Linear Quadratic Gaussian Systems Research Articles

Linear Quadratic Gaussian Controller for Single-Ended Primary Inductor Converter via Integral Linear Quadratic Regulator Merged with an Offline Kalman Filter

This paper introduces a Linear Quadratic Gaussian (LQG) controller for a Single-Ended Primary Inductor Converter (SEPIC). The LQG design is based on merging an integral Linear Quadratic Regulator (LQR) with an offline Kalman Filter (commonly referred to as a Linear Quadratic Estimator (LQE)). The robustness of the LQG controller is guaranteed based on the separation principle. This manuscript addresses the need to use observer-based systems for the fourth-order SEPIC, which needs a sensor reduction as an essential requirement. This paper provides a comprehensive, yet systematic, approach to designing the LQG system. The work validates the convergences of the states in an LQG system to an actual value. Furthermore, it compares the performance of an LQG system with a benchmark Type-II industrial controller by means of a simulation of the switched converter model in the Simulink/MATLAB 2023a environment.

Optimal Innovation-Based Stealthy Attacks in Networked LQG Systems With Attack Cost.

In this article, the optimal innovation-based attack strategy is investigated for the networked linear quadratic Gaussian (LQG) systems. To bypass the detector, the attacks are required to follow strict stealthiness or ϵ -stealthiness described by the Kullback-Leibler divergence. The attackers aim to increase the quadratic control cost and decrease the attack cost, which is formulated as a nonconvex optimization problem. Then, based on the cyclic property of the matrix trace, the nonconvex objective function is transformed into a linear function related to attack matrices and covariance matrices of the tampered innovations. The optimal strictly stealthy attack is obtained by utilizing the matrix decomposition technique. Furthermore, the optimal ϵ -stealthy attack is derived to achieve a higher-attack effect by an integrated convex optimization, which distinguishes from the existing suboptimal attacks developed by a two-stage optimization. Simulation results are provided to show the effectiveness of the designed attacks.

Regret Lower Bounds for Learning Linear Quadratic Gaussian Systems

Regret Lower Bounds for Learning Linear Quadratic Gaussian Systems

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.

Kullback-Leibler Divergence-Based Optimal Stealthy Sensor Attack Against Networked Linear Quadratic Gaussian Systems.

This article concentrates on designing optimal stealthy attack strategies for cyber-physical systems (CPSs) modeled by the linear quadratic Gaussian (LQG) dynamics, where the attacker aims to increase the quadratic cost maximally and keeping a certain level of stealthiness by simultaneously intercepting and modifying the transmitted measurements. In our work, a novel attack model is developed, based on which the attacker can launch strictly stealthy or ϵ -stealthy attacks. To remain strictly stealthy, the attacker only needs to solve an off-line semidefinite program problem. In such a case, the attack performance is optimal but limited. To achieve a higher desired attack effect than that of the strictly stealthy attack, the attacker sometimes needs to sacrifice the stealthy level. Thus, the ϵ -stealthy attack is analyzed, where an upper bound of the optimal attack performance is obtained by solving a convex optimization problem. Then, an optimal ϵ -stealthy attack is designed to achieve the upper bound, which differs from the existing suboptimal ϵ -stealthy attack for the considered LQG systems. Finally, the simulations are provided to verify the developed results.

Optimal control for networked control systems with multiple delays and packet dropouts

This article focuses on the problem of optimal linear quadratic Gaussian control for networked control systems with multiple delays and packet dropouts. The main contributions are twofold. Firstly, based on the introduced maximum principle for linear quadratic Gaussian system with multiple input delays and packet dropouts, a nonhomogeneous relationship between the state and costate is obtained, which is the key technical tool to solve the problem. Secondly, a necessary and sufficient condition for the optimal networked control problem is given in virtue of the coupled Riccati equations, and the explicit expression of the optimal controller is presented. Numerical examples are shown to illustrate the proposed algorithm.

False Data Injection and Detection in LQG Systems: A Game Theoretic Approach

Cyber-physical systems are vulnerable to false data injection by adversaries who compromise cyber communication links. In this paper, an infinite horizon linear quadratic Gaussian (LQG) system is considered wherein the control inputs transmitted over cyber links are vulnerable to compromise and false data injection by adversaries. The adversarial cyber-attack is driven to minimize the performance of the LQG system, and the controller is equipped with an intrusion detection system that monitors the sequence of internal physical states to detect adversarial input modification. The problem is formulated as a two-player zero-sum game with the false alarm probability as the reward, wherein the attacker aims to achieve a target increase in controller cost while maximizing the false alarm probability, and a detector who wishes to minimize the false alarm probability while remaining consistent. It is shown that in such a game, an ε-equilibrium exists. The equilibrium attacker strategy is the one that minimizes the Kullback-Leibler distance between legitimate and falsified state dynamics, and the equilibrium detector strategy is the corresponding likelihood-ratio test. Numerical simulations are presented that showcase the equilibrium strategy pair and the intuitive strategies comparisons.

Optimal controller/observer gains of discounted-cost LQG systems

The linear–quadratic-Gaussian (LQG) control paradigm is well-known in literature. The strategy of minimizing the cost function is available, both for the case where the state is known and where it is estimated through an observer. The situation is different when the cost function has an exponential discount factor, also known as a prescribed degree of stability. In this case, the optimal control strategy is only available when the state is known. This paper builds onward from that result, deriving an optimal control strategy when working with an estimated state. Expressions for the resulting optimal expected cost are also given.

Robust Performance of Fuzzy Supervisory Control for Seismically Excited Cable-Stayed Bridge

This paper investigates the robust performance of fuzzy supervisory control (FSC) technique for seismically excited cable-stayed bridge. The FSC technique utilizes fuzzy logic-based decision-making process to incorporate a set of pre-designed static control gains into a time-varying optimal control gain. To demonstrate the excellent robustness of the FSC technique on response control of earthquake-excited cable-stayed bridge, a conventional linear quadratic Gaussian (LQG) controller with single static gain and two fuzzy supervisory controllers are designed for the benchmark cable-stayed bridge, and their robust performances are examined under uncertainty in bridge model and against failures in actuators and sensors. Under the presence of uncertainty in the bridge model, the FSC system successfully reduces the seismic responses of the bridge without significant increase in the total amount of power and stroke required by the control system, while the LQG system exhibits a substantial increase in the seismic responses. Under conditions of sensor or actuator failures, the FSC system guarantees a more enhanced robust performance than the LQG system as well.

Completion-of-squares: Revisited and extended

Due to its simplicity, the completion-of-squares technique is quite popular in linear optimal control. However, this simple technique is limited to linear quadratic Gaussian systems. In this note, by interpreting the completion-of-squares from a new angle, we extend this technique to performance optimization of general Markov systems with the long run average criterion, leading to a new approach to performance optimization based on direct comparisons of the performance of two policies.

Semi-active control of structures using neuro-predictive algorithm for MR dampers

A semi-active control method for a seismically excited nonlinear benchmark building equipped with a magnetorheological (MR) damper is presented and evaluated. A linear quadratic Gaussian (LQG) controller is designed to estimate the optimal control force. The required voltage for the MR damper to produce the control force estimated by LQG controller is calculated by a neural network predictive control algorithm (NNPC). The LQG controller and the NNPC are linked to control the structure. The coupled LQG and NNPC system are then used to train a semi-active neuro-controller designated as SANC, which produces the necessary control voltage that actuates the MR damper. The effectiveness of the NNPC and SANC is illustrated and verified using simulated response of a 3-story full-scale, nonlinear, seismically excited, benchmark building excited by several historical earthquake records. The semi-active system using the NNPC algorithm is compared with the performances of passive as well as active and clipped optimal control (COC) systems, which are based on the same nominal controller as is used in the NNPC algorithm. The results demonstrate that the SANC algorithm is quite effective in seismic response reduction for wide range of motions from moderate to severe seismic events, compared with the passive systems and performs better than active and COC systems. Copyright © 2008 John Wiley & Sons, Ltd.

Semi-active neuro-control for base-isolation system using magnetorheological (MR) dampers

Vibration mitigation using smart, reliable and cost-effective mechanisms that requires small activation power is the primary objective of this paper. A semi-active controller-based neural network for base-isolation structure equipped with a magnetorheological (MR) damper is presented and evaluated. An inverse neural network model (INV-MR) is constructed to replicate the inverse dynamics of the MR damper. Next, linear quadratic Gaussian (LQG) controller is designed to produce the optimal control force. Thereafter, the LQG controller and the INV-MR models are linked to control the structure. The coupled LQG and INV-MR system was used to train a semi-active neuro-controller, designated as SA-NC, which produces the necessary control voltage that actuates the MR damper. To evaluate the proposed method, the SA-NC is compared to passive lead–rubber bearing isolation systems (LRBs). Results revealed that the SA-NC was quite effective in seismic response reduction for wide range of motions from moderate to severe seismic events compared to the passive systems. In addition, the semi-active MR damper enjoys many desirable features, such as its inherent stability, practicality and small power requirements. The effectiveness of the SA-NC is illustrated and verified using simulated response of a six-degree-of-freedom model of a base-isolated building excited by several historical earthquake records. Copyright © 2006 John Wiley & Sons, Ltd.

Review of Linear Stochastic Optimal Control Systems and Applications

Many complex control systems can be modeled by linear ordinary differential/difference equations with multiplicative and additive noise. The characteristics and behavior of such systems are different from a regular linear quadratic Gaussian system, the basic difference being the inapplicability of the separation or the certainty equivalence principle. Control systems with multiplicative and additive noise are reviewed herein and the fundamental results, in continuous and discrete-time setting, are presented. Furthermore, the advantages and disadvantages are underlined and the need for further research is pointed out.

Joint Estimation and Control of Jump Linear Systems With Multiplicative Noises

Jump Linear Quadratic Gaussian systems are considered in the presence of state-and control-dependent noises. Assuming that the jumps of the model parameters are perfectly observed, it is possible to formulate and solve an optimal input synthesis problem. It is found that the optimal solution does not present the certainty equivalence property, so that the estimation and control synthesis must be treated simultaneously. Optimal equations for the filter and regulator gains are obtained in terms of a set of coupled nonlinear matrix differential equations.

Unified Controls and Strategies Applicable to Both Singular and Non-Singular Cases

The stochastic controls and strategies for linear quadratic Gaussian systems are considered in this paper. We have obtained the unified suboptimal controls and strategies applicable to the general case, whether the covariance matrix of the measurement noise and the weighting matrix of the control action are degenerate or not, and also have given the optimal control and strategy applicable to both the degenerate and the non-degenerate co-variance matrix of the measurement noise when the initial information is unknown.