Quadratic Optimal Tracking Research Articles

Data-Driven Active Learning Control for Bridge Cranes

For positioning and anti-swing control of bridge cranes, the active learning control method can reduce the dependence of controller design on the model and the influence of unmodeled dynamics on the controller’s performance. By only using the real-time online input and output data of the bridge crane system, the active learning control method consists of the finite-dimensional approximation of the Koopman operator and the design of an active learning controller based on the linear quadratic optimal tracking control. The effectiveness of the control strategy for positioning and anti-swing of bridge cranes is verified through numerical simulations.

An improved iterative algorithm for solving optimal tracking control problems of stochastic systems

This paper proposes an improved iterative algorithm based on a Newton iterative algorithm, which is used to research the stochastic linear quadratic optimal tracking (SLQT) control for stochastic continuous-time systems. Firstly, a Newton iterative algorithm for solving stochastic algebraic Riccati equations (SAREs) is derived based on the Frechet derivative. Secondly, an improved iterative algorithm in an incremental form for indirectly solving SAREs is presented by combining the numerical iterative method with the incremental Newton iterative (INI) algorithm and introducing a tuning parameter. Under a suitable initial condition, the convergence of the improved iterative algorithm is talked over. Finally, numerical simulation experiments are carried out to compare our proposed improved iterative algorithm with some known works. The results show that the improved iterative algorithm has a faster convergence rate.

Optimal Tracking for Periodic Linear Hybrid Systems

This note provides a comprehensive characterization of the quadratic optimal tracking problem for hybrid systems with linear dynamics undergoing periodic, time–driven jumps. Solutions to such a problem are proposed for both the finite–horizon and the periodic cases. Furthermore, it is shown that if the reference signals are not known in advance, then the best control strategy to deal with the worst case reference signals is to simply minimize the (scaled) outputs. Finally, the derived optimal solutions are used to solve two relevant control problems: the reconstruction of vector fields from noisy measurements of the corresponding flows and the estimation of the time derivatives of a periodic, sampled, noisy signal.

Stochastic linear quadratic optimal tracking control for discrete-time systems with delays based on Q-learning algorithm

<abstract><p>In this paper, a reinforcement Q-learning method based on value iteration (Ⅵ) is proposed for a class of model-free stochastic linear quadratic (SLQ) optimal tracking problem with time delay. Compared with the traditional reinforcement learning method, Q-learning method avoids the need for accurate system model. Firstly, the delay operator is introduced to construct a novel augmented system composed of the original system and the command generator. Secondly, the SLQ optimal tracking problem is transformed into a deterministic one by system transformation and the corresponding Q function of SLQ optimal tracking control is derived. Based on this, Q-learning algorithm is proposed and its convergence is proved. Finally, a simulation example shows the effectiveness of the proposed algorithm.</p></abstract>

Neural-network-based stochastic linear quadratic optimal tracking control scheme for unknown discrete-time systems using adaptive dynamic programming

Neural-network-based stochastic linear quadratic optimal tracking control scheme for unknown discrete-time systems using adaptive dynamic programming

Real-Time Pricing Control on Generation-Side: Optimal Demand-Tracking Model and Information Fusion Estimation Solver

This paper develops the information fusion based pricing control (IFPC) scheme for the generation-side in the liberalized wholesale electricity market. The market mechanism is described by a feedback system, in which the independent system operator (ISO) interacts with generation companies (GenCOs) via proposing and responding to real-time nodal prices. The linear constrained quadratic optimal tracking problem is formulated; and the solution (nodal price sequence) is repeatedly computed by fusing the recently available information with backward manner and updated over the receding preview horizon. So that the total supply dynamically tracks the demand, the price is stationarized and each GenCO gains the maximal profit for the given price. Numeric results on a 118-bus network validate IFPC's effectiveness and flexibility on incorporating various line rating constraints as well as wind power fluctuation uncertainties. Comparative study demonstrates that IFPC outperforms the negotiated predictive dispatch but elapsing heavier computations. The irrational behavior analysis verifies the convergence to equilibrium; and speculation behavior of GenCOs in the real market is also discussed. Along with the rapid development of smart grid, IFPC is practically enabled by the information and communication technology (ICT); its significance and potentials for renewable energy sources (RES) integration would be realized and exploited.

The Mixed Kalman and H Infinity Filter Based Robust Model Following Control Algorithm for CABG Beating Heart Surgery

In the CABG surgery the robot dynamically cancels the relative motion between the point of interest (POI) on the beating heart and robotic instruments, such that the surgeon can operate as if the heart is stationary. However, the highly nonlinear and non-stationary nature of the beating heart motion poses difficulties for robot to follow the characteristics of the beating heart motion. Furthermore, the surgery has potential safety risk if the robot system could not track the POI properly. Therefore, in order to minimize the effects caused by the uncertainty in the heart motion model during the surgery, a robust prediction based model following control algorithm is proposed here. The adaptive Autoregressive (AR) model integrated the mixed Kalman and H infinity filter to estimate the state of the beating heart motion in the sense of minimizing minimize both RMS motion estimation error and worst case motion estimation error. In addition, the linear quadratic optimal tracking theory was used to implement the model following controller. In such way a complicated heart motion tracking problem transformed to dynamic model following problem and the robust property of the tracking control is more effective. The method is verified by two prerecorded distinguished datasets on 3D test bed robotics.

Optimal Air-to-Fuel Ratio Tracking Control With Adaptive Biofuel Content Estimation for LNT Regeneration

This paper presents an optimal control method of tracking the desired air-to-fuel ratio (AFR) based upon the adaptively estimated biofuel content for internal combustion engines equipped with the lean NOx trap (LNT) aftertreatment system. This biofuel content (or percentage of biofuel) is adaptively estimated based upon the exhaust oxygen AFR sensor signal under both the normal engine operations with lean combustion and the LNT regeneration operations with the closed-loop AFR control. The engine system is approximated by a third-order linear system in this paper. A linear quadratic optimal tracking controller is used to track the desired engine AFR during the LNT regeneration period. The robust stability of the closed-loop tracking control system with the adaptive biofuel content estimation is guaranteed over the entire biofuel range and engine speed between 600 and 5500 rpm by using the robust stability criteria for linear parameter variation systems, where the biofuel gain and engine speed are considered as the variable parameter. Several adaptive control schemes are studied through simulations, and then the selected control strategies are evaluated through dynamometer tests for a lean burn spark ignition engine. The best performance is achieved by the gain-scheduled adaptive scheme.

Design of power system stabilizers using reduced-order models

This paper provides design methods of power system stabilizers using full- and reduced-order models. The methods are based on linear quadratic optimal tracking as well as observer based feedback control. Application to a model representing a single-machine infinite-bus power system has been undertaken and the results obtained show the effectiveness of the design methods.

Optimal hybrid position/force tracking control of a constrained robot

In this paper, a global tracking control problem of a constrained robot is considered to be formulated by the hybrid coordinate frames of the joint-space coordinate for the motion of the robot's joints, and the task-space coordinate for the constraint forces on the robot's end-effector. After model reduction and a proper change of control variable, reduced state-space error dynamics are explicitly obtained and used to derive the nonlinear quadratic optimal tracking controller for the constrained robot. The advantage of the controller is that it provides an asymptotic tracking solution to minimize, simultaneously and systematically, the tracking error about the desired position and velocity of the joint-space motion, with a minimum of applied torques which affect the kinetic energy only. In addition, it is interesting that our controller can achieve the exponential tracking of the task-space constraint force.

Trajectory generation for manipulators using linear quadratic optimal tracking

The reference trajectory is normally known in advance in manipulator control, which makes it possible to apply linear quadratic optimal tracking. This gives a control system which rounds corners and generates optimal feedforward. The method may be used for references consisting of straight-line segments as an alternative to the two-step method of using splines to smooth the reference and then applying feedforward. in addition, the method can be used for more complex trajectories. The actual dynamics of the manipulator are taken into account, and this results in smooth and accurate tracking. The method has been applied in combination with the computed torque technique and excellent performance was demonstrated in a simulation study. The method has also been applied experimentally to an industrial spray-painting robot where a saw-tooth reference was tracked. The corner was rounded well, and the steady-state tracking error was eliminated by the optimal feedforward. >

Polynomial approach to quadratic tracking in discrete linear systems

A new solution to the quadratic optimal tracking problem in linear multivariable discrete-time systems is presented. The approach is based on polynomial input-output models. The optimal control law consists of a plant output feedback and a reference feedforward. It is obtained by performing spectral factorization and then solving two matrix polynomial equations. The design procedure is simple and well suited for systems with inaccessible states.