed in this paper. The robot is designed with center of gravity below the axle to make it statically stable at rest. It is combined with a robot arm with two links, two degrees of freedom. The goal is to maintain equilibrium of the arm tip during motion with the robot-arm is inclined at 0-, 3-, and 120-degree. In this study, simulations to combine a stable coaxial two-wheel robot with the robot arm is performed to confirm the effectiveness of the designed LQ, and LQI controller. From the results, all the controllers are able to maintain the robot-arm tip at 0-degrees. For 120-degrees, LQI performs better than LQ controller in stabilizing the rotation speed of the wheels by 1.7 seconds. In the future, the proposed controller model will be incorporated in the actual robot to confirm the performance for object transportation.

Maximum power tracking for wind energy conversion systems via a high-order optimal disturbance observer-based LQR without a wind speed sensor

A high-order optimal disturbance observer (HOODO) is introduced to precisely estimate the aerodynamic torque and the variable wind speed; and consequently calculate the optimal speed of the generator without measuring the wind speed. As the immeasurable wind speed is varying fast, the aerodynamic torque, which is considered as a disturbance, is also changed fast, then the conventional assumption that the disturbance is slowly-varying (i.e., its first-time derivative is zero), is not applicable. The proposed HOODO design considers the fast and stochastic characteristics of the wind speed by relaxing aforementioned conventional assumption. Moreover, via the linear optimal control theory, the parameters of the HOODO are tuned systematically by proper selection of the elements of the diagonal weighting matrices. In this study, a compromise between the observer’s convergence rate and the ability to Gaussian noise suppression is also considered. This helps to solve the difficulties of many existing observers regarding the gain selection algorithms. Also in the article, for the first time, a control scheme is considered in combination with the proposed HOODO and the LQ controller. To maximize a power captured from the wind, a linear-quadratic regulator (LQR) is utilized to maintain the angular speed of the generator at the optimal speed reference. A stability analysis of the designed control scheme is also discussed. Comparative results of the HOODO under different orders as well as other observers are given to prove the effectiveness of the introduced estimation method. The obtained simulation results reveal that the HOODO has a superior estimation of disturbance. All the simulations are carried out in the MATLAB/Simulink software.

A distributed stochastic approximation algorithm for stochastic LQ control with unknown uncertainty

This paper studies a discrete-time stochastic control problem with linear quadratic criteria over an infinite-time horizon. We focus on control systems whose system matrices are associated with random parameters involving unknown statistical properties. We design a distributed stochastic approximation algorithm to tackle the Riccati equation and derive the optimal controller stabilizing the system. The convergence analysis is provided.

Differentially Private LQ Control

As multi-agent systems proliferate and more user data, new approaches are needed to protect sensitive data while still enabling system operation. To address this need, this article presents a private multiagent LQ control framework. Agents’ state trajectories can be sensitive, and we therefore protect them using differential privacy. We quantify the impact of privacy along three dimensions: the amount of information shared under privacy, the control-theoretic cost of privacy, and the tradeoffs between privacy and performance. These analyses are done in conventional control-theoretic terms, which we use to develop guidelines for calibrating privacy as a function of system parameters. Numerical results indicate that system performance remains within desirable ranges, even under strict privacy requirements.

Innerization and Singular LQ Control Problem for Linear Discrete-Time Systems

In this paper, we discuss the LQ problem for discrete-time linear systems with singular weight. The interactor with all-pass property is used in order to make a given strictly proper system be proper. In our approach, the type of Riccati equation to be solved is different from the result for a square transfer function matrix case, where the input weight equals to zero. The relation between our approach and the singular weight case is discussed. Unlike the square case, the explicit solution to the problem cannot be obtained and a recursive method to solve the Riccati equation is shown. An application to the finite settling-time control is also discussed.

On LQ Control Problem for Linear Discrete-Time Systems with Singular Weightings

On LQ Control Problem for Linear Discrete-Time Systems with Singular Weightings

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.

예선 연계 바지선 운동제어전략과 강인제어계 설계에 관한 연구

In this study, a motion control system design of barge-type surface ship is considered. The barge ships are used in numerous applications for a variety of purposes. Especially, in the ship building industries, heavy and huge equipment and assembly parts are carried by these ships. However, it is difficult to achieve desirable motion because the propulsion systems are not installed on it. Therefore, the assistance of several tugboats is necessary to guarantee safe and quick operations. So far, automatic control techniques have not been incorporated with these systems. Hence, in this study, a useful control strategy is suggested to provide a solution for this issue in order to obtain the desirable motion control performance. Accordingly, a motion control system configuration is presented, and a robust control is derived. The usefulness of proposed control system is verified by comparison study with LQ control. The various simulations are carried out to provide a better look at the performance of the barge ships while being controlled.

Explicit Solution to the FBSDEs With Asymmetric Information and Application

This brief is focused on the linear forward-backward stochastic differential equations with asymmetric information and multiplicative noises. The main contribution is that we give the explicit solution in terms of Riccati equations. The key lies in establishing the relationship among the forward process and the backward processes. As an application, we solved a kind of stochastic LQ control problems under the asymmetric information by using the derived explicit solution.

Pareto Optimal Strategy under H∞ Constraint for Discrete-Time Stochastic Systems

This paper investigates the Pareto optimal strategy of discrete-time stochastic systems under H∞ constraint, in which the weighting matrices of the weighted sum cost function can be indefinite. Combining the H∞ control theory with the indefinite LQ control theory, the generalized difference Riccati equations (GDREs) are obtained. By means of the solution of the GDREs, the Pareto optimal strategy with H∞ constraint is derived, and the necessary and sufficient conditions for the existence of the strategy are presented. Then the Pareto optimal solution under the worst-case disturbance is solved. Finally, the efficiency of the obtained results is illustrated by a numerical example.

The turnpike property and the longtime behavior of the Hamilton–Jacobi–Bellman equation for finite-dimensional LQ control problems

We analyze the consequences that the so-called turnpike property has on the longtime behavior of the value function corresponding to a finite-dimensional linear-quadratic optimal control problem with general terminal cost and constrained controls. We prove that, when the time horizon T tends to infinity, the value function asymptotically behaves as $$W(x) + c\, T + \lambda $$ , and we provide a control interpretation of each of these three terms, making clear the link with the turnpike property. As a by-product, we obtain the longtime behavior of the solution to the associated Hamilton–Jacobi–Bellman equation in a case where the Hamiltonian is not coercive in the momentum variable. As a result of independent interest, we showed that linear-quadratic optimal control problems with constrained control enjoy a turnpike property, also particularly when the steady optimum may saturate the control constraints.

LQG Control Performance With Low-Bitrate Periodic Coding

Several specific low-bitrate coding strategies are examined through their effect on LQ control performance. By limiting the subject to these methods, we are able to identify principles underlying coding for control; a subject of significant recent interest but few tangible, i.e. implementable, results. In particular, we consider coding the quantized output signal deploying period-two codes of differing delay-versus-accuracy tradeoff. The quantification of coding performance is via the LQ control cost over a long but finite horizon up to a specified average \textit{escape time}. Infinite-horizon stabilization is replaced by a mean-time-before-failure property, which is a new viewpoint but allows contact with uncoded controllers. The feedback control system comprises the coder-decoder in the path between the output and the state estimator, which is followed by linear state-variable feedback, as is optimal in the memoryless case. The static quantizer is treated as the functional composition of an infinitely-long linear staircase function and a saturation. This permits the analysis to subdivide into estimator computations, seemingly independent of the control performance criterion, and

Constrained stochastic LQ control with regime switching and application to portfolio selection

This paper is concerned with a stochastic linear-quadratic optimal control problem with regime switching, random coefficients and cone control constraint. The randomness of the coefficients comes from two aspects: the Brownian motion and the Markov chain. Using Itô’s lemma for Markov chain, we obtain the optimal state feedback control and optimal cost value explicitly via two new systems of extended stochastic Riccati equations (ESREs). We prove the existence and uniqueness of the two ESREs using tools including multidimensional comparison theorem, truncation function technique, log transformation and the John–Nirenberg inequality. These results are then applied to study mean-variance portfolio selection problems with and without short-selling prohibition with random parameters depending on both the Brownian motion and the Markov chain. Finally, the efficient portfolios and efficient frontiers are presented in closed forms.

Stochastic LQ Control and Associated Riccati Equation of PDEs Driven by State- and Control-Dependent White Noise

Stochastic LQ Control and Associated Riccati Equation of PDEs Driven by State- and Control-Dependent White Noise

Adaptive Path-Following Control for Autonomous Semi-Trailer Docking

Maneuvering a truck-trailer system while docking is extremely challenging. This article aims to alleviate this problem by presenting an enhanced path-following control framework for autonomous semi-trailer docking. In the proposed system, adaptive controllers that utilize gain scheduling are introduced for forward and reverse path-following tasks in docking maneuvers to increase the robustness and path-following performance. The system includes an improved pure pursuit controller with adaptive look-ahead distance for forward path following; a cascade controller of reverse pure pursuit and a gain-scheduled LQ control for reverse path-following. In the evaluation of the path-following performance of forward and reverse controllers, the closed-loop system of path-following controllers with the truck-trailer kinematic model is simulated in MATLAB/Simulink for various test cases, and the results are compared with those of other studies. Furthermore, different docking scenarios are generated via the cascade path planning algorithm for autonomous semitrailer docking. These are tested with a high degree semi-trailer model within the IPG TruckMaker simulation environment, and with a full truck-trailer vehicle in the test field. The results of both simulations and physical testing clearly demonstrate improvements in terms of the control problem formulation, i.e., the stabilized path-following is obtained with acceptable path-following errors.