• Journal of Institute of Control, Robotics and Systems
• /
• v.13 no.11
• /
• pp.1048-1052
• /
• 2007

This paper presents a rank-constrained linear matrix inequality(LMI) approach to simultaneous linear-quadratic(LQ) optimal control by static output feedback. Simultaneous LQ optimal control is formulated as an LMI optimization problem with a nonconvex rank condition. An iterative penalty method recently developed is applied to solve this rank-constrained LMI optimization problem. Numerical experiments are performed to illustrate the proposed method, and the results are compared with those of previous work.

• Proceedings of the KSME Conference
• /
• 2001.06b
• /
• pp.140-145
• /
• 2001

Various control algorithms are available to suppress the vibration of a system subjected to disturbances. LQ algorithm is simple and easy to implement the hardwares, but it lacks robustness for uncertainties and often causes difficulty in determining the weighting matrices. This study focuses on the effectiveness ILQ(Inverse Linear Quadratic optimal control) algorithm as the alternative to LQ applied to control the vibration of a building under the seismic excitation. The building is of moment resisting steel frames and assumed to behave within the elastic range. The brief overview of LQ and ILQ algorithms is introduced, and the displacement responses of the structure using ILQ algorithm are compared with those obtained from LQ control. The magnitude of control forces are also determined and compared for both LQ and ILQ algorithm.

• 제어로봇시스템학회:학술대회논문집
• /
• 1988.10b
• /
• pp.729-733
• /
• 1988

In this paper, a new procedure for selecting weighting matrices in linear discrete time quadratic optimal control problems (LQ-problem) is proposed. In LQ problems, the quadratic weighting matrices are usually decided on trial and error in order to get a good response. But using the proposed method, the quadratic weights are decided in such a way that all poles of the closed loop system are located in a desired area for good responses as well as for stability and values of the quadratic cost functional are kept less then a specified value. The closed loop systems constructed by this method have merits of LQ problems as well as those of pole assignment problems. Taking into consideration that little is known about the relationship among the quadratic weights, the poles and the values of cost functional, this procedure is also interesting from the theoretical point of view.

• 제어로봇시스템학회:학술대회논문집
• /
• 1989.10a
• /
• pp.884-889
• /
• 1989

In this paper, a new procedure for selecting weighting matrices in linear discrete time quadratic optimal control problem (LQ-problem) is proposed. In LQ-problems, the quadratic weighting matrices are usually decided on trial and error in order to get a good response. But using the proposed method, the quadratic weights are decided in such a way that all poles of the closed loop system are located in a desired region for good responses as well as for stability and values of the quadratic cost function are kept less then a specified value.

• Journal of Institute of Control, Robotics and Systems
• /
• v.20 no.5
• /
• pp.526-532
• /
• 2014

In this paper, we present and analyze a LQ (Linear Quadratic) inverse optimal state-consensus protocol for continuous-time multi-agent systems with undirected graph topology. By Lyapunov analysis of the state-consensus error dynamics, we show the sufficient conditions on the algebraic connectivity of the graph to guarantee LQ inverse optimality and closed-loop stability. A more relaxed stability condition is also provided in terms of the algebraic connectivity. Finally, a formation control protocol for multiple mobile robots is proposed based on the target LQ inverse optimal consensus protocol, and the simulation results are provided to verify the performance of the proposed LQ inverse formation control method.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.19 no.3
• /
• pp.217-234
• /
• 2015

In this tutorial the theoretical background of LQ optimal guidance is reviewed, starting from calculus of variations. LQ optimal control is then introduced and applied to missile guidance to obtain the basic form of LQ optimal guidance laws. Extension of LQ optimal guidance methodology for handling weighted cost function, dynamic lag associated with the missile dynamics and the autopilot, constrained impact angle, and constrained impact time is also described with a brief discussion on the asymptotic properties of the optimal guidance laws. Furthermore, an introduction to polynomial guidance and generalized impactangle-control guidance, which are closed related with LQ optimal guidance, is provided to demonstrate the current status of missile guidance techniques.

• Proceedings of the KSME Conference
• /
• 2001.06b
• /
• pp.93-98
• /
• 2001

This paper studies on the design of an ILQ(Inverse Linear Quadratic optimal control) looper control system for hot strip mills. The looper which is placed between each stand plays an important role in controlling strip width by regulating strip tension variation generated from the velocity difference of main work rolls. The mathematical model for looper is firstly obtained by Taylor's linearization of nonlinear differential equations, where it is given as a linear and time invariant state-space equation. Secondly, a looper servo controller is designed by ILQ control algorithm, which is an inverse problem of LQ(Linear Quadratic optimal control) control. By tunning control gain arbitration parameters and time constants, it is shown that the ILQ looper servo controller has the performance that makes well to follow desired trajectories of both strip tension and looper angle.

• 제어로봇시스템학회:학술대회논문집
• /
• 1999.10a
• /
• pp.57-60
• /
• 1999

An optimal control technique designed for simultaneous tracking and quality control for batch processes. The proposed technique is designed by transforming quadratic-criterion based iterative learning control(Q-ILC) into linear quadratic control problem. For real-time quality inferential control, the quality is modeled by linear combination of control input around target qualify and then the relationship between quality and control input can be transformed into time-varying linear state space model. With this state space model, the real-time quality inferential control can be incorporated to LQ control Problem. As a consequence, both the quality variable as well as other controlled variables can progressively reduce their control error as the batch number increases while rejecting real-time disturbances, and finally reach the best achievable states dictated by a quadratic criterion even in case that there is significant model error Also the computational burden is much reduced since the most computation is calculated in off-line. The Proposed control technique is applied to a semi-batch reactor model where series-parallelreactions take place.

• Journal of applied mathematics & informatics
• /
• v.13 no.1_2
• /
• pp.85-97
• /
• 2003

An indefinite stochastic linear-quadratic(LQ) optimal control problem with cross term over an infinite time horizon is studied, allowing the weighting matrices to be indefinite. A systematic approach to the problem based on semidefinite programming (SDP) and .elated duality analysis is developed. Several implication relations among the SDP complementary duality, the existence of the solution to the generalized Riccati equation and the optimality of LQ problem are discussed. Based on these relations, a numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is given: it identifies a stabilizing optimal feedback control or determines the problem has no optimal solution. An example is provided to illustrate the results obtained.

• Journal of Institute of Control, Robotics and Systems
• /
• v.21 no.5
• /
• pp.434-441
• /
• 2015

In this paper, we propose an inverse optimal distributed protocol for the formation and velocity consensus of nonholonomic mobile robots. The communication among mobile robots is described by a simple undirected graph, and the mobile robots' kinematics are considered. The group of mobile robots driven by the proposed protocols asymptotically achieves the desired formation and group velocity in an inverse optimal fashion. The design of the protocols is based on dynamic feedback linearization and the proposed linear quadratic (LQ) inverse optimal second-order consensus protocol. A numerical simulation is given to verify the effectiveness of the proposed scheme.