Quick gradient algorithm for solving model prediction control law in real time

Abstract

The invention discloses a quick gradient algorithm for solving a model prediction control law in real time, and belongs to the technical field of model prediction control. Firstly a general MPC problem is converted into a standard quadratic programming problem; inequality constraints are relaxed by utilizing an augmented Lagrangian multiplier method; a dual problem of the problem is solved by utilizing an original quick gradient algorithm; in the process of solving the dual problem, an internal QP problem with equality constraints needs to be solved; KKT conditions can be used for performing solving; and a Lipschitz constant is obtained by offline solving an SDP problem, so that the algorithm has different step lengths in different solving directions during iteration. The MPC problem withgeneral input state constraints is solved; an objective function is not required to be a strict convex function; the MPC problem types which a quick gradient method is suitable for are expanded; and the convergence speed of the algorithm is greatly increased.

Description

technical field [0001] The invention belongs to the field of model predictive control technology (MPC), and relates to the solution of model predictive control problems, in particular to quickly solving ill-conditioned model predictive control problems by using a fast gradient algorithm. Background technique [0002] At present, the methods used to solve the model predictive control problem online mainly include the effective set method and the interior point method. In solving the real-time MPC problem, only convergence is not enough. In order to ensure the real-time performance of MPC, it is necessary to ensure the convergence within the sampling period, so The speed of convergence of the method is important. Although the effective set method converges, the convergence speed is unknown. The convergence speed of the interior point method is theoretically known, but it is too conservative. Different from the effective set method and the interior point method, the fast gradi...

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Problems solved by technology

[0004] When solving practical MPC problems, two types of MPC problems are generally encountered, one is a convex MPC problem, and the other is a strongly convex MPC problem. The two forms of MPC problems are mainly converted into standard QP problems. Form, the Hessian matrix of the convex MPC problem is semi-positive definite, and the Hessian matrix of the strongly convex MPC problem is positive definite. The main difference is that when the Hessian matrix is ​​positive definite, the local optimal solution is the global optimal solution, and is Unique, but when the Hessian matrix is ​​positive semi-definite, the optimal solution is not unique

The premise of most fast gradient algorithms is that the MPC problem to be solved must be strongly convex. For example, the original fast gradient algorithm only solves the strongly convex MPC problem with simple input constraints; the GPAD algorithm solves the problem with general input and output by relaxing inequality constraints. Constrained strong convex MPC problem, and when solving the interior, because it is not sure whether the interior optimization problem is positive definite, so the KKT condition cannot be used to solve it; the generalized fast dual gradient algorithm improves the convergence speed of the algorithm by changing the iteration step size, but It is difficult to use in time-varying systems; when the objective function is not strongly convex, the above methods cannot be used. The FALM algorithm combined with the augmented Lagrangian multiplier method expands the applicable MPC type of the fast gradient algorithm, but only solves problems with simple The convex MPC problem with box input and output constraints, and the accumulation of internal problem errors will affect the convergence speed of the algorithm

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