arXiv subjects

Ankush Chakrabarty

Publications and source records attributed to Ankush Chakrabarty.

23 records · Page 2Linked to original sources

arXiv2021

Safe Learning-based Observers for Unknown Nonlinear Systems using Bayesian Optimization

Data generated from dynamical systems with unknown dynamics enable the learning of state observers that are: robust to modeling error, computationally tractable to design, and capable of operating with guaranteed performance. In this paper, a modular design methodology is formulated, that consists of three design phases: (i) an initial robust observer design that enables one to learn the dynamics without allowing the state estimation error to diverge (hence, safe); (ii) a learning phase wherein the unmodeled components are estimated using Bayesian optimization and Gaussian processes; and, (iii) a re-design phase that leverages the learned dynamics to improve convergence rate of the state estimation error. The potential of our proposed learning-based observer is demonstrated on a benchmark nonlinear system. Additionally, certificates of guaranteed estimation performance are provided.

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arXiv2019

Safe Approximate Dynamic Programming Via Kernelized Lipschitz Estimation

We develop a method for obtaining safe initial policies for reinforcement learning via approximate dynamic programming (ADP) techniques for uncertain systems evolving with discrete-time dynamics. We employ kernelized Lipschitz estimation and semidefinite programming for computing admissible initial control policies with provably high probability. Such admissible controllers enable safe initialization and constraint enforcement while providing exponential stability of the equilibrium of the closed-loop system.

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arXiv2019

Approximate Dynamic Programming For Linear Systems with State and Input Constraints

Enforcing state and input constraints during reinforcement learning (RL) in continuous state spaces is an open but crucial problem which remains a roadblock to using RL in safety-critical applications. This paper leverages invariant sets to update control policies within an approximate dynamic programming (ADP) framework that guarantees constraint satisfaction for all time and converges to the optimal policy (in a linear quadratic regulator sense) asymptotically. An algorithm for implementing the proposed constrained ADP approach in a data-driven manner is provided. The potential of this formalism is demonstrated via numerical examples.

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arXiv2019

L2 Observers for a Class of Nonlinear Systems with Unknown Inputs

We consider the problem of estimating the state and unknown input for a large class of nonlinear systems subject to unknown exogenous inputs. The exogenous inputs themselves are modeled as being generated by a nonlinear system subject to unknown inputs. The nonlinearities considered in this work are characterized by multiplier matrices that include many commonly encountered nonlinearities. We obtain a linear matrix inequality (LMI), that, if feasible, provides the gains for an observer which results in certified L2 performance of the error dynamics associated with the observer. We also present conditions which guarantee that the L2 norm of the error can be made arbitrarily small and investigate conditions for feasibility of the proposed LMIs.

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arXiv2015

Simultaneous state and exogenous input estimation for nonlinear systems using boundary-layer sliding mode observers

While sliding mode observers (SMOs) using discontinuous relays are widely analyzed, most SMOs are implemented computationally using a continuous approximation of the discontinuous relays. This approximation results in the formation of a boundary layer in a neighborhood of the sliding manifold in the observer error space. Therefore, it becomes necessary to develop methods for attenuating the effect of the boundary layer and guaranteeing performance bounds on the resulting state estimation error. In this paper, a method is proposed for constructing boundary-layer SMOs (BL-SMOs) with prescribed state estimation error bounds. The BL-SMO formulation is then extended to simultaneously estimate exogenous inputs (disturbance signals in the state and output vector fields), along with the system state. Two numerical examples are presented to illustrate the effectiveness of the proposed approach.

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