Linear Quadratic Optimal Control Design Research Articles

Suboptimal consensus protocol design for a class of multiagent systems

This article presents a new technique for suboptimal consensus protocol design for a class of multiagent systems. The proposed technique is based upon the extension of newly developed sufficient conditions for suboptimal linear–quadratic optimal control design, which are derived in this paper by an explication of a noniterative solution technique of the infinite-horizon linear quadratic regulation problem in Krotov framework. For suboptimal consensus protocol design, the structural requirements on the overall feedback gain matrix, which are inherently imposed by agents dynamics and their interaction topology, are recast on a specific matrix introduced in a suitably formulated convex optimization problem. As a result, preassigning the identical feedback gain matrices to a network of homogeneous agents, which act on the relative state variables with respect to their neighbors is not required. The suboptimality of the computed control laws is quantified by implicitly deriving an upper bound on the cost in terms of the solution of a convex optimization problem and initial conditions of the agents instead of specifying it a priori. Numerical examples are provided to demonstrate the implementation of proposed approaches and their comparison with existing methods in the literature.

Linear Quadratic Optimal Control Design: A Novel Approach Based on Krotov Conditions

This paper revisits the problem of synthesizing the optimal control law for linear systems with a quadratic cost. For this problem, traditionally, the state feedback gain matrix of the optimal controller is computed by solving the Riccati equation, which is primarily obtained using calculus of variations- (CoV-) based and Hamilton–Jacobi–Bellman (HJB) equation-based approaches. To obtain the Riccati equation, these approaches require some assumptions in the solution procedure; that is, the former approach requires the notion of costates and then their relationship with states is exploited to obtain the closed-form expression of the optimal control law, while the latter requires a priori knowledge regarding the optimal cost function. In this paper, we propose a novel method for computing linear quadratic optimal control laws by using the global optimal control framework introduced by V. F. Krotov. As shall be illustrated in this article, this framework does not require the notion of costates and any a priori information regarding the optimal cost function. Nevertheless, using this framework, the optimal control problem gets translated to a nonconvex optimization problem. The novelty of the proposed method lies in transforming this nonconvex optimization problem into a convex problem. The convexity imposition results in a linear matrix inequality (LMI), whose analysis is reported in this work. Furthermore, this LMI reduces to the Riccati equation upon imposing optimality requirements. The insights along with the future directions of the work are presented and gathered at appropriate locations in this article. Finally, numerical results are provided to demonstrate the proposed methodology.

Based on Linear Quadratic Regulator Optimal Control of Single Inverted Pendulum System Co-Simulation of ADAMS and SIMULINK

In this paper, based on linear quadratic optimal control design the controller of single inverted pendulum system, using the current epidemic method of Co-simulation to play each of the strengths of two software for simulation, Through two methods of the static and dynamic to observe and analyze the quality of feedback controller the based on linear quadratic optimal control.

A computational method for simultaneous LQ optimal control design via piecewise constant output feedback

The paper is concerned with simultaneous linear-quadratic (LQ) optimal control design for a set of LTI systems via piecewise constant output feedback. First, the discrete-time simultaneous LQ optimal control design problem is reduced to solving a set of coupled matrix inequalities and an iterative LMI algorithm is presented to compute the feedback gain. Then, simultaneous stabilization and simultaneous LQ optimal control design of a set of LTI continuous-time systems are considered via periodic piecewise constant feedback gain. It is shown that the design of a periodic piecewise constant feedback gain simultaneously minimizing a set of given continuous-time performance indexes can be reduced to that of a constant feedback gain minimizing a set of equivalent discrete-time performance indexes. Explicit formulas for computing the equivalent discrete-time systems and performance indexes are derived. Examples are used to demonstrate the effectiveness of the proposed method.

Frequency reshaped quadratic control of a low-cost human-level performance belt-driven robot

Belt-driven robots are desirable for many industrial applications that require a fast response for a relatively large amount of travel in a system. A belt-drive is a simple, lightweight device that is also cost effective in comparison to other methods of arm positioning. The tradeoff of a belt-driven robot is the need for an effective control strategy to reject time-varying disturbances due to the belt stiffness variation and the presence of resonance excited by disturbances of high frequencies. In this paper, we present the dynamic model and control of a low-cost belt-driven robot. We present here the modeling and control of an intelligent integrated belt-driven manipulator (IIBM) developed at Georgia Tech. The belt-driven robot is a low-cost human-level performance robot, specifically meant to meet or exceed the performance of a human taking shrink wrapped packages off a conveyor and placing them in a basket for delivery. Therefore, such attributes as speed and accuracy are dictated by the level of performance a human can achieve. The control design for the IIBM presents a challenge in that a control system for the belt-driven axis must be designed by using a low-order plant model that is robust enough to variations in both the parameter changes and the un-modeled high frequency dynamics. For these reasons, we investigate the use of frequency reshaped linear quadratic (FRLQ)) control in the development of a low-cost IIBM, which combines the time domain linear quadratic optimal control design with classical frequency response methods. The control strategy, based on the FRLQ method, has been implemented on the first axis of an IIBM. The performance has been evaluated analytically by simulation and experimentally, the results of which are compared against the control system originally used by the IIBM designers, a well-tuned PD controller. Experimental implementation has demonstrated that the frequency reshaped linear quadratic control has a potential to significantly improve the performance of the belt-driven robot.

Multivariable model reference linear quadratic optimal systems

This paper deals with model reference linear quadratic optimal control design in the frequency-domain for multiple-input-multiple-output systems. An explicit equation is given for the 1DOF (one degree-of-freedom) controller, which minimizes a given quadratic cost function. Some optimal systems are shown to be the special cases of this generalized result. For the system with minimum-phase zeros, the equivalent 2DOF (two degrees-of-freedom) control system is designed so that the loop transfer matrix can satisfy the return difference equality, i.e. the system can recover the robustness properties as in time-domain LQR optimal systems.

A quadratic weight selection algorithm

A new algorithm is presented which determines a positive semi-definite state weighting matrix in the linear-quadratic optimal control design problem. The algorithm chooses the weighting matrix by attempting to place dosed-loop eigenvalues and eigenvectors near desired locations using optimal feedback gains. A simplified flight control design example is used to illustrate the algorithm's capabilities.