arXiv subjects

Monimoy Bujarbaruah

Publications and source records attributed to Monimoy Bujarbaruah.

24 records · Page 2Linked to original sources

arXiv2019

Modeling of Dynamical Systems via Successive Graph Approximations

In this work, we propose a non-parametric technique for online modeling of systems with unknown nonlinear Lipschitz dynamics. The key idea is to successively utilize measurements to approximate the graph of the state-update function using envelopes described by quadratic constraints. The proposed approach is then demonstrated on two control applications: (i) computation of tractable bounds for unmodeled dynamics, and (ii) computation of positive invariant sets. We further highlight the efficacy of the proposed approach via a detailed numerical example.

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arXiv2019

Optimization Based Planner Tracker Design for Safety Guarantees

We present a safe-by-design approach to path planning and control for nonlinear systems. The planner uses a low fidelity model of the plant to compute reference trajectories by solving an MPC problem, while the plant being controlled utilizes a feedback control law that tracks those trajectories with an upper-bound on the tracking error. Our main goal is to allow for maximum permissiveness (that is, room for constraint feasibility) of the planner, while maintaining safety after accounting for the tracking error bound. We achieve this by parametrizing the state and input constraints imposed on the planner and deriving corresponding parametrized tracking control laws and tracking error bounds, which are computed offline through Sum-of-Squares programming. The parameters are then optimally chosen to maximize planner permissiveness, while guaranteeing safety.

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arXiv2019

Safe and Near-Optimal Policy Learning for Model Predictive Control using Primal-Dual Neural Networks

In this paper, we propose a novel framework for approximating the explicit MPC law for linear parameter-varying systems using supervised learning. In contrast to most existing approaches, we not only learn the control policy, but also a "certificate policy", that allows us to estimate the sub-optimality of the learned control policy online, during execution-time. We learn both these policies from data using supervised learning techniques, and also provide a randomized method that allows us to guarantee the quality of each learned policy, measured in terms of feasibility and optimality. This in turn allows us to bound the probability of the learned control policy of being infeasible or suboptimal, where the check is performed by the certificate policy. Since our algorithm does not require the solution of an optimization problem during run-time, it can be deployed even on resource-constrained systems. We illustrate the efficacy of the proposed framework on a vehicle dynamics control problem where we demonstrate a speedup of up to two orders of magnitude compared to online optimization with minimal performance degradation.

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arXiv2018

Adaptive MPC for Autonomous Lane Keeping

This paper proposes an Adaptive Robust Model Predictive Control strategy for lateral control in lane keeping problems, where we continuously learn an unknown, but constant steering angle offset present in the steering system. Longitudinal velocity is assumed constant. The goal is to minimize the outputs, which are distance from lane center line and the steady state heading angle error, while satisfying respective safety constraints. We do not assume perfect knowledge of the vehicle lateral dynamics model and estimate and adapt in real-time the maximum possible bound of the steering angle offset from data using a robust Set Membership Method based approach. Our approach is even well-suited for scenarios with sharp curvatures on high speed, where obtaining a precise model bias for constrained control is difficult, but learning from data can be helpful. We ensure persistent feasibility using a switching strategy during change of lane curvature. The proposed methodology is general and can be applied to more complex vehicle dynamics problems.

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arXiv2018

Adaptive MPC with Chance Constraints for FIR Systems

This paper proposes an adaptive stochastic Model Predictive Control (MPC) strategy for stable linear time invariant systems in the presence of bounded disturbances. We consider multi-input multi-output systems that can be expressed by a finite impulse response model, whose parameters we estimate using a linear Recursive Least Squares algorithm. Building on the work of [1],[2], our approach is able to handle hard input constraints and probabilistic output constraints. By using tools from distributionally robust optimization, we formulate our MPC design task as a convex optimization problem that can be solved using existing tools. Furthermore, we show that our adaptive stochastic MPC algorithm is persistently feasible. The efficacy of the developed algorithm is demonstrated in a numerical example and the results are compared with the adaptive robust MPC algorithm of [2].

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arXiv2018

Adaptive MPC for Iterative Tasks

This paper proposes an Adaptive Learning Model Predictive Control strategy for uncertain constrained linear systems performing iterative tasks. The additive uncertainty is modeled as the sum of a bounded process noise and an unknown constant offset. As new data becomes available, the proposed algorithm iteratively adapts the believed domain of the unknown offset after each iteration. An MPC strategy robust to all feasible offsets is employed in order to guarantee recursive feasibility. We show that the adaptation of the feasible offset domain reduces conservatism of the proposed strategy, compared to classical robust MPC strategies. As a result, the controller performance improves. Performance is measured in terms of following trajectories with lower associated costs at each iteration. Numerical simulations highlight the main advantages of the proposed approach.

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