2,266 research outputs found
Regret-Optimal LQR Control
We consider the infinite-horizon LQR control problem. Motivated by
competitive analysis in online learning, as a criterion for controller design
we introduce the dynamic regret, defined as the difference between the LQR cost
of a causal controller (that has only access to past disturbances) and the LQR
cost of the \emph{unique} clairvoyant one (that has also access to future
disturbances) that is known to dominate all other controllers. The regret
itself is a function of the disturbances, and we propose to find a causal
controller that minimizes the worst-case regret over all bounded energy
disturbances. The resulting controller has the interpretation of guaranteeing
the smallest regret compared to the best non-causal controller that can see the
future. We derive explicit formulas for the optimal regret and for the
regret-optimal controller for the state-space setting. These explicit solutions
are obtained by showing that the regret-optimal control problem can be reduced
to a Nehari extension problem that can be solved explicitly. The regret-optimal
controller is shown to be linear and can be expressed as the sum of the
classical state-feedback law and an -th order controller ( is the
state dimension), and its construction simply requires a solution to the
standard LQR Riccati equation and two Lyapunov equations. Simulations over a
range of plants demonstrate that the regret-optimal controller interpolates
nicely between the and the optimal controllers, and generally
has and costs that are simultaneously close to their optimal
values. The regret-optimal controller thus presents itself as a viable option
for control systems design
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Cooperative distributed LQR control for longitudinal flight of a formation of non-identical low-speed experimental UAV's
In this paper, an established distributed LQR control methodology applied to identical linear systems is extended to control arbitrary formations of non-identical UAV's. The nonlinear model of a low-speed experimental UAV known as X-RAE1 is utilized for simulation purposes. The formation is composed of four dynamically decoupled X-RAE1 which differ in their masses and their products of inertia about the xz plane. In order to design linear controllers the nonlinear models are linearized for horizontal flight conditions at constant velocity. State-feedback, input and similarity transformations are applied to solve model-matching type problems and compensate for the mismatch in the linearized models due to mass and symmetry discrepancies among the X-RAE1 models. It is shown that the method is based on the controllability indices of the linearized models. Distributed LQR control employed in networks of identical linear systems is appropriately adjusted and applied to the formation of the nonidentical UAV's. The applicability of the approach is illustrated via numerous simulation results
Effects of model error on control of large flexible space antenna with comparisons of decoupled and linear quadratic regulator control procedures
An analysis was performed to determine the effects of model error on the control of a large flexible space antenna. Control was achieved by employing two three-axis control-moment gyros (CMG's) located on the antenna column. State variables were estimated by including an observer in the control loop that used attitude and attitude-rate sensors on the column. Errors were assumed to exist in the individual model parameters: modal frequency, modal damping, mode slope (control-influence coefficients), and moment of inertia. Their effects on control-system performance were analyzed either for (1) nulling initial disturbances in the rigid-body modes, or (2) nulling initial disturbances in the first three flexible modes. The study includes the effects on stability, time to null, and control requirements (defined as maximum torque and total momentum), as well as on the accuracy of obtaining initial estimates of the disturbances. The effects on the transients of the undisturbed modes are also included. The results, which are compared for decoupled and linear quadratic regulator (LQR) control procedures, are shown in tabular form, parametric plots, and as sample time histories of modal-amplitude and control responses. Results of the analysis showed that the effects of model errors on the control-system performance were generally comparable for both control procedures. The effect of mode-slope error was the most serious of all model errors
Decoupled and linear quadratic regulator control of a large, flexible space antenna with an observer in the control loop
An analysis is performed to compare decoupled and linear quadratic regulator (LQR) procedures for the control of a large, flexible space antenna. Control objectives involve: (1) commanding changes in the rigid-body modes, (2) nulling initial disturbances in the rigid-body modes, or (3) nulling initial disturbances in the first three flexible modes. Control is achieved with two three-axis control-moment gyros located on the antenna column. Results are presented to illustrate various effects on control requirements for the two procedures. These effects include errors in the initial estimates of state variables, variations in the type, number, and location of sensors, and deletions of state-variable estimates for certain flexible modes after control activation. The advantages of incorporating a time lag in the control feedback are also illustrated. In addition, the effects of inoperative-control situations are analyzed with regard to control requirements and resultant modal responses. Comparisons are included which show the effects of perfect state feedback with no residual modes (ideal case). Time-history responses are presented to illustrate the various effects on the control procedures
Combating False Reports for Secure Networked Control in Smart Grid via Trustiness Evaluation
Smart grid, equipped with modern communication infrastructures, is subject to
possible cyber attacks. Particularly, false report attacks which replace the
sensor reports with fraud ones may cause the instability of the whole power
grid or even result in a large area blackout. In this paper, a trustiness
system is introduced to the controller, who computes the trustiness of
different sensors by comparing its prediction, obtained from Kalman filtering,
on the system state with the reports from sensor. The trustiness mechanism is
discussed and analyzed for the Linear Quadratic Regulation (LQR) controller.
Numerical simulations show that the trustiness system can effectively combat
the cyber attacks to smart grid.Comment: It has been submitted to IEEE International Conference on
Communications (ICC
Stabilizing periodic orbits above the elliptic plane in the solar sail 3-body problem
We consider periodic orbits high above the ecliptic plane in the Elliptic Restricted Three-Body Problem where the third massless body is a solar sail. Periodic orbits above the ecliptic are of practical interest as they are ideally positioned for the year-round constant imaging of, and communication with, the poles. Initially we identify an unstable periodic orbit by using a numerical continuation from a known periodic orbit above the ecliptic in the circular case with the eccentricity as the varying parameter. This orbit is then used to construct a reference trajectory for the sail to track. In addition we illustrate an alternative method for constructing a periodic reference trajectory based on a time-delayed feedback mechanism. The reference trajectories are then tracked using a linear feedback regulator (LQR) where the control actuation is delivered by varying the solar sails orientation. Using this method it is shown that a 'near term' solar sail is capable of performing stable periodic motions high above the ecliptic
Tip position control of single flexible manipulators based on LQR with the Mamdani model
Flexible manipulators have been actively used in various fields, such as aerospace, industry and medical treatment. It remains that the tip of the flexible manipulator should accurately trail the target trajectory without vibration. This paper proposes a novel method of the tip position control of a single flexible manipulator based on LQR with the Mamdani model. Firstly, using the assumed mode method and the Lagrange equations, the dynamic model of the single flexible manipulator is established. Then, the state equations are derived by the dynamic model. Based on the Mamdani model, the fuzzy algorithm is added to the traditional LQR control, and the self-adaptive adjustment of the LQR control variable R is conducted, which improves the adaptability of the control system. Finally, numerical simulations and experiments are presented. The results demonstrate that the novel control method presented in this paper can rapidly achieve the location in the position control and effectively suppress the elastic vibration of the single flexible manipulator, which has more considerable effect compared with the traditional LQR control method
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