| 1. |
- Bakarac, Peter, et al.
(författare)
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Explicit MPC Based on Approximate Dynamic Programming
- 2018
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Ingår i: 2018 EUROPEAN CONTROL CONFERENCE (ECC). - 9783952426982 - 9781538653036
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Konferensbidrag (refereegranskat)abstract
- In this paper we show how to synthesize simple explicit MPC controllers based on approximate dynamic programming. Here, a given MPC optimization problem over a finite horizon is solved iteratively as a series of problems of size one. The optimal cost function of each subproblem is approximated by a quadratic function that serves as a cost-to-go function for the subsequent iteration. The approximation is designed in such a way that closed-loop stability and recursive feasibility is maintained. Specifically, we show how to employ sum-of-squares relaxations to enforce that the approximate cost-to-go function is bounded from below and from above for all points of its domain. By resorting to quadratic approximations, the complexity of the resulting explicit MPC controller is considerably reduced both in terms of memory as well as the on-line computations. The procedure is applied to control an inverted pendulum and experimental data are presented to demonstrate viability of such an approach.
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| 2. |
- Kvasnica, Michal, et al.
(författare)
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Low-Complexity Polynomial Approximation of Explicit MPC via Linear Programming
- 2010
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Ingår i: Proceedings of the 2010 American Control Conference. - 9781424474264 ; , s. 4713-4718
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Konferensbidrag (refereegranskat)abstract
- This paper addresses the issue of the practical implementation of Model Predictive Controllers (MPC) to processes with short sampling times. Given an explicit solution to an MPC problem, the main idea is to approximate the optimal control law defined over state space regions by a single polynomial of pre-specified degree which, when applied as a state-feedback, guarantees closed-loop stability, constraint satisfaction, and a bounded performance decay. It is shown how to search for such a polynomial by solving a single linear program.
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| 3. |
- Kvasnica, Michal, et al.
(författare)
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Stabilizing Polynomial Approximation of Explicit MPC
- 2011
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Ingår i: Automatica. - : Elsevier. - 0005-1098 .- 1873-2836. ; 47:10, s. 2292-2297
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Tidskriftsartikel (refereegranskat)abstract
- A given explicit piecewise affine representation of an MPC feedback law is approximated by a single polynomial, computed using linear programming. This polynomial state feedback control law guarantees closed-loop stability and constraint satisfaction. The polynomial feedback can be implemented in real time even on very simple devices with severe limitations on memory storage.
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| 4. |
- Oravec, Juraj, et al.
(författare)
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Computationally Tractable Formulations for Optimal Path Planning with Interception of Targets Neighborhoods
- 2017
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Ingår i: Journal of Guidance Control and Dynamics. - : AMER INST AERONAUTICS ASTRONAUTICS. - 0731-5090 .- 1533-3884. ; 40:5, s. 1221-1230
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Tidskriftsartikel (refereegranskat)abstract
- Devising the planar routes of minimal length that are required to pass through predefined neighborhoods of target points plays an important role in reducing the missions operating cost. Two versions of the problem are considered. The first one assumes that the ordering of the targets is fixed a priori. In such a case, the optimal route is devised by solving a convex optimization problem formulated either as a second-order cone program or as a sum-of-squares optimization problem. Additional route properties, such as continuity and minimal curvature, are considered as well. The second version allows the ordering of the targets to be optimized to further reduce the route length. We show that such a problem can be solved by introducing additional binary variables, which allows the route to be designed using off-the-shelf mixed-integer solvers. A case study that shows that the proposed strategy is computationally tractable is presented.
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