Explicit MPC Based on Approximate Dynamic Programming

Funding agencies: Scientific Grant Agency of the Slovak Republic [1/0403/15]; Slovak Research and Development Agency [APVV-15-0007]
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.

Holaza, JurajSlovak Univ. of Tech. in Bratislava, Slovakia (author)
Kaluz, MartinSlovak Univ. of Tech. in Bratislava, Slovakia (author)
Klauco, MartinSlovak Univ. of Tech. in Bratislava, Slovakia (author)
Löfberg, Johan,1974-Linköpings universitet,Reglerteknik,Tekniska fakulteten(Swepub:liu)johlo46 (author)
Kvasnica, MichalSlovak Univ. of Tech. in Bratislava, Slovakia (author)
Slovak Univ. of Tech. in Bratislava, SlovakiaReglerteknik (creator_code:org_t)

By the author/editor: Bakarac, Peter; Holaza, Juraj; Kaluz, Martin; Klauco, Martin; Löfberg, Johan, ...; Kvasnica, Michal

About the subject

ENGINEERING AND TECHNOLOGY: ENGINEERING AND ...; and Electrical Engin ...; and Control Engineer ...

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