An Execution-time-certified Riccati-based IPM Algorithm for RTI-based Input-constrained NMPC (2402.16186v1)
Abstract: Establishing an execution time certificate in deploying model predictive control (MPC) is a pressing and challenging requirement. As nonlinear MPC (NMPC) results in nonlinear programs, differing from quadratic programs encountered in linear MPC, deriving an execution time certificate for NMPC seems an impossible task. Our prior work \cite{wu2023direct} introduced an input-constrained MPC algorithm with the exact and only \textit{dimension-dependent} (\textit{data-independent}) number of floating-point operations ([flops]). This paper extends it to input-constrained NMPC problems via the real-time iteration (RTI) scheme, which results in \textit{data-varying} (but \textit{dimension-invariant}) input-constrained MPC problems. Therefore, applying our previous algorithm can certify the execution time based on the assumption that processors perform fixed [flops] in constant time. As the RTI-based scheme generally results in MPC with a long prediction horizon, this paper employs the efficient factorized Riccati recursion, whose computational cost scales linearly with the prediction horizon, to solve the Newton system at each iteration. The execution-time certified capability of the algorithm is theoretically and numerically validated through a case study involving nonlinear control of the chaotic Lorenz system.
- L. Wu and R. D. Braatz, “A direct optimization algorithm for input-constrained MPC,” arXiv preprint arXiv:2306.15079, 2023.
- M. Forgione, D. Piga, and A. Bemporad, “Efficient calibration of embedded MPC,” IFAC-PapersOnLine, vol. 53, no. 2, pp. 5189–5194, 2020.
- S. Richter, C. N. Jones, and M. Morari, “Computational complexity certification for real-time MPC with input constraints based on the fast gradient method,” IEEE Transactions on Automatic Control, vol. 57, no. 6, pp. 1391–1403, 2011.
- A. Bemporad and P. Patrinos, “Simple and certifiable quadratic programming algorithms for embedded linear model predictive control,” IFAC Proceedings Volumes, vol. 45, no. 17, pp. 14–20, 2012.
- P. Giselsson, “Execution time certification for gradient-based optimization in model predictive control,” in 51st IEEE Conference on Decision and Control, 2012, pp. 3165–3170.
- G. Cimini and A. Bemporad, “Exact complexity certification of active-set methods for quadratic programming,” IEEE Transactions on Automatic Control, vol. 62, no. 12, pp. 6094–6109, 2017.
- D. Arnström and D. Axehill, “A unifying complexity certification framework for active-set methods for convex quadratic programming,” IEEE Transactions on Automatic Control, vol. 67, no. 6, pp. 2758–2770, 2021.
- Y. Wang and S. Boyd, “Fast model predictive control using online optimization,” IEEE Transactions on Control Systems Technology, vol. 18, no. 2, pp. 267–278, 2009.
- H. Ferreau, C. Kirches, A. Potschka, H. Bock, and M. Diehl, “qpOASES: A parametric active-set algorithm for quadratic programming,” Mathematical Programming Computation, vol. 6, pp. 327–363, 2014.
- B. Stellato, G. Banjac, P. Goulart, A. Bemporad, and S. Boyd, “OSQP: An operator splitting solver for quadratic programs,” Mathematical Programming Computation, vol. 12, no. 4, pp. 637–672, 2020.
- L. Wu and A. Bemporad, “A simple and fast coordinate-descent augmented-Lagrangian solver for model predictive control,” IEEE Transactions on Automatic Control, vol. 68, no. 11, pp. 6860–6866, 2023.
- ——, “A construction-free coordinate-descent augmented-Lagrangian method for embedded linear MPC based on ARX models,” IFAC-PapersOnLine, vol. 56, no. 2, pp. 9423–9428, 2023.
- S. Gros, M. Zanon, R. Quirynen, A. Bemporad, and M. Diehl, “From linear to nonlinear MPC: Bridging the gap via the real-time iteration,” International Journal of Control, vol. 93, no. 1, pp. 62–80, 2020.
- M. Diehl, “Real-time Optimization for Large Scale Nonlinear Processes,” Ph.D. dissertation, Universität Heidelberg, Germany, 2001.
- M. Diehl, R. Findeisen, F. Allgöwer, H. G. Bock, and J. P. Schlöder, “Nominal stability of real-time iteration scheme for nonlinear model predictive control,” IEE Proceedings-Control Theory and Applications, vol. 152, no. 3, pp. 296–308, 2005.
- L. Wu, K. Ganko, and R. D. Braatz, “Time-certified input-constrained NMPC via Koopman Operator,” arXiv preprint arXiv:2401.04653, 2024.
- M. Korda and I. Mezić, “Linear predictors for nonlinear dynamical systems: Koopman operator meets model predictive control,” Automatica, vol. 93, pp. 149–160, 2018.
- G. Frison and J. B. Jørgensen, “Efficient implementation of the Riccati recursion for solving linear-quadratic control problems,” in IEEE International Conference on Control Applications, 2013, pp. 1117–1122.
- E. N. Lorenz, “Deterministic nonperiodic flow,” Journal of Atmospheric Sciences, vol. 20, no. 2, pp. 130–141, 1963.