An optimized LQG servo controller design using LQI tracker for VSP-based AC/DC interconnected systems

Using the dual Youla parametrizations of controller based coprime factor plant perturbations and plant based coprime factor controller perturbations, the authors provide a computational procedure for computing an optimal infinite horizon linear quadratic Gaussian (LQG) controller from any stabilizing controller. The method allows the authors to calculate a new optimal LQG controller from a previous one when the plant has slightly changed, and to quantify the change in the controller as a function of the change in the plant. In addition, the authors compute the degradation in the achieved LQG cost when the LQG controller is computed on the basis of a plant model that is "close to" the real plant, where the closeness is measured by some norm of the perturbation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

This paper presents the design of an internal reference model-based optimal linear quadratic Gaussian (LQG) controller for the lateral positioning of a piezoelectric tube actuator (PTA) used in an atomic force microscope (AFM). In this control design, internal modeling of the reference signal and system error are considered. As a result, the steady-state tracking error is minimized. In addition to the LQG controller, a vibration compensator is incorporated with the plant to suppress the vibration of the PTA at the resonance frequency. It achieves a high closed-loop bandwidth and significant damping of the resonant mode of the PTA, which enables a reference triangular signal to be tracked. Comparison of performance of the optimal LQG controller augmented with a vibration compensator and a PI controller demonstrates that the proposed controller shows significant improvements over the existing AFM PI controller.

This paper focuses on the optimal linear quadratic Gaussian (LQG) control problem for stochastic discrete-time systems with multiplicative noise and multiple delays in the state. The relationship between the state and the costate is obtained by using the Pontryagin's maximum principle. The necessary and sufficient condition for the problem existing a unique optimal controller is given. Moreover, an explicit expression of the optimal LQG controller and the associated minimum cost function are presented in terms of coupled Riccati equations. It should be stressed that these results are based on the key technical tool, which established relations between the state and the costate of the LQG systems.

This paper is concerned with designing linear quadratic Gaussian (LQG) controller based on coherent quantum observer. In more concrete terms, we aim to design a stabilizing coherent quantum controller, which possesses the property of a coherent quantum observer, for a linear quantum plant in order to minimize a mean-square cost for the closed-loop quantum feedback system. In contrast to previous established work, we give a numerical approach to solving this problem via simulated annealing algorithm. Moreover, an illustrative example of designing locally optimal coherent quantum LQG controller are provided in order to demonstrate the algorithm performance proposed in the paper.

By modeling the networked robot system (NRS) that drops packets randomly, we considered the problem of optimal linear quadratic Gaussian (LQG) control and analyzed the stability of a NRS. We presented a mathematical model based on a packet-based setting, extended the familiar LQG separation principle that allows us to solve this problem using a standard LQR state-feedback design, proposed an optimal algorithm irrespective of the packet drop pattern by constructing an encoder for the unreliable channel and designing the decoder that uses the information it receives across the link to construct an estimate of the state of the networked robot. For the case of packet drops occurring according to a Markov chain, the stability analysis was carried out. Because the separation theorem for linear systems and quadratic cost does not apply to the general framework of NRSs, we used the uncertainty threshold principle to show that under certain conditions there was a rate for dropped packets for which an undisturbed networked control system with imperfect state observation was mean square stable, used a sub-optimal method to simplify the calculation of the estimator and controller, got the solution to the Riccati-like equation and guaranteed the mean square stability of the NRS with perfect state information. This design does not assume any statistical model of the packet drop events and can be implemented as a small modification of an existing LQG control design

This paper studies the linear quadratic Gaussian (LQG) control problem for wireless networked control systems in which control inputs are randomly dropped without the packet acknowledgment The packet acknowledgment is based on a signal scheme between the actuator and the estimator, which make the estimator know whether control packets are dropped or not. For such systems, the calculation of the optimal LQG controller has been shown to be computationally prohibitive and impractical, and sub-optimal solutions are usually obtained under an optimality criteria which is different from that for the optimal LQG problem. An approximate optimal LQG controller is obtained by introducing two approximations in computing the optimal estimation and control. Illustrative examples are provided to verify effectiveness of the proposed design scheme.

The state-space model-based control design for a two-area interconnected AC electric power system using the linear quadratic Gaussian (LQG) controller is realized in this paper. In industry, the classical integer-order proportional-integral (PI) and proportional-integral-derivative (PID) controllers have been broadly adopted for automatic generation control (AGC). The conventional PI and PID controllers leverage area control error (ACE) measurements to eliminate steady-state errors in frequency and the-ltne interchange active-power flow. This paper presents a comparison amongst the dynamic response of the conventional PI controller and observer-based servo controllers designed using pole placement as well as LQG techniques. The overarching goal of this work is to improve the dynamic response of AGC systems through an optimal control method, namely, LQG. This paper investigates AGC systems for interconnected power systems and shows that LQG controllers perform better than both the classical PI controller as well as the observer-based one designed using pole placement.

This paper deals with the modelling and the linear quadratic Gaussian (LQG) control design of a quadrotor unmanned aerial vehicle (UAV) using different particle swarm optimisation (PSO) variants. Such a PSO-designed LQG controller is optimised in order to stabilise the position and the heading of the studied vertical take-off and landing (VTOL) quadrotor. Both canonical and recent variants of PSO algorithm, with linearly decreasing of inertia weight (PSO-In) and perturbed updating strategy (PSO-gbest), are considered for the systematically design and tuning of the LQG weighting matrices. These effective control parameters of the LQG approach represent the decision variables of the PSO-based LQG optimisation problem. Such an optimisation problem is formulated to minimise various performance time-domain criteria, like the integral of absolute error (IAE) and the maximum overshoot (MO) index, under nonlinear constraints related to the step responses of the closed-loop quadrotor dynamics. All proposed PSO algorithms are compared with each other and with the well known harmony search algorithm (HSA) and water cycle algorithm (WCA) metaheuristics for the stabilisation problem of the position and heading dynamics of the VTOL drone. Demonstrative simulation results are carried out in order to show the effectiveness of the proposed PSO variants-tuned LQG control approach.

This paper deals with the modelling and the linear quadratic Gaussian (LQG) control design of a quadrotor unmanned aerial vehicle (UAV) using different particle swarm optimisation (PSO) variants. Such a PSO-designed LQG controller is optimised in order to stabilise the position and the heading of the studied vertical take-off and landing (VTOL) quadrotor. Both canonical and recent variants of PSO algorithm, with linearly decreasing of inertia weight (PSO-In) and perturbed updating strategy (PSO-gbest), are considered for the systematically design and tuning of the LQG weighting matrices. These effective control parameters of the LQG approach represent the decision variables of the PSO-based LQG optimisation problem. Such an optimisation problem is formulated to minimise various performance time-domain criteria, like the integral of absolute error (IAE) and the maximum overshoot (MO) index, under nonlinear constraints related to the step responses of the closed-loop quadrotor dynamics. All proposed PSO algorithms are compared with each other and with the well known harmony search algorithm (HSA) and water cycle algorithm (WCA) metaheuristics for the stabilisation problem of the position and heading dynamics of the VTOL drone. Demonstrative simulation results are carried out in order to show the effectiveness of the proposed PSO variants-tuned LQG control approach.

In this paper we present a Linear Quadratic Gaussian (LQG) control design for large-dimensional network dynamic systems using the idea of network clustering. When networks have tens of thousands of nodes spread over a wide geographical span, the design of conventional output feedback controllers becomes numerically challenging, and their implementation requires a large number of communication links. Our proposed algorithm bypasses these difficulties by clustering the network nodes using structural properties of its closed-loop transfer matrix. The cluster assignment is applied for constructing a structured projection matrix P, which is used to pose a significantly lower-dimensional controller design. The problem is, therefore, posed in terms of finding the optimal set of clusters or P that minimizes the ℋ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> -norm of the error between the transfer matrices of the full-order network with a conventional LQG controller and that with the projected LQG controller. We derive an upper bound on this error as a function of P, and design a P that minimizes this bound.

Linear Quadratic Gaussian Control for Discrete-time Systems with Delay and Multiplicative Noise

Previous article Next article Conditions for Positive and Nonnegative Definiteness in Terms of PseudoinversesArthur AlbertArthur Alberthttps://doi.org/10.1137/0117041PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Richard Bellman, Introduction to matrix analysis, McGraw-Hill Book Co., Inc., New York, 1960xx+328 MR0122820 0124.01001 Google Scholar[2] A. Ben-Israel and , A. Charnes, Contributions to the theory of generalized inverses, J. Soc. Indust. Appl. Math., 11 (1963), 667–699 10.1137/0111051 MR0179192 0116.32202 LinkISIGoogle Scholar[3] T. N. E. Greville, Some applications of the pseudoinverse of a matrix, SIAM Rev., 2 (1960), 15–22 10.1137/1002004 MR0110185 0168.13303 LinkISIGoogle Scholar[4] Charles A. Rohde, Generalized inverses of partitioned matrices, J. Soc. Indust. Appl. Math., 13 (1965), 1033–1035 10.1137/0113070 MR0190161 0145.03801 LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited ByDetails Error Analysis of Multirate Leapfrog-Type Methods for Second-Order Semilinear OdesConstantin Carle and Marlis HochbruckSIAM Journal on Numerical Analysis, Vol. 60, No. 5 | 13 October 2022AbstractPDF (1129 KB)The truncated moment problem on the union of parallel linesLinear Algebra and its Applications, Vol. 649 | 1 Sep 2022 Cross Ref On the non-symmetric semidefinite Procrustes problemLinear Algebra and its Applications, Vol. 648 | 1 Sep 2022 Cross Ref Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation riskJournal of Industrial & Management Optimization, Vol. 18, No. 1 | 1 Jan 2022 Cross Ref Stability and Functional Superconvergence of Narrow-Stencil Second-Derivative Generalized Summation-By-Parts DiscretizationsJournal of Scientific Computing, Vol. 90, No. 1 | 10 December 2021 Cross 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This paper considers H ∞ control for wireless networked control systems with data packet loss. In wireless networked control systems, the control performance deteriorates due to packet loss. Therefore, packet loss is one of major weakness in the wireless networked control systems. To overcome this weakness, this paper proposes a new control design that considers the influence of packet loss as a disturbance. Our new control design belongs to the H ∞ control design and can reduce the influence of disturbances acting on the controlled object. Numerical examples show that the proposed H ∞ control design can more effectively reduce control performance deterioration due to packet loss. This paper provides not only the proposal of the new control design but also control performance comparisons of the proposed control design and the Linear Quadratic (LQ) control design. Numerical examples show that the control performance of the proposed H ∞ control design is better than that of the LQ control design.

For model based control designs like boldsymbol{H}{2} and boldsymbol{H}{ boldsymbol{ infty}} optimal control, the controller order is typically equal to the model order. However, the synthesis and real-time implementation of these controllers may be hampered for models of large order due to computational limitations. Several closed-loop relevant order reduction techniques have been developed in order to overcome this problem. One technique is Linear Quadratic Gaussian (LQG) balanced truncation, which is closely related to LQG and boldsymbol{H}{2} optimal controller design. This paper demonstrates the non-optimality of this technique for constrained order boldsymbol{H}{2} optimal controller design. Furthermore, improvements to reduce the loss of performance as a result of truncation are proposed. These improvements can be applied to a large class of controller designs and order reduction techniques as well.

ABSTRACTIn this paper, we study a cooperative linear quadratic Gaussian (LQG) control system realized by a cloud‐based structure, consisting of a user and a server. In this system, the user runs a plant to control and employ the server, sharing necessary information with it to obtain the optimal LQG control inputs. However, the user considers its state trajectories as private. Therefore, we propose a privacy scheme utilizing a public privacy processor, whose certain parameters are also open to the server. This scheme manages to make the server unable to directly access the states of the user, so that the user's privacy is preserved; meanwhile, the server's public knowledge of the privacy processor allows the user to have satisfactory performance of LQG control. We then analyze the performances of privacy preservation and LQG control. Lastly, we propose an optimization problem to analyze the trade‐off between privacy and LQG control, which we solve using an efficient numerical method.