References

Agarwal, Alekh, Nan Jiang, Sham M Kakade, and Wen Sun. 2022. “Reinforcement Learning: Theory and Algorithms.” CS Dept., UW Seattle, Seattle, WA, USA, Tech. Rep 32.
Andrieu, Vincent, and Laurent Praly. 2006. “On the Existence of a Kazantzis–Kravaris/Luenberger Observer.” SIAM Journal on Control and Optimization 45 (2): 432–56.
Arnold, William F, and Alan J Laub. 1984. “Generalized Eigenproblem Algorithms and Software for Algebraic Riccati Equations.” Proceedings of the IEEE 72 (12): 1746–54.
Astolfi, Alessandro, and Romeo Ortega. 2003. “Immersion and Invariance: A New Tool for Stabilization and Adaptive Control of Nonlinear Systems.” IEEE Transactions on Automatic Control 48 (4): 590–606.
Bemporad, Alberto, Manfred Morari, Vivek Dua, and Efstratios N Pistikopoulos. 2002. “The Explicit Linear Quadratic Regulator for Constrained Systems.” Automatica 38 (1): 3–20.
Bernard, Pauline. 2019. Observer Design for Nonlinear Systems. Vol. 479. Springer.
Bernard, Pauline, Vincent Andrieu, and Daniele Astolfi. 2022. “Observer Design for Continuous-Time Dynamical Systems.” Annual Reviews in Control.
Bertsekas, Dimitri. 1972. “Infinite Time Reachability of State-Space Regions by Using Feedback Control.” IEEE Transactions on Automatic Control 17 (5): 604–13.
———. 2012. Dynamic Programming and Optimal Control: Volume i. Vol. 1. Athena scientific.
Besançon, Gildas, Guy Bornard, and Hassan Hammouri. 1996. “Observer Synthesis for a Class of Nonlinear Control Systems.” European Journal of Control 2 (3): 176–92.
Blekherman, Grigoriy, Pablo A Parrilo, and Rekha R Thomas. 2012. Semidefinite Optimization and Convex Algebraic Geometry. SIAM.
Borrelli, Francesco, Alberto Bemporad, and Manfred Morari. 2017. Predictive Control for Linear and Hybrid Systems. Cambridge University Press.
Chen, Chi-Tsong. 1984. Linear System Theory and Design. Saunders college publishing.
Dai, Hongkai, and Frank Permenter. 2023. “Convex Synthesis and Verification of Control-Lyapunov and Barrier Functions with Input Constraints.” In 2023 American Control Conference (ACC), 4116–23. IEEE.
Davison, E., and W. Wonham. 1968. “On Pole Assignment in Multivariable Linear Systems.” IEEE Transactions on Automatic Control 13 (6): 747–48. https://doi.org/10.1109/TAC.1968.1099056.
Dawson, Charles, Sicun Gao, and Chuchu Fan. 2023. “Safe Control with Learned Certificates: A Survey of Neural Lyapunov, Barrier, and Contraction Methods for Robotics and Control.” IEEE Transactions on Robotics.
Ebenbauer, Christian, Jonathan Renz, and F Allgower. 2005. “Polynomial Feedback and Observer Design Using Nonquadratic Lyapunov Functions.” In Proceedings of the 44th IEEE Conference on Decision and Control, 7587–92. IEEE.
Gilbert, Elmer G, and K Tin Tan. 1991. “Linear Systems with State and Control Constraints: The Theory and Application of Maximal Output Admissible Sets.” IEEE Transactions on Automatic Control 36 (9): 1008–20.
Hammouri, Hassan, and Jesus de Leon Morales. 1990. “Observer Synthesis for State-Affine Systems.” In 29th IEEE Conference on Decision and Control, 784–85. IEEE.
Janny, Steeven, Vincent Andrieu, Madiha Nadri, and Christian Wolf. 2021. “Deep Kkl: Data-Driven Output Prediction for Non-Linear Systems.” In 2021 60th IEEE Conference on Decision and Control (CDC), 4376–81. IEEE.
Kalman, Rudolph E, and Richard S Bucy. 1961. “New Results in Linear Filtering and Prediction Theory.”
Kalman, Rudolph Emil. 1960. “A New Approach to Linear Filtering and Prediction Problems.”
Kang, Shucheng, Yuxiao Chen, Heng Yang, and Marco Pavone. 2023. “Verification and Synthesis of Robust Control Barrier Functions: Multilevel Polynomial Optimization and Semidefinite Relaxation.” In 2023 62nd IEEE Conference on Decision and Control (CDC).
Karagiannis, Dimitrios, and Alessandro Astolfi. 2005. “Nonlinear Observer Design Using Invariant Manifolds and Applications.” In Proceedings of the 44th IEEE Conference on Decision and Control, 7775–80. IEEE.
Kazantzis, Nikolaos, and Costas Kravaris. 1998. “Nonlinear Observer Design Using Lyapunov’s Auxiliary Theorem.” Systems & Control Letters 34 (5): 241–47.
Kelly, Matthew. 2017. “An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation.” SIAM Review 59 (4): 849–904.
Kolmanovsky, Ilya, Elmer G Gilbert, et al. 1998. “Theory and Computation of Disturbance Invariant Sets for Discrete-Time Linear Systems.” Mathematical Problems in Engineering 4: 317–67.
Lasserre, Jean B. 2001. “Global Optimization with Polynomials and the Problem of Moments.” SIAM Journal on Optimization 11 (3): 796–817.
Lasserre, Jean Bernard. 2009. Moments, Positive Polynomials and Their Applications. Vol. 1. World Scientific.
Levine, Nir, Tom Zahavy, Daniel J Mankowitz, Aviv Tamar, and Shie Mannor. 2017. “Shallow Updates for Deep Reinforcement Learning.” Advances in Neural Information Processing Systems 30.
Luenberger, David G. 1964. “Observing the State of a Linear System.” IEEE Transactions on Military Electronics 8 (2): 74–80.
Magron, Victor, and Jie Wang. 2023. Sparse Polynomial Optimization: Theory and Practice. World Scientific.
Miao, Keyan, and Konstantinos Gatsis. 2023. “Learning Robust State Observers Using Neural ODEs.” In Learning for Dynamics and Control Conference, 208–19. PMLR.
Mnih, Volodymyr, Koray Kavukcuoglu, David Silver, Andrei A Rusu, Joel Veness, Marc G Bellemare, Alex Graves, et al. 2015. “Human-Level Control Through Deep Reinforcement Learning.” Nature 518 (7540): 529–33.
Murray, Riley, Venkat Chandrasekaran, and Adam Wierman. 2021. “Signomial and Polynomial Optimization via Relative Entropy and Partial Dualization.” Mathematical Programming Computation 13: 257–95.
Niazi, Muhammad Umar B, John Cao, Xudong Sun, Amritam Das, and Karl Henrik Johansson. 2023. “Learning-Based Design of Luenberger Observers for Autonomous Nonlinear Systems.” In 2023 American Control Conference (ACC), 3048–55. IEEE.
Nie, Jiawang. 2023. Moment and Polynomial Optimization. SIAM.
Nocedal, Jorge, and Stephen J Wright. 1999. Numerical Optimization. Springer.
Reif, Konrad, Stefan Gunther, Engin Yaz, and Rolf Unbehauen. 1999. “Stochastic Stability of the Discrete-Time Extended Kalman Filter.” IEEE Transactions on Automatic Control 44 (4): 714–28.
Slotine, Jean-Jacques E, Weiping Li, et al. 1991. Applied Nonlinear Control. Vol. 199. 1. Prentice hall Englewood Cliffs, NJ.
Sontag, Eduardo D. 1983. “A Lyapunov-Like Characterization of Asymptotic Controllability.” SIAM Journal on Control and Optimization 21 (3): 462–71.
Thrun, S, W Burgard, and D Fox. 2005. “Probabilistic Robotics.” MIT Press.
Van Der Merwe, Rudolph. 2004. Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models. Oregon Health & Science University.
Vinograd, Robert Èlyukimovich. 1957. “Inapplicability of the Method of Characteristic Exponents to the Study of Non-Linear Differential Equations.” Matematicheskii Sbornik 83 (4): 431–38.
Wang, Jie. 2022. “Nonnegative Polynomials and Circuit Polynomials.” SIAM Journal on Applied Algebra and Geometry 6 (2): 111–33.
Yang, Alan, and Stephen Boyd. 2023. “Value-Gradient Iteration with Quadratic Approximate Value Functions.” arXiv Preprint arXiv:2307.07086.
Yang, Heng, and Luca Carlone. 2022. “Certifiably Optimal Outlier-Robust Geometric Perception: Semidefinite Relaxations and Scalable Global Optimization.” IEEE Transactions on Pattern Analysis and Machine Intelligence 45 (3): 2816–34.
Yang, Heng, Ling Liang, Luca Carlone, and Kim-Chuan Toh. 2022. “An Inexact Projected Gradient Method with Rounding and Lifting by Nonlinear Programming for Solving Rank-One Semidefinite Relaxation of Polynomial Optimization.” Mathematical Programming, 1–64.
Yang, Tao, Prashant G Mehta, and Sean P Meyn. 2013. “Feedback Particle Filter.” IEEE Transactions on Automatic Control 58 (10): 2465–80.
Zhou, Kemin, JC Doyle, and Keither Glover. 1996. “Robust and Optimal Control.” Control Engineering Practice 4 (8): 1189–90.