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We present a simple model-free control algorithm that is able to robustly learn and stabilize an unknown discrete time linear system with full control and state feedback subject to arbitrary bounded disturbance and noise sequences. The controller does not require any prior knowledge of the system dynamics, disturbances or noise, yet can guarantee robust stability, uniform asymptotic bounds and uniform worst-case bounds on the state-deviation. Rather than the algorithm itself, we would like to highlight the new approach taken towards robust stability analysis which served as a key enabler in providing the presented stability and performance guarantees. We will conclude with simulation results that show that despite the generality and simplicity, the controller demonstrates good closed-loop performance.
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Energetically-optimal Discrete And Continuous Stabilization Of The Rimless Wheel With Torso
In this work, we discuss the modeling, control, and implementation of a rimless wheel with a torso. We derive and compare two control methodologies: a discrete-time controller (DT) that updates the controls once-per-step and a continuous-time controller (CT) that updates gains continuously. For the discrete controller, we use least-squares estimation method to approximate the Poincare ́ map on a certain section and use discrete- linear-quadratic-regulator (DQLR) to stabilize a (closed-form) linearization of this map. For the continuous controller, we introduce moving Poincare ́ sections and stabilize the transverse dynamics along these moving sections. For both controllers, we estimate the region of attraction of the closed-loop system using sum-of-squares methods. Analysis of the impact map yields a refinement of the controller that stabilizes a steady-state walking gait with minimal energy loss. We present both simulation and experimental results that support the validity of the proposed approaches. We find that the CT controller has a larger region of attraction and smoother stabilization as compared with the DT controller.
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- Award ID(s):
- 1816925
- PAR ID:
- 10104235
- Date Published:
- Journal Name:
- ASME-International Design Engineering & Technical Conference
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Accepted Manuscript1.0
- Conference Paper:
- The DOI is not currently available.
