Symmetry in optimal control: a multiobjective model predictive control approach. (English) Zbl 1457.37111
Junge, Oliver (ed.) et al., Advances in dynamics, optimization and computation. A volume dedicated to Michael Dellnitz on the occasion of his 60th birthday. Cham: Springer. Stud. Syst. Decis. Control 304, 209-237 (2020).
The authors propose a model predictive control (MPC) algorithm which exploits symmetries in nonlinear dynamical systems with multiple objectives aiming at reducing computational effort. They determine and store, in a motion planning library Pareto, optimal motion primitives based on Lie group symmetries. These primitives, which are equivalence classes with respect to the symmetry of the optimal control problems are selected based on the decision maker’s preference and applied to the plant over the control horizon length. The main advantage over classical approaches from motion planning is that only Pareto optimal controls have to be stored which, due to symmetry, are very easy to store. The MPC algorithm is applied for a mobile robot example using trims corresponding to straight motions with constant velocity.
For the entire collection see [Zbl 1445.37003].
For the entire collection see [Zbl 1445.37003].
Reviewer: Liviu Goraş (Iaşi)
MSC:
| 37N35 | Dynamical systems in control |
| 37C79 | Symmetries and invariants of dynamical systems |
| 37M21 | Computational methods for invariant manifolds of dynamical systems |
| 93C85 | Automated systems (robots, etc.) in control theory |
| 93B45 | Model predictive control |
Keywords:
dynamical systems with symmetry; model predictive control; motion planning; motion primitives; multiobjective optimization; optimal control; relative equilibria; scalarization methodsReferences:
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