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Yaguang Yang

Publications and source records attributed to Yaguang Yang.

31 records · Page 2Linked to original sources
arXiv2018

Two computationally efficient polynomial-iteration infeasible interior-point algorithms for linear programming

Since the beginning of the development of interior-point methods, there exists a puzzling gap between the results in theory and the observations in numerical experience, i.e., algorithms with good polynomial bound are not computationally efficient and algorithms demonstrated efficiency in computation do not have a good or any polynomial bound. Todd raised a question in 2002: "Can we find a theoretically and practically efficient way to reoptimize?" This paper is an effort to close the gap. We propose two arc-search infeasible interior-point algorithms with infeasible central path neighborhood wider than all existing infeasible interior-point algorithms that are proved to be convergent. We show that the first algorithm is polynomial and its simplified version, if it terminates in finite iterations, has a complexity bound equal to the best known complexity bound for all (feasible or infeasible) interior-point algorithms. We demonstrate the computational efficiency of the proposed algorithms by testing all Netlib linear programming problems in standard form and comparing the numerical results to those obtained by Mehrotra's predictor-corrector algorithm and a recently developed more efficient arc-search algorithm (the convergence of these two algorithms is unknown). We conclude that the newly proposed algorithms are not only polynomial but also computationally competitive comparing to both Mehrotra's predictor-corrector algorithm and the efficient arc-search algorithm.

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arXiv2018

Model Predictive Control in Spacecraft Rendezvous and Soft Docking

This paper discusses translation and attitude control in spacecraft rendezvous and soft docking. The target spacecraft orbit can be either circular or elliptic. The high fidelity model for this problem is intrinsically a nonlinear system but can be viewed as a linear time varying system (LTV). Therefore, a model predictive control (MPC) based design is proposed to deal with the time-varying feature of the problem. A robust pole assignment method is used in the MPC-based design because of the following merits and/or considerations: (a) no overshoot of the relative position and attitude between the target and the chaser to achieve soft docking by placing all closed-loop poles in the negative real axis of the complex plan, which avoids oscillation of the relative position and attitude, in particular, in the final stage, (b) fast on-line computation, (c) modeling error tolerance, and (d) disturbance rejection. We will discuss these considerations and merits, and use a design simulation to demonstrate that the desired performance is indeed achieved.

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arXiv2017

An Efficient LQR Design for Discrete-Time Linear Periodic System Based on a Novel Lifting Method

This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The linear quadratic optimal control is then based on the solution of the discrete-time algebraic Riccati equation associated with the augmented linear time-invariant model. An efficient algorithm for solving the Riccati equation is derived by using the special structure of the augmented linear time-invariant system. It is shown that the proposed method is very efficient compared to the ones that use algorithms for discrete-time periodic algebraic Riccati equation. The efficiency and effectiveness of the proposed algorithm is demonstrated by the simulation test for the design problem of spacecraft attitude control using magnetic torques.

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arXiv2016

Singularity-Free Spacecraft Attitude Control Using Variable-Speed Control Moment Gyroscopes

This paper discusses spacecraft control using variable-speed CMGs. A new operational concept for VSCMGs is proposed. This new concept makes it possible to approximate the complex nonlinear system by a linear time-varying system (LTV). As a result, an effective control system design method, Model Predictive Control (MPC) using robust pole assignment, can be used to design the spacecraft control system using VSCMGs. A nice feature of this design is that the control system does not have any singular point. A design example is provided. The simulation result shows the effectiveness of the proposed method.

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arXiv2016

Spacecraft Attitude and Reaction Wheel Desaturation Combined Control Method

Two popular types of spacecraft actuators are reaction wheels and magnetic torque coils. Magnetic torque coils are particularly interesting because they can be used for both attitude control and reaction wheel momentum management (desaturation control). Although these two tasks are performed at the same time using the same set of actuators, most design methods deal with only one of the these tasks or consider these two tasks separately. In this paper, a design with these two tasks in mind is formulated as a single problem. A periodic time-varying linear quadratic regulator design method is then proposed to solve this problem. A simulation example is provided to describe the benefit of the new strategy.

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arXiv2016

An Efficient Algorithm for Periodic Riccati Equation for Spacecraft Attitude Control Using Magnetic Torques

Spacecraft attitude control using only magnetic torques is a periodic time-varying system as the Earth magnetic field in the spacecraft body frame changes periodically while the spacecraft circles around the Earth. The optimal controller design therefore involves the solutions of the periodic Riccati differential or algebraic equations. This paper proposes an efficient algorithm for the periodic discrete-time Riccati equation arising from a linear periodic time-varying system $(\A,\B)$, which explores and utilizes the fact that $\A$ is time-invariant and only $\B$ is time-varying in the system, a special properties associated with the problem of spacecraft attitude control using only magnetic torques.

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arXiv2015

Controllability of Spacecraft Using Only Magnetic Torques

Spacecraft attitude control using only magnetic torques is a time-varying system. Many designs were proposed using LQR and H-infinity formulations. The existence of the solutions depends on the controllability of the linear time-varying systems which has not been established. In this paper, we will derive the conditions of the controllability for this linear time-varying systems.

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arXiv2014

Arc-Search Infeasible Interior-Point Algorithm for Linear Programming

Mehrotra's algorithm has been the most successful infeasible interior-point algorithm for linear programming since 1990. Most popular interior-point software packages for linear programming are based on Mehrotra's algorithm. This paper proposes an alternative algorithm, arc-search infeasible interior-point algorithm. We will demonstrate, by testing Netlib problems and comparing the test results obtained by arc-search infeasible interior-point algorithm and Mehrotra's algorithm, that the proposed arc-search infeasible interior-point algorithm is a more efficient algorithm than Mehrotra's algorithm.

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arXiv2013

An Analytic Solution to Wahba's Problem

All spacecraft attitude estimation methods are based on Wahba's optimization problem. This problem can be reduced to finding the largest eigenvalue and the corresponding eigenvector for Davenport's $K$-matrix. Several iterative algorithms, such as QUEST and FOMA, were proposed, aiming at reducing the computational cost. But their computational time is unpredictable because the iteration number is not fixed and the solution is not accurate in theory. Recently, an analytical solution, ESOQ was suggested. The advantages of analytical solutions are that their computational time is fixed and the solution should be accurate in theory if there is no numerical error. In this paper, we propose a different analytical solution to the Wahba's problem. We use simple and easy to be verified examples to show that this method is numerically more stable than ESOQ, potentially faster than QUEST and FOMA. We also use extensive simulation test to support this claim.

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arXiv2013

An Efficient Polynomial Interior-Point Algorithm for Linear Programming

For interior-point algorithms in linear programming, it is well-known that the selection of the centering parameter is crucial for proving polynomility in theory and for efficiency in practice. However, the selection of the centering parameter is usually by heuristics and separate from the selection of the line-search step size. The heuristics are quite different while developing practically efficient algorithms, such as MPC, and theoretically efficient algorithms, such as short-step path-following algorithm. This introduces a dilemma that some algorithms with the best-known polynomial bound are least efficient in practice, and some most efficient algorithms may not be polynomial. In this paper, we propose a systematic way to optimally select the centering parameter and line-search step size at the same time, and we show that the algorithm based on this strategy has the best-known polynomial bound and may be very efficient in computation for real problems.

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arXiv2013

Constrained LQR Design Using Interior-Point Arc-Search Method for Convex Quadratic Programming with Box Constraints

Although the classical LQR design method has been very successful in real world engineering designs, in some cases, the classical design method needs modifications because of the saturation in actuators. This modified problem is sometimes called the constrained LQR design. For discrete systems, the constrained LQR design problem is equivalent to a convex quadratic programming problem with box constraints. We will show that the interior-point method is very efficient for this problem because an initial interior point is available, a condition which is not true for general convex quadratic programming problem. We will devise an effective and efficient algorithm for the constrained LQR design problem using the special structure of the box constraints and a recently introduced arc-search technique for the interior-point algorithm. We will prove that the algorithm is polynomial and has the best-known complexity bound for the convex quadratic programming. The proposed algorithm is implemented in MATLAB. An example for the constrained LQR design is provided to show the effectiveness and efficiency of the design method. The proposed algorithm can easily be used for model predictive control.

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arXiv2012

A Globally and Quadratically Convergent Algorithm with Efficient Implementation for Unconstrained Optimization

In this paper, an efficient modified Newton type algorithm is proposed for nonlinear unconstrianed optimization problems. The modified Hessian is a convex combination of the identity matrix (for steepest descent algorithm) and the Hessian matrix (for Newton algorithm). The coefficients of the convex combination are dynamically chosen in every iteration. The algorithm is proved to be globally and quadratically convergent for (convex and nonconvex) nonlinear functions. Efficient implementation is described. Numerical test on widely used CUTE test problems is conducted for the new algorithm. The test results are compared with those obtained by MATLAB optimization toolbox function {\tt fminunc}. The test results are also compared with those obtained by some established and state-of-the-art algorithms, such as a limited memory BFGS, a descent and conjugate gradient algorithm, and a limited memory and descent conjugate gradient algorithm. The comparisons show that the new algorithm is promising.

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