LQG Control Problem Research Articles

Decentralized Output-Feedback Control With Asymmetric One-Step Delayed Information

This paper considers the decentralized LQG control problem for discrete-time decentralized system controlled by two players. In this scenario, player 1 shares a unit delayed observations and control inputs with the controller of player 2, whereas due to the limiting capacity, the controller of player 1 cannot obtain the observations and control inputs of player 2 which leads to the asymmetric one-step delay information. It should be emphasized that this structure makes the classical separation principle fail. Under the assumption of linear control strategies, we derive the optimal estimators based on asymmetric information. In virtue of the Pontryagin's maximum principle, the optimal explicit decentralized controllers are obtained by solving the forward and backward stochastic difference equations (FBSDEs). It is noted that the control gains are coupled with the estimation gains. Moreover, the estimation gains satisfy the forward Riccati equations and the control gains follow the backward Riccati equations which cannot be solved simultaneously. To this end, we present iterative solutions to the coupled forward and backward Riccati equations. Finally, a sufficient condition for the stabilization problem is given in terms of the coupled algebraic Riccati equations. Numerical examples are illustrated to show the effectiveness of the proposed algorithm.

Adaptive transmission rate for LQG control over Wi-Fi: A cross-layer approach

This work studies the problem of LQG control when the link between the sensor and the controller relies on a Wi-Fi network. Unfortunately, the communication on a wireless medium is sensitive to noise in the transmission band, which is characterized by the Signal-to-Noise Ratio (SNR). Wi-Fi allows to switch among different bit-rates in real-time thus permitting to trade-off lower loss probabilities for larger latency or vice-versa to achieve better closed-loop performance. To exploit this feature, under a constant SNR scenario, we propose a cross-layer approach where the bit-rate is optimally selected based on a control performance metric (i.e. minimum LQG cost) and a model-based controller is used to compensate for the packet losses. Under time-varying SNR, we additionally propose a (sub-optimal) on-line rate adaptation strategy and we guarantee the closed-loop stability under some mild conditions. Numerical comparisons with emulation-based approaches using TrueTime, a realistic Matlab-based Wi-Fi simulator, are included to show the benefits of the adaptive approach under time-varying SNR scenarios.

Optimal LQG Control for Networked Control Systems with Remote and Local Controllers

We consider the finite horizon optimal LQG control problem for networked control systems with a remote controller, a local controller and communication channels with packet dropouts and transmission delays. The local controller can directly observe state signals and send them to the remote controller via a packet-dropout channel. Then the remote controller sends the received measurement signals to the local controller. Afterwards, the two controllers operate the plant through a delayed channel. The contributions of this paper are as follows: Firstly, at the side of the remote controller, we develop an optimal estimator to show that the separation principle holds. Secondly, we derive a non-homogeneous relationship between the state and the costate of systems in virtue of the maximum principle. Finally, a necessary and sufficient condition for the optimal control problem is derived in terms of the two coupled Riccati equations. Numerical examples are employed to illustrate the theoretical results.

A separation theorem for guaranteed H2 performance through matrix inequalities

The usage of convex optimisation programs that leverage linear matrix inequalities allows for numerical solutions to the design of output-feedback controllers with guaranteed H2 performance. As decreed by the classical separation theorem for the related LQG control problem, the H2 control problem admits an optimal solution in terms of those of the separate optimal state-estimation and state-feedback design problems. This work details a new and alternative proof of this separation theorem. The proof builds on techniques for (linear) matrix inequalities and shows, in particular, that feasible but sub-optimal solutions of the state-feedback and the state-estimation problem yield a sub-optimal output feedback controller with guaranteed H2 performance.

Dynamic Teams and Decentralized Control Problems With Substitutable Actions

This technical note considers two problems—a dynamic team problem and a decentralized control problem. The problems we consider do not belong to the known classes of “simpler” dynamic team/decentralized control problems such as partially nested or quadratically invariant problems. However, we show that our problems admit simple solutions under an assumption referred to as the substitutability assumption. Intuitively, substitutability in a team (resp. decentralized control) problem means that the effects of one team member's (resp. controller's) action on the cost function and the information (resp. state dynamics) can be achieved by an action of another member (resp. controller). For the non-partially-nested LQG dynamic team problem, it is shown that under certain conditions linear strategies are optimal. For the non-partially-nested decentralized LQG control problem, the state structure can be exploited to obtain optimal control strategies with recursively update-able sufficient statistics. These results suggest that substitutability can work as a counterpart of the information structure requirements that enable simplification of dynamic teams and decentralized control problems.

Quantum Noises, Physical Realizability and Coherent Quantum Feedback Control

Arbitrary linear time invariant systems can be implemented as quantum systems if additional quantum noises are permitted in the implementation. We give several results concerning how many additional quantum noise channels are necessary to implement state space realizations and transfer functions as quantum systems. We also give algorithms to do so. We demonstrate the utility of these results with an algorithm for obtaining a suboptimal solution to a coherent quantum LQG control problem.

Structural properties, LQG control and scheduling of a networked control system with bandwidth limitations and transmission delays

The problem of simultaneous LQG control and scheduling of a Networked Control System (NCS) with constant network induced delays at input and output and bandwidth limitations is investigated. Delays are considered at plant as well as controller side. Sufficient conditions for controllability, stabilizability, reconstructibility and detectability of the underlying networked control system are drawn. The proposed conditions extend previous works on structural properties of NCS by capturing both plant and controller side delays together with bandwidth limitations. A framework for computing the optimal LQG controller for the NCS with a fixed scheduling is provided. The proposed modeling approach facilitates use of LQG as well as other control methods for NCSs with delays and bandwidth limitations. In order to optimize performance, a semi-online scheduling procedure is proposed based on an offline look up table. The look up table assigns an optimal schedule with associated optimal LQG controller to initial conditions. The proposed scheme improves previous results by online deployment of schedule and LQG control with stability guarantees and very low computational overhead. A simulation example with communication delays, packet losses and bandwidth limitations in both sensor and actuator sides is included. Static optimal periodic communication sequence, Optimal Pointer Placement (OPP) approach proposed in previous works, a random access scheduling method representing contention based access policies and the proposed method are simulated and compared.

Necessary and Sufficient Conditions for Global External Stochastic Stabilization of Linear Systems With Input Saturation

We consider the problem of global external stochastic stabilization for linear plants with saturating actuators, driven by a stochastic external disturbance, and having random Gaussian-distributed initial conditions. The objective is to control such plants by a possibly nonlinear static state feedback law that achieves global asymptotic stability in the absence of disturbances, while guaranteeing a bounded variance of the state vector for all time in the presence of disturbances and Gaussian distributed initial conditions. Results for continuous-time open-loop critically stable plants as well as for a chain of integrators have been obtained before. The goal of this technical note is to extend this result to critically unstable plants. We view our contribution in this technical note as a critical step in solving the LQG control problem for linear systems subject to saturated inputs which is a research problem with a long history in our field.

Optimal Block Length for Data-Rate Minimization in Networked LQG Control

Abstract: We consider a discrete-time networked LQG control problem in which state information must be transmitted to the controller over a noiseless binary channel using prefix-free codewords. Quantizer, encoder and controller are jointly designed to minimize average data-rate while satisfying required LQG control performance. We study the effects of selecting large block-lengths (data transmission intervals) from the perspectives of information-theoretic advantage due to coding efficiency and control-theoretic disadvantage due to delay. In particular, we demonstrate that the performance of networked control scheme by Tanaka et al. (2016) can be improved by adjusting the block-length optimally. As a byproduct of this study, we also show that the data-rate theorem for mean-square stability similar to Nair and Evans (2004) can be recovered by considering sufficiently large block-lengths.

An Optimal Compensation Framework for Linear Quadratic Gaussian Control Over Lossy Networks

In this technical note, we study the compensation problem of LQG control over two lossy networks under TCP-like protocols and propose a new static and latest-control based compensation framework. Compared to two popular strategies, the zero-input and hold-input compensators and the recent generalized hold-input compensator by Moayedi et al. our new one is more general. The contribution of the new framework is in three aspects. Firstly, it takes the problem of LQG control over lossy networks to a new level by suggesting that the original problem should be more properly posed as a two-variable instead of a one-variable optimization problem. Secondly, it links the compensator gain selection and the minimization of quadratic cost together and bridges the gap between the two by providing an optimal gain selection. Thirdly, it incorporates the above three classes of compensators as special cases. The issue as to why none of the zero-input and hold-input compensation strategies can be claimed to be better than the other is to a great extent settled. Performance comparisons of the proposed method and the predictive outage compensator by Henriksson et al. and the generalized hold-input strategy by Moayedi et al. are made through numerical examples.

Design of coherent quantum observers for linear quantum systems

Quantum versions of control problems are often more difficult than their classical counterparts because of the additional constraints imposed by quantum dynamics. For example, the quantum LQG and quantum optimal control problems remain open. To make further progress, new, systematic and tractable methods need to be developed. This paper gives three algorithms for designing coherent quantum observers, i.e., quantum systems that are connected to a quantum plant and their outputs provide information about the internal state of the plant. Importantly, coherent quantum observers avoid measurements of the plant outputs. We compare our coherent quantum observers with a classical (measurement-based) observer by way of an example involving an optical cavity with thermal and vacuum noises as inputs.

On global external stochastic stabilization of linear systems with input saturation

We consider the problem of global external stochastic stabilization for linear plants with saturating actuators, driven by a stochastic external disturbance, and having random Gaussian-distributed initial conditions. The aim of this stabilization is to control such plants by a possibly nonlinear static state feedback law that achieves global asymptotic stability in the absence of disturbances, while guaranteeing a bounded variance of the state vector for all time in the presence of disturbances and Gaussian distributed initial conditions. Results for continuous-time open-loop critically stable plants have been obtained before. This paper shows how to extend this result to plants consisting of a chain of integrators. We view our contribution in this paper as a first critical step in solving the LQG control problem for linear systems subject to saturated inputs which is a research problem with a long history in our field.

Two Schemes of Data Dropout Compensation for LQG Control of Networked Control Systems

AbstractThis paper investigates the LQG control problem for networked control systems (NCSs) with packet losses, where the packet losses are considered to appear in both the sensor‐to‐controller channel and controller‐to‐actuator channel. Bernoulli random processes are used to describe the packet losses in the two channels. Two simple compensation schemes are explored for state estimation with missing measurements in which the input of the plant is set to zero if a packet is lost, and the hold‐input strategy, in which the previous input is used with packet dropout. The optimal static controller gains and the critical loss probabilities for the two schemes are presented, and their performances are compared in terms of numerical simulations. The conclusion is that neither of the two schemes can be claimed to be superior to the other, as the stability regions of the two strategies are reversely complemented to each other whether for the scalar or vector example.

Optimal design of remote controllers for LTI plants over erasure channels

In this paper we consider the remote control of a noisy linear time-invariant (LTI) plant over erasure channels located in both the plant-to-controller and controller-to-plant links. We restrict our attention to a class of controllers where all processing is affine, except for some elementary use of sensor-to-controller channel state information. For such controller class, we show that optimal designs separate into an estimation and a state feedback design problem when perfect packet acknowledgements are available at the controller. Interestingly, our results also show that the affine part of the controller converges, as the time goes to infinity, to an LTI filter under the same conditions which guarantee mean-square stability in the well-known LQG control problem over erasure channels. However, our infinite horizon proposal is computationally inexpensive and its steady-state behaviour can be characterized straightforwardly.

LQG Control of Unmanned Aerial Vehicles Under Communication Constraints

This paper addresses the LQG control problem for unmanned aerial vehicles (UAV) with time delays. In particular, the case with data-rate limitations is considered. It is shown in our results that the data rate of the communication channel has important effects on the control performances. It is derived that there exists a tradeoff between the data rate and the LQG cost. A quantization, coding, and control scheme is proposed to stabilize the unstable plant. Simulation results show the validity of the proposed scheme. DOI: http://dx.doi.org/10.11591/telkomnika.v11i9.2426

Distributed Output-Feedback LQG Control with Delayed Information Sharing

This paper develops a controller synthesis method for distributed LQG control problems under output-feedback. We consider a system consisting of three interconnected linear subsystems with a delayed information sharing structure. While the state-feedback case has previously been solved, the extension to output-feedback is nontrivial as the classical separation principle fails. To find the optimal solution, the controller is decomposed into two independent components: a centralized LQG-optimal controller under delayed state observations, and a sum of correction terms based on additional local information available to decision makers. Explicit discrete-time equations are derived whose solutions are the gains of the optimal controller.

Sampled-data LQG control for a class of linear quantum systems

In this paper, an LQG control problem is solved for a class of linear quantum systems for the case of sampled-data measurements. The methodology adopted involves an equivalence between the quantum problem and an auxiliary classical stochastic problem.

Output Variance–Constrained LQG Control of Discrete-Time Systems

The constrained infinite-horizon LQG control problem can be solved via semidefinite programming if the state-control constraints are given by variance-bounds on linear functions of the state and control input. Given a nonzero initial state covariance matrix, each suboptimal dynamic output feedback controller is initially time-varying but reaches time-invariance after a finite number of time steps. This number of time steps can be determined iteratively via repetitive execution of semidefinite programs.

Optimal Output Regulation for Discrete-Time Switched and Markovian Jump Linear Systems

First, three different but related output regulation performance criteria for the linear time-varying system are defined in the discrete-time domain, namely, the peak impulse response, peak output variance, and average output variance per unit time. Then they are extended for switched linear systems and Markovian jump linear systems, and characterized by an increasing union of finite-dimensional linear matrix inequality conditions. Finally, the infinite-horizon suboptimal LQG control problem, which aims to maintain the average output variance below a given level subject to the uniform exponential stability of the closed-loop system, is solved for both switched linear systems and Markovian jump linear systems; the solution is given by a dynamic linear output feedback controller that not only perfectly observes the present mode but also recalls a finite number of past modes.

Numerical computation of cross-coupled algebraic Riccati equations related to H∞-constrained LQG control problem

In this paper, the numerical algorithm for solving the state and output feedback H ∞-constrained LQG control problem is investigated. Although the equations that have to be solved to design the controller consist of the nonlinear cross-coupled algebraic Riccati equations (CAREs), it is newly proven that both the uniqueness and the positive semidefiniteness of the iterative solutions can be guaranteed when disturbance attenuation level γ is sufficiently large. The computational examples are given to demonstrate the efficiency of the proposed algorithm.