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A descent algorithm for the optimal control of constrained nonlinear switched dynamical systems

Published: 12 April 2010 Publication History

Abstract

One of the oldest problems in the study of dynamical systems is the calculation of an optimal control. Though the determination of a numerical solution for the general non-convex optimal control problem for hybrid systems has been pursued relentlessly to date, it has proven difficult, since it demands nominal mode scheduling. In this paper, we calculate a numerical solution to the optimal control problem for a constrained switched nonlinear dynamical system with a running and final cost. The control parameter has a discrete component, the sequence of modes, and two continuous components, the duration of each mode and the continuous input while in each mode. To overcome the complexity posed by the discrete optimization problem, we propose a bi-level hierarchical optimization algorithm: at the higher level, the algorithm updates the mode sequence by using a single-mode variation technique, and at the lower level, the algorithm considers a fixed mode sequence and minimizes the cost functional over the continuous components. Numerical examples detail the potential of our proposed methodology.

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  1. A descent algorithm for the optimal control of constrained nonlinear switched dynamical systems

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      cover image ACM Conferences
      HSCC '10: Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
      April 2010
      308 pages
      ISBN:9781605589558
      DOI:10.1145/1755952
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      Published: 12 April 2010

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      1. constrained optimal control
      2. switched hybrid systems

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      • (2023)Model Predictive Control of Switched Linear Systems With Persistent Dwell-Time Constraints: Recursive Feasibility and StabilityIEEE Transactions on Automatic Control10.1109/TAC.2023.324827968:12(7887-7894)Online publication date: Dec-2023
      • (2023)The minimum principle of hybrid optimal control theoryMathematics of Control, Signals, and Systems10.1007/s00498-023-00374-136:1(21-70)Online publication date: 10-Nov-2023
      • (2023)Bi-level Dynamic Optimization of Path-Constrained Switched SystemsDynamic Optimization of Path-Constrained Switched Systems10.1007/978-3-031-23428-6_2(31-60)Online publication date: 8-Feb-2023
      • (2023)IntroductionDynamic Optimization of Path-Constrained Switched Systems10.1007/978-3-031-23428-6_1(1-30)Online publication date: 8-Feb-2023
      • (2022)A Numerical Approach for Stochastic Switched Polynomial Optimal Control and Approximating Control Lyapunov FunctionsIranian Journal of Science and Technology, Transactions A: Science10.1007/s40995-022-01265-x46:2(563-582)Online publication date: 22-Feb-2022
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      • (2020)Hybrid parametric minimum principleNonlinear Analysis: Hybrid Systems10.1016/j.nahs.2020.10090237(100902)Online publication date: Aug-2020
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