RISE controllers

The Robust Integral of the Sign of the Error controllers or RISE controllers constitute a class of continuous robust control algorithms developed for nonlinear, control‐affine systems subject to uncertainties and disturbances. Distinguished by their capability to guarantee asymptotic tracking of reference trajectories even in the presence of bounded modeling errors, RISE controllers can be used where the exact system dynamics are unknown.^[1]^[2] Recent theoretical advancements have further extended these results to prove exponential stability under appropriate conditions.^[3]^[4]^[5]

^ Qu, Z.; Xu, J. X. (2002). "Model-based learning controls and their comparisons using Lyapunov direct method". Asian Journal of Control. 4 (1): 99–110. doi:10.1111/j.1934-6093.2002.tb00336.x.
^ Xian, B.; Dawson, D.M.; de Queiroz, M.S.; Chen, J. (2004). "A continuous asymptotic tracking control strategy for uncertain nonlinear systems". IEEE Transactions on Automatic Control. 49 (7): 1206–1211. doi:10.1109/TAC.2004.831148. ISSN 1558-2523.
^ Patil, Omkar Sudhir; Isaly, Axton; Xian, Bin; Dixon, Warren E. (2022). "Exponential Stability With RISE Controllers". IEEE Control Systems Letters. 6: 1592–1597. doi:10.1109/LCSYS.2021.3127134. ISSN 2475-1456.
^ Patil, Omkar Sudhir; Stubbs, Kimberly J.; Amy, Patrick M.; Dixon, Warren E. (2022). "Exponential Stability with RISE Controllers for Uncertain Nonlinear Systems with Unknown Time-Varying State Delays". 2022 IEEE 61st Conference on Decision and Control (CDC). pp. 6431–6435. doi:10.1109/CDC51059.2022.9993171. ISBN 978-1-6654-6761-2.
^ Patil, Omkar Sudhir; Kamalapurkar, Rushikesh; Dixon, Warren E. (2025). "Saturated RISE Controllers With Exponential Stability Guarantees: A Projected Dynamical Systems Approach". IEEE Transactions on Automatic Control: 1–8. doi:10.1109/TAC.2025.3543246. ISSN 1558-2523.

[1] Qu, Z.; Xu, J. X. (2002). "Model-based learning controls and their comparisons using Lyapunov direct method". Asian Journal of Control. 4 (1): 99–110. doi:10.1111/j.1934-6093.2002.tb00336.x.

[2] Xian, B.; Dawson, D.M.; de Queiroz, M.S.; Chen, J. (2004). "A continuous asymptotic tracking control strategy for uncertain nonlinear systems". IEEE Transactions on Automatic Control. 49 (7): 1206–1211. doi:10.1109/TAC.2004.831148. ISSN 1558-2523.

[:0-3] Patil, Omkar Sudhir; Isaly, Axton; Xian, Bin; Dixon, Warren E. (2022). "Exponential Stability With RISE Controllers". IEEE Control Systems Letters. 6: 1592–1597. doi:10.1109/LCSYS.2021.3127134. ISSN 2475-1456.

[:1-4] Patil, Omkar Sudhir; Stubbs, Kimberly J.; Amy, Patrick M.; Dixon, Warren E. (2022). "Exponential Stability with RISE Controllers for Uncertain Nonlinear Systems with Unknown Time-Varying State Delays". 2022 IEEE 61st Conference on Decision and Control (CDC). pp. 6431–6435. doi:10.1109/CDC51059.2022.9993171. ISBN 978-1-6654-6761-2.

[:2-5] Patil, Omkar Sudhir; Kamalapurkar, Rushikesh; Dixon, Warren E. (2025). "Saturated RISE Controllers With Exponential Stability Guarantees: A Projected Dynamical Systems Approach". IEEE Transactions on Automatic Control: 1–8. doi:10.1109/TAC.2025.3543246. ISSN 1558-2523.

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