Gradient Algorithm in Subspace Predictive Control
Volume 6, Issue 2, June 2018, Pages: 39-44
Received: Feb. 5, 2018;
Accepted: Jul. 20, 2018;
Published: Aug. 22, 2018
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Wang Xiao-ping, School of Mechanical and Electronic Engineering, Jingdezhen Ceramic Institute, Jingdezhen, China
Wang Jian-hong, School of Electronic Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou, China
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In this paper, subspace predictive control strategy is applied to design predictive controller. Given the state space model, the output estimations corresponding to the predictive output is derived to be one explicit function of the measured input-output data. Then using these output estimations, the problem of designing predictive controller is formulated as one optimization problem with equality and inequality conditions. In order to solve this constrain optimization problem, we use dual decomposition idea to change the original constrain optimization problem into an unconstrain optimization problem. So the classical gradient algorithm is put forth to solve the primal dual optimization problem. The problem of designing dual decomposition controller is studied for subspace predictive control strategy under fault condition. For state space equation with fault condition, we establish one function form between fault and residual using only input-output measured data sequence, and construct one least squares optimization problem to obtain fault estimation. The statistical property about residual is analyzed based on our derived output prediction, then the Kronecker product is used to derive the detailed structure corresponding to residual vector at every time instant. After substituting our output prediction into objective function of predictive control, one quadratic programming problem with equality and inequality constraints is considered. For solving this constrained optimization problem, fast gradient method is not suited for this complex optimization problem, as one regularization term is added in our objective function. So in order to solve this complex quadratic optimization problem, we propose a dual decomposition idea so that this dual decomposition idea can convert the former constrained optimization into unconstrained optimization, then one nearest neighbor gradient algorithm is given to solve its optimal value.
Subspace Predictive Control, Dual Decomposition, Gradient Algorithm
To cite this article
Gradient Algorithm in Subspace Predictive Control, Communications.
Vol. 6, No. 2,
2018, pp. 39-44.
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