Print Email Facebook Twitter Approximate dynamic programming for constrained linear systems Title Approximate dynamic programming for constrained linear systems: A piecewise quadratic approximation approach Author He, K. (TU Delft Team Bart De Schutter) Shi, S. (TU Delft Team Bart De Schutter) van den Boom, A.J.J. (TU Delft Team Ton van den Boom) De Schutter, B.H.K. (TU Delft Delft Center for Systems and Control) Department Delft Center for Systems and Control Date 2024 Abstract Approximate dynamic programming (ADP) faces challenges in dealing with constraints in control problems. Model predictive control (MPC) is, in comparison, well-known for its accommodation of constraints and stability guarantees, although its computation is sometimes prohibitive. This paper introduces an approach combining the two methodologies to overcome their individual limitations. The predictive control law for constrained linear quadratic regulation (CLQR) problems has been proven to be piecewise affine (PWA) while the value function is piecewise quadratic. We exploit these formal results from MPC to design an ADP method for CLQR problems with a known model. A novel convex and piecewise quadratic neural network with a local–global architecture is proposed to provide an accurate approximation of the value function, which is used as the cost-to-go function in the online dynamic programming problem. An efficient decomposition algorithm is developed to generate the control policy and speed up the online computation. Rigorous stability analysis of the closed-loop system is conducted for the proposed control scheme under the condition that a good approximation of the value function is achieved. Comparative simulations are carried out to demonstrate the potential of the proposed method in terms of online computation and optimality. Subject Approximate dynamic programmingConstrained linear quadratic regulationModel predictive controlNeural networksReinforcement learningValue function approximation To reference this document use: http://resolver.tudelft.nl/uuid:3f015c0d-f06e-4c04-a2f0-34b28640141a DOI https://doi.org/10.1016/j.automatica.2023.111456 ISSN 0005-1098 Source Automatica, 160 Part of collection Institutional Repository Document type journal article Rights © 2024 K. He, S. Shi, A.J.J. van den Boom, B.H.K. De Schutter Files PDF 1-s2.0-S0005109823006234-main.pdf 1.19 MB Close viewer /islandora/object/uuid:3f015c0d-f06e-4c04-a2f0-34b28640141a/datastream/OBJ/view