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Predictive control – the basic algorithm
Published in J.A. Rossiter, Model-Based Predictive Control, 2004
The conventional approach is the active set method. This has guarantees of convergence and is fairly simple to code; the theoretical limits on the number of iterations is very large but rarely approached in practice.
Data fusion for a GPS/INS tightly coupled positioning system with equality and inequality constraints using an aggregate constraint unscented Kalman filter
Published in Journal of Spatial Science, 2020
Hang Yu, Zengke Li, Jian Wang, Houzeng Han
When, however, a priori information standing for inequality constraints is considered, the inequality constrained problem needs to be handled. The inequality constraints may come from the following three aspects, i.e. the nature of the problem itself, the requirements that have to be met or the partial knowledge of the system states (Julier et al. 2000, Zhu et al. 2005). Incorporating inequality constraints requires not only a non-linear framework but also an optimization method for estimation, for which there are no analytical solutions with the simplicity of the equality constrained KF. However, the optimization methods, such as sequential quadratic programming (SQP), active set and trust region reflective methods, are usually time-consuming (Fletcher 2000). For instance, the computational effort grows exponentially with the number of constraints while using an active set method (Simon 2010).
A novel on-line OCID method and its application to input-constrained active fault-tolerant tracker design for unknown nonlinear systems
Published in International Journal of Systems Science, 2019
Jason Sheng-Hong Tsai, Tzu-Hsien Yu, Te Jen Su, Shu-Mei Guo, Leang-San Shieh, Jose I. Canelon
At each step, the active set method (Wang, 2009) solves an optimisation problem with equality constraints. If all Lagrange multipliers then it is a local solution to the original problem. On the other hand, if there exists a the value of the objective function can be decreased by relaxing the i-th constraint.