Linear Quadratic Control Research Articles

Special issue on “Optimal design and operation of energy systems”

Special issue on “Optimal design and operation of energy systems”

Performance-based active controller design for nonlinear structures using modified black hole optimization

This paper presents a novel approach that facilitates the design of active controllers to mitigate seismically induced damage in structural systems. The proposed method is based on stochastic Modified Black Hole optimization algorithm. Two traditional controllers, namely Proportional-Integral-Derivative (PID) and Linear–Quadratic Gaussian (LQG) controllers were designed, and their performance was demonstrated on a benchmark 20-story steel-framed building. Evaluation criteria were defined to satisfy constraints on various response quantities, including drift, base shear, ductility, residual story drift, and control force. The constraint limits were defined in view of performance-based design requirements for the benchmark structure. The performance of the controllers was contrasted with that of traditional LQG, and significant reductions of all response quantities were achieved for design-level earthquakes.

Optimal stealthy false data injection attacks for networked linear quadratic Gaussian control systems with two channels

SummaryIn this paper, a security problem in networked control systems which are modeled as linear quadratic Gaussian control systems is investigated from the perspective of attackers. We consider the scenario that the attackers can inject false data into two channels: sensor‐to‐controller and controller‐to‐actuator channels. The goal of attackers is to design the optimal stealthy false data injection attacks to maximize the linear quadratic Gaussian control cost function, where Kullback‐Leiber divergence is used as a stealthiness metric. Firstly, the cost function is divided into a fixed part and a part which is related to a remote estimation error covariance. Then, when the two channels are attacked by attackers, the recursion of remote estimation error covariance is derived. In the presence of attacks, the optimization problem with multiple decision variables, which may not be a convex problem, is transformed into a convex optimization problem and the corresponding optimal solution is obtained. In addition, an upper bound of benefit loss when using the optimal solution of the convex optimization problem is presented. Finally, a simulation example is presented to show the effectiveness of the obtained results.

Imitation and Transfer Learning for LQG Control

In this paper we study an imitation and transfer learning setting for Linear Quadratic Gaussian (LQG) control, where (i) the system dynamics, noise statistics and cost function are unknown and expert data is provided (that is, sequences of optimal inputs and outputs) to learn the LQG controller, and (ii) multiple control tasks are performed for the same system but with different LQG costs. We show that the LQG controller can be learned from a set of expert trajectories of length $n(l+2)-1$, with $n$ and $l$ the dimension of the system state and output, respectively. Further, the controller can be decomposed as the product of an estimation matrix, which depends only on the system dynamics, and a control matrix, which depends on the LQG cost. This data-based separation principle allows us to transfer the estimation matrix across different LQG tasks, and to reduce the length of the expert trajectories needed to learn the LQG controller to~$2n+m-1$ with $m$ the dimension of the inputs (for single-input systems with $l=2$, this yields approximately a $50\%$ reduction of the required expert data).

Data Driven Linear Quadratic Gaussian Control Design

The implementation of the Linear Quadratic Gaussian (LQG) scheme is often considered problematic as it requires a dynamic model of the system as a whole. The challenges come from state variables without a physical representation and the interference factors that affect the reading process. This paper presents and assesses a combination of methods to adapt the LQG scheme to a discrete-time linear system. The method KalmanNet constructed by the Long-Short Term Memory architecture (LSTM) is employed to replace the role of Kalman Filter (KF). The Value Iteration (VI) algorithm supersedes the role of the Linear Quadratic Regulator (LQR) controller in solving quadratic regulation issues. The assessment of the proposed algorithm on a cart-pole system and batch distillation column with a disturbance factor in uncorrelated Gaussian white noise is carried out in a simulated way under a discrete-time linear system. The result indicates that the solving of regulation problems through the conventional LQG method is not conclusive as the output response oscillation is still in progress. The combination of the KalmanNet and VI algorithm, as aforementioned, provides better results as it proves to solve the regulation problem as well as to compel the system output to converge.

Linear Quadratic Gaussian Control for UAVs With Improved State Estimation Against Gyroscope and Accelerometer Biases

This paper proposes a linear quadratic Gaussian control for trajectory tracking of a quadrotor UAV. It involves implementing an optimal linear quadratic regulator control with integral action in an inner-outer loop control architecture. The full-state multi-rate extended Kalman filter generates the feedback required for the optimal control. Biases in gyroscope and accelerometer measurements are also incorporated into the Kalman filter to avoid degradation of the closed-loop response and to provide accurate state estimates. The proposed control architecture is tested on an experimental test bed consisting of a quadrotor UAV platform. The onboard inertial measurement unit, altimeter, and motion capture system provides the necessary measurements. The recorded results validate the performance of the proposed control scheme with improved state feedback generated through the extended Kalman filter.

Periodic LQG Wind Turbine Control with Adaptive Load Reduction

A periodic linear quadratic Gaussian (LQG) control law augmented with a reference point adaption to enable adequate rotor speed tracking and sufficient load reductions for a wind turbine is presented. The solution of the periodic LQG control problem is based on solving two periodic Ricatti differential equations in continuous time with a multiple shooting integration technique. For this, the available gridded linear time-variant description of the turbine is converted to a harmonic representation using harmonic Fourier approximation. While the periodic LQG controller provides rotor speed tracking and effective damping of the aeroelastic blade modes, the reference point adaption explicitly reduces the loads resulting from the periodic operation of the turbine rotor at the rotor rotational frequency. The performance of the proposed control system is compared against a baseline controller in realistic wind scenarios using a high fidelity nonlinear simulator. The results show a significant damage equivalent load reduction while maintaining adequate rotor speed tracking.

Cooperative Differentially Private LQG Control With Measurement Aggregation

When multiple agents solve cooperatively a joint optimal control problem, it is generally beneficial for them to coordinate their control signals. However, such strategies require that the agents share their local measurements, which may be privacy-sensitive. Motivated by this issue, this letter considers the Linear Quadratic Gaussian (LQG) control problem subject to differential privacy constraints. Differential privacy ensures that the published signals of an algorithm are not too sensitive to the data of any single participating agent. We propose a two-stage architecture for differentially private LQG control and show how to optimize it by leveraging a solution that we previously developed for the Kalman filtering problem. The first stage of this architecture is most easily implemented by a coordinator aggregating and perturbing the agents’ measurements appropriately, but it can also be implemented without a trusted aggregator by using a secure sum protocol. Numerical simulations illustrate the performance improvement of this architecture over simpler alternatives such as directly perturbing the agents’ measurements.

Enhanced the Control Strategy of a Triple Link Robotic System (Robogymnast)

This research aims to optimise performance in a Fuzzy Linear Quadratic Regulator controller by implementing 2 types of algorithm to stabilise the triple-link ‘Robogymnast’ robotic system. The Robogymnast recreates the movements of a human gymnast, with the hand/arm element of the system securely attached to a high bar with ball0bearing mountings, which can rotate freely. This article explores the complex factors involved in swing-up control in the underactuated Robogymnast and presents a linearisation of the mathematical modelling for the system, considering methods which apply Lagrangian equations in defining state space in such systems. Both the Teaching-Learning-Based Optimization (TLBO) and Particle Swarm Optimization (PSO) algorithm were used for tuning the hybrid Fuzzy Linear Quadratic Regulator controller for later application with the robot and assessment of response stability. In addition, MATLAB Simulink was used to simulate performance and show the effect of altering parameters including time for rising, settling and overshoot. This work aims primarily to explore how a Linear Quadratic Regulator/Fuzzy Logic controller can be applied with acrobatic robots.

Stability and the Separation Principle in Output-Feedback Stochastic MPC with Random Packet Losses

This paper considers a linear quadratic Gaussian (LQG) control problem with constraints on system inputs and random packet losses occurring on the communication channel between plant and controller. It is well known that, in the absence of constraints, the Separation Principle between estimator and controller holds when the channel employs a TCP-like protocol but not so under a UDP-like protocol. This paper gives a counterexample that shows that, under a model predictive control (MPC) scheme that handles the constraints, the Separation Principle does not hold even in the TCP-like case. Theoretical analysis characterizes and reveals a trade-off between estimation errors in the estimator and prediction errors in the controller. Counterintuitively, the poorer on-average performance of the estimator in the UDP case may be compensated by smaller prediction errors in the controller.

Learning-based Optimal Control for Linear Systems with Model Uncertainties

The problem of optimal control with unknown dynamics is important and challenging. Most existing learning-based methods usually do not utilize the prior knowledge of the model and choose to learn the system model from scratch, leading to high identification costs and unbounded identification time. In practice, prior knowledge of the model may be available. Therefore, in this paper, we investigate the Linear Quadratic Gaussian (LQG) control problem for an unknown system but with prior knowledge of model uncertainties. We develop an effective learning procedure to identify the optimal controller parameters, leading to the least possible cost. Specifically, we analyze the performance of the optimal observer under unknown system dynamics and reveal the relationship between the regression error and the observer performance. We propose a learning procedure to design the optimal controller incorporating prior knowledge of the system. Simulations are conducted to illustrate the effectiveness of our controller design.

Dynamics and Control of Flexible Satellite Using Reaction Sphere Actuators

This paper presents a disturbance observer-based linear quadratic Gaussian (LQG) control strategy to stabilize the flexible spacecraft considering the vibration suppression of flexible appendages using an orthogonal cluster of magnetically suspended reaction sphere actuators. The nonlinear dynamic equation of a flexible satellite is given and then linearized using the Jacobian method to get a linear state-space model. The dynamic equation of the reaction sphere actuators is derived by considering 2 virtual gimbals. A new steering law is designed to produce the tilt angle commands of orthogonal reaction sphere actuators. The proposed disturbance observer-based LQG considers process disturbances and measurement noises, and performs a trade-off search between control efforts and regulation performance. Numerical simulations are performed to evaluate the proposed strategies for an attitude stabilization scenario, and the results illustrate that the disturbances are effectively mitigated.

Validation of Stochastic Optimal Control Models for Goal-Directed Human Movements on the Example of Human Driving Behavior

Stochastic Optimal Control models represent the state-of-the-art in modeling goal-directed human movements. The linear-quadratic sensorimotor (LQS) model based on signal-dependent noise processes in state and output equation is the current main representative. With our newly introduced Inverse Stochastic Optimal Control algorithm building upon two bi-level optimizations, we can identify its unknown model parameters, namely cost function matrices and scaling parameters of the noise processes, for the first time. In this paper, we use this algorithm to identify the parameters of a deterministic linear-quadratic, a linear-quadratic Gaussian and a LQS model from human measurement data to compare the models’ capability in describing goal-directed human movements. Human steering behavior in a simplified driving task shown to posses similar features as point-ot-point human hand reaching movements serves as our example movement. The results show that the identified LQS model outperforms the others with statistical significance. Particularly, the average human steering behavior is modeled significantly better by the LQS model. This validates the positive impact of signal-dependent noise processes on modeling human average behavior.

An Adaptive Predictive Control Algorithm for Comprehensive Dendritic Canal Systems

Automatic canal control is essential to improve water utilization efficiency in irrigation districts. Water level error in the model used by the control algorithm significantly impacts performance. The integrator delay model, which has a linear structure, is widely used in multi-input/multioutput control algorithms, including linear-quadratic control and model predictive control. However, the integrator delay model is suboptimal for large irrigation districts; the canals are long, the flows are large, there are many scattered offtakes, and the operating conditions vary. We developed an adaptive predictive control mode for the Qinhan Canal in Ningxia Province, China. We used a segment integrator delay model for this large irrigation district and employed a differential evolution algorithm for online system identification; this minimizes error. We analyzed and controlled for various uncertainties (i.e., flow observation noise, geometric and hydraulic parameter errors, and accidental interference with the automatic control system). Simulations indicated that the water level fitting errors were significantly reduced compared with the original model, and water level regulation was significantly improved, especially in terms of the maximum absolute error. Adaptive predictive control was better than linear-quadratic control and model predictive control approach for water level. Adaptive predictive control coped well with several uncertainties. The main factors affecting water level control were the flow observation and gate opening control accuracy, and the extent of real-time data coverage. These features require careful attention when automating and modernizing irrigation districts.

LQG Control Over SWIPT-enabled Wireless Communication Network

In this paper, we consider using simultaneous wireless information and power transfer (SWIPT) to recharge the sensor in the LQG control, which provides a new approach to prolonging the network lifetime. We analyze the stability of the proposed system model and show that there exist two critical values for the power splitting ratio α. Then, we propose an optimization problem to derive the optimal value of α. This problem is non-convex but its numerical solution can be derived by our proposed algorithm efficiently. Moreover, we provide the feasible condition of the proposed optimization problem. Finally, simulation results are presented to verify and illustrate the main theoretical results.

Linear-Quadratic-Gaussian mean-field controls of social optima

<p style='text-indent:20px;'>This paper investigates a class of unified stochastic linear-quadratic-Gaussian (LQG) social optima problems involving a large number of weakly-coupled interactive agents under a generalized setting. For each individual agent, the control and state process enters both diffusion and drift terms in its linear dynamics, and the control weight might be <i>indefinite</i> in cost functional. This setup is innovative and has great theoretical and realistic significance as its applications in mathematical finance (e.g., portfolio selection in mean-variation model). Using some <i>fully-coupled</i> variational analysis under the person-by-person optimality principle, and the mean-field approximation method, the decentralized social control is derived by a class of new type consistency condition (CC) system for typical representative agent. Such CC system is some mean-field forward-backward stochastic differential equation (MF-FBSDE) combined with <i>embedding representation</i>. The well-posedness of such forward-backward stochastic differential equation (FBSDE) system is carefully examined. The related social asymptotic optimality is related to the convergence of the average of a series of weakly-coupled backward stochastic differential equation (BSDE). They are verified through some Lyapunov equations.</p>

Decentralized LQG Control With $d$-Step Delayed Information Sharing Pattern

In this article, we study a class of discrete-time decentralized linear-quadratic-Gaussian (LQG) control problems with two controllers and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$d$</tex-math></inline-formula> -step delayed information sharing pattern. An explicit form of the pair of optimal linear controllers is obtained in terms of backward Riccati equations and forward equations of estimation error covariance. To overcome the difficulty that arises due to the coupling of the backward–forward equations, we propose a forward iteration approach to derive a steady-state solution. This accordingly leads to an asymptotically optimal linear controller where the feedback gains are designed by using the convergent steady-state solutions.

Infinite coexisting attractors in an autonomous hyperchaotic megastable oscillator and linear quadratic regulator-based control and synchronization

Infinite coexisting attractors in an autonomous hyperchaotic megastable oscillator and linear quadratic regulator-based control and synchronization

CONTROL OF DYNAMIC TRIM FOR PLANING VESSELS WITH INTERCEPTORS IN TERMS OF COMFORT AND MINIMUM DRAG

Nowadays, interceptors are often used to decrease total resistance and enhance comfort by reducing dynamic trim for high-speed planing vessels. They can be controlled manually as well as automatically by using a suitable closed-loop control system. Thus, in the present study, an automatically controllable system is presented to minimize the total resistance by reducing the dynamic trim in calm water. To reach this aim, a mathematical model which can represent the 2 degree of freedom vertical motion of a prismatic planing vessel is presented. The coefficients used in the model are calculated by using the Savitsky method. The standard dynamic trim angle and the optimum ones in terms of resistance are calculated by using the same method. For control action, a linear full state feedback control strategy (linear quadratic regulator) is applied, and instantaneous blade heights are found considering the change in forward speed. Therefore, the control-oriented model is able to change the blade height to reach the optimum trim angle in terms of the total resistance of the vessel for different forward speeds and speed profiles. The results show that the designed linear quadratic regulator control strategy is successful for reference trim tracking problems.

A Survey of LQE and MPC Discrete-Control for Acrobot

This paper surveys the Linear Quadratic Estimation (LQE) and Model Predictive Control (MPC) discrete control methods applied to the Acrobot system. Both techniques aim to achieve and maintain a balanced position for the Acrobot. Through evaluation and comparison, we highlight their strengths, limitations, and potential applications, offering insights for future robotic control research.