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Model Predictive Bang-Bang Controller Synthesis via Approximate Value Functions (2402.08148v2)
Published 13 Feb 2024 in math.OC
Abstract: In this paper, we propose a novel method for addressing Optimal Control Problems (OCPs) with input-affine dynamics and cost functions. This approach adopts a Model Predictive Control (MPC) strategy, wherein a controller is synthesized to handle an approximated OCP within a finite time horizon. Upon reaching this horizon, the controller is re-calibrated to tackle another approximation of the OCP, with the approximation updated based on the final state and time information. To tackle each OCP instance, all non-polynomial terms are Taylor-expanded about the current time and state and the resulting Hamilton-Jacobi-BeLLMan (HJB) PDE is solved via Sum-of-Squares (SOS) programming, providing us with an approximate polynomial value function that can be used to synthesize a bang-bang controller.
- The switch point algorithm. SIAM Journal on Control and Optimization, 59(4), 2570–2593.
- ApS, M. (2019). Mosek optimization toolbox for matlab. User’s Guide and Reference Manual, Version, 4, 1.
- Viscosity solutions: a primer. Viscosity Solutions and Applications: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (CIME) held in Montecatini Terme, Italy, June 12–20, 1995, 1–43.
- Large-scale nonlinear programming using ipopt: An integrating framework for enterprise-wide dynamic optimization. Computers & Chemical Engineering, 33(3), 575–582.
- Time-optimal control of power systems requiring multiple switchings of series capacitors. IEEE transactions on power systems, 13(2), 367–373.
- On the computation of optimal singular and bang–bang controls. Optimal Control Applications and Methods, 19(4), 287–297.
- Nonlinear control of single-machine-infinite-bus transient stability. In 2006 IEEE Power Engineering Society General Meeting, 8–pp. IEEE.
- Suboptimal feedback control of pdes by solving hjb equations on adaptive sparse grids. Journal of Scientific Computing, 70, 1–28.
- Snopt: An sqp algorithm for large-scale constrained optimization. SIAM review, 47(1), 99–131.
- Ichihara, H. (2009). Optimal control for polynomial systems using matrix sum of squares relaxations. IEEE Transactions on Automatic Control, 54(5), 1048–1053.
- Computation of optimal singular controls. IEEE Transactions on Automatic Control, 15(1), 67–73.
- Performance bounds for optimal control of polynomial systems: A convex optimization approach. SICE Journal of Control, Measurement, and System Integration, 4(6), 423–429.
- Polynomial approximation of value functions and nonlinear controller design with performance bounds. arXiv preprint arXiv:2010.06828.
- Polynomial approximation of high-dimensional hamilton–jacobi–bellman equations and applications to feedback control of semilinear parabolic pdes. SIAM Journal on Scientific Computing, 40(2), A629–A652.
- On infinite linear programming and the moment approach to deterministic infinite horizon discounted optimal control problems. IEEE control systems letters, 1(1), 134–139.
- Computations for bang–bang constrained optimal control using a mathematical programming formulation. Optimal control applications and methods, 25(6), 295–308.
- Khalil, H. (2002). Nonlinear systems. 3rd edition.
- High-speed switch-on of a semiconductor gas discharge image converter using optimal control methods. Journal of Computational Physics, 170(1), 395–414.
- Controller design and value function approximation for nonlinear dynamical systems. Automatica, 67, 54–66.
- Optimal bang-bang controls for a two-compartment model in cancer chemotherapy. Journal of optimization theory and applications, 114, 609–637.
- Liberzon, D. (2011). Calculus of variations and optimal control theory: a concise introduction. Princeton university press.
- Lofberg, J. (2004). Yalmip: A toolbox for modeling and optimization in matlab. In 2004 IEEE international conference on robotics and automation (IEEE Cat. No. 04CH37508), 284–289. IEEE.
- Iclocs2: Try this optimal control problem solver before you try the rest. In 2018 UKACC 12th international conference on control (CONTROL), 336–336. IEEE.
- Method for solving bang-bang and singular optimal control problems using adaptive radau collocation. Computational Optimization and Applications, 81(3), 857–887.
- Gpops-ii: A matlab software for solving multiple-phase optimal control problems using hp-adaptive gaussian quadrature collocation methods and sparse nonlinear programming. ACM Transactions on Mathematical Software (TOMS), 41(1), 1–37.
- On the convergence of the gradient projection method for convex optimal control problems with bang–bang solutions. Computational Optimization and Applications, 70, 221–238.
- Putinar, M. (1993). Positive polynomials on compact semi-algebraic sets. Indiana University Mathematics Journal, 42(3), 969–984.
- Dynamic approximate solutions of the hj inequality and of the hjb equation for input-affine nonlinear systems. IEEE Transactions on Automatic Control, 57(10), 2490–2503.
- Generic smoothing for optimal bang-off-bang spacecraft maneuvers. Journal of Guidance, Control, and Dynamics, 41(11), 2470–2475.
- Control synthesis for nonlinear optimal control via convex relaxations. In 2017 American Control Conference (ACC), 2654–2661. IEEE.
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